%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW356+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 : n017.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 18:08:16 EDT 2024 % Result : Theorem 183.90s 184.42s % Output : CNFRefutation 183.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SWW356+1 : TPTP v8.2.0. Released v5.2.0. % 0.07/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n017.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 06:05:39 EDT 2024 % 0.11/0.33 % CPUTime : % 0.19/0.57 start to proof:theBenchmark % 183.37/184.25 %------------------------------------------- % 183.37/184.25 % File :CSE---1.7 % 183.37/184.25 % Problem :theBenchmark % 183.37/184.25 % Transform :cnf % 183.37/184.25 % Format :tptp:raw % 183.37/184.25 % Command :java -jar mcs_scs.jar %d %s % 183.37/184.25 % 183.37/184.25 % Result :Theorem 169.430000s % 183.37/184.25 % Output :CNFRefutation 169.430000s % 183.37/184.25 %------------------------------------------- % 183.46/184.26 %------------------------------------------------------------------------------ % 183.46/184.26 % File : SWW356+1 : TPTP v8.2.0. Released v5.2.0. % 183.46/184.26 % Domain : Software Verification % 183.46/184.26 % Problem : Hoare's Logic with Procedures 435362, 5000 axioms selected % 183.46/184.26 % Version : Especial. % 183.46/184.26 % English : % 183.46/184.26 % 183.46/184.26 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 183.46/184.26 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 183.46/184.26 % Source : [Bla11] % 183.46/184.26 % Names : hoare_435362.5000.p [Bla11] % 183.46/184.26 % 183.46/184.26 % Status : ContradictoryAxioms % 183.46/184.26 % Rating : 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.87 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 183.46/184.26 % Syntax : Number of formulae : 5244 (1740 unt; 0 def) % 183.46/184.26 % Number of atoms : 12601 (4547 equ) % 183.46/184.26 % Maximal formula atoms : 13 ( 2 avg) % 183.46/184.26 % Number of connectives : 8365 (1008 ~; 155 |; 721 &) % 183.46/184.26 % ( 892 <=>;5589 =>; 0 <=; 0 <~>) % 183.46/184.26 % Maximal formula depth : 22 ( 6 avg) % 183.46/184.26 % Maximal term depth : 19 ( 2 avg) % 183.46/184.26 % Number of predicates : 144 ( 143 usr; 1 prp; 0-6 aty) % 183.46/184.26 % Number of functors : 388 ( 388 usr; 53 con; 0-7 aty) % 183.46/184.26 % Number of variables : 16681 (16538 !; 143 ?) % 183.46/184.26 % SPC : FOF_CAX_RFO_SEQ % 183.46/184.26 % 183.46/184.26 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 183.46/184.26 % 2011-03-01 12:26:58 % 183.46/184.26 %------------------------------------------------------------------------------ % 183.46/184.26 %----Relevant facts (4987) % 183.46/184.26 fof(fact_ext,axiom, % 183.46/184.26 ! [V_g_2,V_f_2] : % 183.46/184.26 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 183.46/184.26 => V_f_2 = V_g_2 ) ). % 183.46/184.26 % 183.46/184.26 fof(fact_empty,axiom, % 183.46/184.26 ! [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))) ). % 183.46/184.26 % 183.46/184.26 fof(fact_hoare__derivs_OSkip,axiom, % 183.46/184.26 ! [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)))) ). % 183.46/184.26 % 183.46/184.26 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 183.46/184.26 ! [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))) ). % 183.46/184.26 % 183.46/184.26 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 183.46/184.26 ! [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)))) ). % 183.46/184.26 % 183.46/184.26 fof(fact_triple_Oinject,axiom, % 183.46/184.26 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 183.46/184.26 ( 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) % 183.46/184.26 <=> ( V_fun1_2 = V_fun1_H_2 % 183.46/184.26 & V_com_2 = V_com_H_2 % 183.46/184.26 & V_fun2_2 = V_fun2_H_2 ) ) ). % 183.46/184.26 % 183.46/184.26 fof(fact_cut,axiom, % 183.46/184.26 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 183.46/184.26 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 183.46/184.27 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 183.46/184.27 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_hoare__derivs_Oinsert,axiom, % 183.46/184.27 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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)))) % 183.46/184.27 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 183.46/184.27 => 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)) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_derivs__insertD,axiom, % 183.46/184.27 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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)) % 183.46/184.27 => ( 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)))) % 183.46/184.27 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_OSkip,axiom, % 183.46/184.27 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc__elim__cases_I1_J,axiom, % 183.46/184.27 ! [V_t,V_s] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 183.46/184.27 => V_t = V_s ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_weak__Body,axiom, % 183.46/184.27 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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)))) % 183.46/184.27 => 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)))) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_BodyN,axiom, % 183.46/184.27 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 183.46/184.27 ( 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)))) % 183.46/184.27 => 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)))) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_MGT__def,axiom, % 183.46/184.27 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 183.46/184.27 % 183.46/184.27 fof(fact_bot__fun__def,axiom, % 183.46/184.27 ! [V_x_2,T_b,T_a] : % 183.46/184.27 ( class_Orderings_Obot(T_a) % 183.46/184.27 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I18_J,axiom, % 183.46/184.27 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I19_J,axiom, % 183.46/184.27 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_Oequations_I1_J,axiom, % 183.46/184.27 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 183.46/184.27 % 183.46/184.27 fof(fact_triple_Orecs,axiom, % 183.46/184.27 ! [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) ). % 183.46/184.27 % 183.46/184.27 fof(fact_triple_Osimps_I2_J,axiom, % 183.46/184.27 ! [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) ). % 183.46/184.27 % 183.46/184.27 fof(fact_MGF__complete,axiom, % 183.46/184.27 ! [V_Q_2,V_P_2,V_ca_2] : % 183.46/184.27 ( 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_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 183.46/184.27 => ( 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 183.46/184.27 => 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_OBody,axiom, % 183.46/184.27 ! [V_s1,V_s0,V_pn] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 183.46/184.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc__elim__cases_I6_J,axiom, % 183.46/184.27 ! [V_s1,V_s,V_P] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 183.46/184.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_hoare__sound,axiom, % 183.46/184.27 ! [V_ts_2,V_Ga_2,T_a] : % 183.46/184.27 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 183.46/184.27 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_Oequations_I9_J,axiom, % 183.46/184.27 ! [V_a3_2,V_a2_2,V_a1_2] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 183.46/184.27 <=> hBOOL(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)) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com__det,axiom, % 183.46/184.27 ! [V_u,V_t,V_s,V_c] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 183.46/184.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 183.46/184.27 => V_u = V_t ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I6_J,axiom, % 183.46/184.27 ! [V_pname_H_2,V_pname_2] : % 183.46/184.27 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 183.46/184.27 <=> V_pname_2 = V_pname_H_2 ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_bot__apply,axiom, % 183.46/184.27 ! [V_x_2,T_b,T_a] : % 183.46/184.27 ( class_Orderings_Obot(T_a) % 183.46/184.27 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_MGT__alternI,axiom, % 183.46/184.27 ! [V_ca_2,V_Ga_2] : % 183.46/184.27 ( 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_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 183.46/184.27 => 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)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_MGT__alternD,axiom, % 183.46/184.27 ! [V_ca_2,V_Ga_2] : % 183.46/184.27 ( c_Hoare__Mirabelle_Ostate__not__singleton % 183.46/184.27 => ( 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)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 183.46/184.27 => 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_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_singleton__inject,axiom, % 183.46/184.27 ! [V_b_2,V_a_2,T_a] : % 183.46/184.27 ( 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))) % 183.46/184.27 => V_a_2 = V_b_2 ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_doubleton__eq__iff,axiom, % 183.46/184.27 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.46/184.27 ( 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_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 183.46/184.27 <=> ( ( V_a_2 = V_ca_2 % 183.46/184.27 & V_b_2 = V_d_2 ) % 183.46/184.27 | ( V_a_2 = V_d_2 % 183.46/184.27 & V_b_2 = V_ca_2 ) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_insert__not__empty,axiom, % 183.46/184.27 ! [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)) ). % 183.46/184.27 % 183.46/184.27 fof(fact_empty__not__insert,axiom, % 183.46/184.27 ! [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) ). % 183.46/184.27 % 183.46/184.27 fof(fact_escape,axiom, % 183.46/184.27 ! [V_Q_2,V_ca_2,V_Ga_2,T_a,V_P_2] : % 183.46/184.27 ( ! [B_Z,B_s] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 183.46/184.27 => 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_ca_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)))) ) % 183.46/184.27 => 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_conseq1,axiom, % 183.46/184.27 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.27 => ( ! [B_Z,B_s] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 183.46/184.27 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 183.46/184.27 => 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_conseq2,axiom, % 183.46/184.27 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.27 => ( ! [B_Z,B_s] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 183.46/184.27 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 183.46/184.27 => 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_Comp,axiom, % 183.46/184.27 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.27 ( 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.27 => ( 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)))) % 183.46/184.27 => 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_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_LoopF,axiom, % 183.46/184.27 ! [V_ca_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_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 183.46/184.27 % 183.46/184.27 fof(fact_finite__dom__body,axiom, % 183.46/184.27 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_OWhileFalse,axiom, % 183.46/184.27 ! [V_ca_2,V_s_2,V_b_2] : % 183.46/184.27 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.46/184.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_OWhileTrue,axiom, % 183.46/184.27 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 183.46/184.27 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 183.46/184.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 183.46/184.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 183.46/184.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_OSemi,axiom, % 183.46/184.27 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 183.46/184.27 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 183.46/184.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I46_J,axiom, % 183.46/184.27 ! [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) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I47_J,axiom, % 183.46/184.27 ! [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) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I3_J,axiom, % 183.46/184.27 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 183.46/184.27 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 183.46/184.27 <=> ( V_com1_2 = V_com1_H_2 % 183.46/184.27 & V_com2_2 = V_com2_H_2 ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_com_Osimps_I5_J,axiom, % 183.46/184.27 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 183.46/184.27 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 183.46/184.27 <=> ( V_fun_2 = V_fun_H_2 % 183.46/184.27 & V_com_2 = V_com_H_2 ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_Oequations_I7_J,axiom, % 183.46/184.27 ! [V_a2_2,V_a3_2,V_a1_2] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 183.46/184.27 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.46/184.27 => ? [B_s1] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 183.46/184.27 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 183.46/184.27 % 183.46/184.27 fof(fact_evalc_Oequations_I8_J,axiom, % 183.46/184.27 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 183.46/184.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 183.46/184.27 <=> ( ( V_a5_2 = V_a2_2 % 183.46/184.27 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 183.46/184.27 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.46/184.27 & ? [B_s1] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 183.46/184.28 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I59_J,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I58_J,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I16_J,axiom, % 183.46/184.28 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I17_J,axiom, % 183.46/184.28 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 183.46/184.28 % 183.46/184.28 fof(fact_evalc_Oequations_I4_J,axiom, % 183.46/184.28 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 183.46/184.28 <=> ? [B_s1] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 183.46/184.28 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I49_J,axiom, % 183.46/184.28 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I48_J,axiom, % 183.46/184.28 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I12_J,axiom, % 183.46/184.28 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 183.46/184.28 % 183.46/184.28 fof(fact_com_Osimps_I13_J,axiom, % 183.46/184.28 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 183.46/184.28 % 183.46/184.28 fof(fact_insert__absorb2,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_insert__commute,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_insert__code,axiom, % 183.46/184.28 ! [V_x_2,V_A_2,V_y_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 183.46/184.28 <=> ( V_y_2 = V_x_2 % 183.46/184.28 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite_OinsertI,axiom, % 183.46/184.28 ! [V_a_2,V_A_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.46/184.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite_OemptyI,axiom, % 183.46/184.28 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 183.46/184.28 % 183.46/184.28 fof(fact_the__elem__eq,axiom, % 183.46/184.28 ! [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 ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__insert,axiom, % 183.46/184.28 ! [V_A_2,V_a_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 183.46/184.28 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite_Oequations_I1_J,axiom, % 183.46/184.28 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 183.46/184.28 % 183.46/184.28 fof(fact_evalc__elim__cases_I4_J,axiom, % 183.46/184.28 ! [V_t,V_s,V_c2,V_c1] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 183.46/184.28 => ~ ! [B_s1] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 183.46/184.28 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Loop__sound__lemma,axiom, % 183.46/184.28 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.28 => 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_ca_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)))) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Loop,axiom, % 183.46/184.28 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.28 => 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_ca_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)))) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 183.46/184.28 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.46/184.28 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.46/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.46/184.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 => 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)) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__code,axiom, % 183.46/184.28 ! [V_A_2,T_a] : % 183.46/184.28 ( class_Finite__Set_Ofinite(T_a) % 183.46/184.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite,axiom, % 183.46/184.28 ! [V_A_2,T_a] : % 183.46/184.28 ( class_Finite__Set_Ofinite(T_a) % 183.46/184.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Body__sound__lemma,axiom, % 183.46/184.28 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_Procs_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_Procs_2)) % 183.46/184.28 => 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_Procs_2)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__imageI,axiom, % 183.46/184.28 ! [V_h_2,T_b,V_F_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.46/184.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_ball__Un,axiom, % 183.46/184.28 ! [V_P_2,V_B_2,V_A_2,T_a] : % 183.46/184.28 ( ! [B_x] : % 183.46/184.28 ( 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))) % 183.46/184.28 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.46/184.28 <=> ( ! [B_x] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.46/184.28 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.46/184.28 & ! [B_x] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 183.46/184.28 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_bex__Un,axiom, % 183.46/184.28 ! [V_P_2,V_B_2,V_A_2,T_a] : % 183.46/184.28 ( ? [B_x] : % 183.46/184.28 ( 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))) % 183.46/184.28 & hBOOL(hAPP(V_P_2,B_x)) ) % 183.46/184.28 <=> ( ? [B_x] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.46/184.28 & hBOOL(hAPP(V_P_2,B_x)) ) % 183.46/184.28 | ? [B_x] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 183.46/184.28 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__assoc,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__Un,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__left__commute,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__left__absorb,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__commute,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__absorb,axiom, % 183.46/184.28 ! [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 ). % 183.46/184.28 % 183.46/184.28 fof(fact_folding__one__idem_Oidem,axiom, % 183.46/184.28 ! [V_x_2,V_F_2,V_f_2,T_a] : % 183.46/184.28 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.46/184.28 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__image,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__Un,axiom, % 183.46/184.28 ! [V_Ga_2,V_F_2,T_a] : % 183.46/184.28 ( 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))) % 183.46/184.28 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.46/184.28 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__UnI,axiom, % 183.46/184.28 ! [V_Ga_2,V_F_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.46/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 183.46/184.28 => 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))) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_folding__one__idem_Ounion__idem,axiom, % 183.46/184.28 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.46/184.28 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.46/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.46/184.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.46/184.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 => 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)) ) ) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__is__empty,axiom, % 183.46/184.28 ! [V_A_2,V_f_2,T_a,T_b] : % 183.46/184.28 ( 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)) % 183.46/184.28 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__empty,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_empty__is__image,axiom, % 183.46/184.28 ! [V_A_2,V_f_2,T_b,T_a] : % 183.46/184.28 ( 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) % 183.46/184.28 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__insert,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__empty,axiom, % 183.46/184.28 ! [V_B_2,V_A_2,T_a] : % 183.46/184.28 ( 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)) % 183.46/184.28 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__empty__right,axiom, % 183.46/184.28 ! [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 ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__empty__left,axiom, % 183.46/184.28 ! [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 ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__insert__left,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Un__insert__right,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_peek__and__def,axiom, % 183.46/184.28 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 183.46/184.28 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 183.46/184.28 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 183.46/184.28 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_insert__is__Un,axiom, % 183.46/184.28 ! [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) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__constant__conv,axiom, % 183.46/184.28 ! [V_ca_2,T_b,T_a,V_A_2] : % 183.46/184.28 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 183.46/184.28 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.46/184.28 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_hoare__derivs_OBody,axiom, % 183.46/184.28 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_Procs_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_Procs_2)) % 183.46/184.28 => 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_Procs_2)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_Body1,axiom, % 183.46/184.28 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_Procs_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_Procs_2)) % 183.46/184.28 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 183.46/184.28 => 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)))) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_hoare__derivs_OIf,axiom, % 183.46/184.28 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 183.46/184.28 ( 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_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 183.46/184.28 => ( 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)))) % 183.46/184.28 => 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_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_finite__pointwise,axiom, % 183.46/184.28 ! [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] : % 183.46/184.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 183.46/184.28 => ( ! [B_p] : % 183.46/184.28 ( 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)))) % 183.46/184.28 => 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)))) ) % 183.46/184.28 => ( 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)) % 183.46/184.28 => 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)) ) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_sup1E,axiom, % 183.46/184.28 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.46/184.28 ( 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)) % 183.46/184.28 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 183.46/184.28 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_sup1CI,axiom, % 183.46/184.28 ! [T_a,V_A_2,V_x_2,V_B_2] : % 183.46/184.28 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 183.46/184.28 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 183.46/184.28 => 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)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_sup__fun__def,axiom, % 183.46/184.28 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 183.46/184.28 ( class_Lattices_Olattice(T_a) % 183.46/184.28 => 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)) ) ). % 183.46/184.28 % 183.46/184.28 fof(fact_image__compose,axiom, % 183.46/184.28 ! [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)) ). % 183.46/184.28 % 183.46/184.28 fof(fact_sup__apply,axiom, % 183.46/184.28 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 183.46/184.28 ( class_Lattices_Olattice(T_a) % 183.46/184.28 => 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)) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_sup__eq__bot__iff,axiom, % 183.51/184.28 ! [V_y_2,V_x_2,T_a] : % 183.51/184.28 ( class_Lattices_Obounded__lattice__bot(T_a) % 183.51/184.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 183.51/184.28 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 183.51/184.28 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_sup__bot__right,axiom, % 183.51/184.28 ! [V_x,T_a] : % 183.51/184.28 ( class_Lattices_Obounded__lattice__bot(T_a) % 183.51/184.28 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_sup__bot__left,axiom, % 183.51/184.28 ! [V_x,T_a] : % 183.51/184.28 ( class_Lattices_Obounded__lattice__bot(T_a) % 183.51/184.28 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_folding__idem_Ounion__idem,axiom, % 183.51/184.28 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.28 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.51/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.28 => 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)) ) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_equalityCE,axiom, % 183.51/184.28 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 183.51/184.28 ( V_A_2 = V_B_2 % 183.51/184.28 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.28 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 183.51/184.28 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_emptyE,axiom, % 183.51/184.28 ! [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)))) ). % 183.51/184.28 % 183.51/184.28 fof(fact_insertE,axiom, % 183.51/184.28 ! [V_A_2,V_b_2,V_a_2,T_a] : % 183.51/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 183.51/184.28 => ( V_a_2 != V_b_2 % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_insertCI,axiom, % 183.51/184.28 ! [V_b_2,V_B_2,V_a_2,T_a] : % 183.51/184.28 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 183.51/184.28 => V_a_2 = V_b_2 ) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_image__eqI,axiom, % 183.51/184.28 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 183.51/184.28 ( V_b_2 = hAPP(V_f_2,V_x_2) % 183.51/184.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_UnE,axiom, % 183.51/184.28 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_UnCI,axiom, % 183.51/184.28 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 183.51/184.28 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 183.51/184.28 % 183.51/184.28 fof(fact_evalc_OIfFalse,axiom, % 183.51/184.28 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 183.51/184.28 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.51/184.28 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 183.51/184.28 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_evalc_OIfTrue,axiom, % 183.51/184.29 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 183.51/184.29 ( hBOOL(hAPP(V_b_2,V_s_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_evalc__elim__cases_I5_J,axiom, % 183.51/184.29 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 183.51/184.29 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 183.51/184.29 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 183.51/184.29 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.51/184.29 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I4_J,axiom, % 183.51/184.29 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 183.51/184.29 ( 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) % 183.51/184.29 <=> ( V_fun_2 = V_fun_H_2 % 183.51/184.29 & V_com1_2 = V_com1_H_2 % 183.51/184.29 & V_com2_2 = V_com2_H_2 ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_pred__equals__eq,axiom, % 183.51/184.29 ! [V_S_2,V_R_2,T_a] : % 183.51/184.29 ( 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) % 183.51/184.29 <=> V_R_2 = V_S_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_eq__mem,axiom, % 183.51/184.29 ! [V_y_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 183.51/184.29 <=> V_x_2 = V_y_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_mem__def,axiom, % 183.51/184.29 ! [V_A_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_eqset__imp__iff,axiom, % 183.51/184.29 ! [V_x_2,T_a,V_B_2,V_A_2] : % 183.51/184.29 ( V_A_2 = V_B_2 % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_eqelem__imp__iff,axiom, % 183.51/184.29 ! [V_A_2,T_a,V_y_2,V_x_2] : % 183.51/184.29 ( V_x_2 = V_y_2 % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_eq__mem__trans,axiom, % 183.51/184.29 ! [V_A_2,T_a,V_b_2,V_a_2] : % 183.51/184.29 ( V_a_2 = V_b_2 % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_bot__empty__eq,axiom, % 183.51/184.29 ! [V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 183.51/184.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__Un__eq,axiom, % 183.51/184.29 ! [V_x_2,V_S_2,V_R_2,T_a] : % 183.51/184.29 ( 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)) % 183.51/184.29 <=> 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))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_all__not__in__conv,axiom, % 183.51/184.29 ! [V_A_2,T_a] : % 183.51/184.29 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_ex__in__conv,axiom, % 183.51/184.29 ! [V_A_2,T_a] : % 183.51/184.29 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.29 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_empty__iff,axiom, % 183.51/184.29 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 183.51/184.29 % 183.51/184.29 fof(fact_equals0D,axiom, % 183.51/184.29 ! [V_a_2,T_a,V_A_2] : % 183.51/184.29 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insertI1,axiom, % 183.51/184.29 ! [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))) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insert__iff,axiom, % 183.51/184.29 ! [V_A_2,V_b_2,V_a_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 183.51/184.29 <=> ( V_a_2 = V_b_2 % 183.51/184.29 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insert__ident,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_x_2,T_a] : % 183.51/184.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.51/184.29 => ( 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) % 183.51/184.29 <=> V_A_2 = V_B_2 ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insertI2,axiom, % 183.51/184.29 ! [V_b_2,V_B_2,V_a_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insert__absorb,axiom, % 183.51/184.29 ! [V_A_2,V_a_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.29 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_image__iff,axiom, % 183.51/184.29 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 183.51/184.29 <=> ? [B_x] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.29 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_imageI,axiom, % 183.51/184.29 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => 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))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_rev__image__eqI,axiom, % 183.51/184.29 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Un__iff,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.29 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_UnI1,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_UnI2,axiom, % 183.51/184.29 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__idem_Oin__comp__idem,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => 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) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_evalc_Oequations_I5_J,axiom, % 183.51/184.29 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 183.51/184.29 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.51/184.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 183.51/184.29 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.51/184.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_evalc_Oequations_I6_J,axiom, % 183.51/184.29 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 183.51/184.29 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.51/184.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 183.51/184.29 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.51/184.29 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I55_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I54_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I53_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I52_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I44_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I45_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I14_J,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_com_Osimps_I15_J,axiom, % 183.51/184.29 ! [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 ). % 183.51/184.29 % 183.51/184.29 fof(fact_singleton__iff,axiom, % 183.51/184.29 ! [V_a_2,V_b_2,T_a] : % 183.51/184.29 ( 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))))) % 183.51/184.29 <=> V_b_2 = V_a_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_singletonE,axiom, % 183.51/184.29 ! [V_a_2,V_b_2,T_a] : % 183.51/184.29 ( 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))))) % 183.51/184.29 => V_b_2 = V_a_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_insert__image,axiom, % 183.51/184.29 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__idem_Oidem__left__comp,axiom, % 183.51/184.29 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__idem_Oidem__comp,axiom, % 183.51/184.29 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one__idem_Oin__idem,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__assoc,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I6_J,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup_Oassoc,axiom, % 183.51/184.29 ! [V_c,V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__left__commute,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I7_J,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup_Oleft__commute,axiom, % 183.51/184.29 ! [V_c,V_a,V_b,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__left__idem,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I8_J,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup_Oleft__idem,axiom, % 183.51/184.29 ! [V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__commute,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I5_J,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup_Ocommute,axiom, % 183.51/184.29 ! [V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup__idem,axiom, % 183.51/184.29 ! [V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup_Oidem,axiom, % 183.51/184.29 ! [V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup1I2,axiom, % 183.51/184.29 ! [V_A_2,T_a,V_x_2,V_B_2] : % 183.51/184.29 ( hBOOL(hAPP(V_B_2,V_x_2)) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_sup1I1,axiom, % 183.51/184.29 ! [V_B_2,T_a,V_x_2,V_A_2] : % 183.51/184.29 ( hBOOL(hAPP(V_A_2,V_x_2)) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__eq__elim,axiom, % 183.51/184.29 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 183.51/184.29 ( 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_ca_2),V_d_2) % 183.51/184.29 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__eq__dest,axiom, % 183.51/184.29 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 183.51/184.29 ( 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_ca_2),V_d_2) % 183.51/184.29 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__apply,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__assoc,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_image__constant,axiom, % 183.51/184.29 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_image__ident,axiom, % 183.51/184.29 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__def,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__idem_Oinsert__idem,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one_Oinsert,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => 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)) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Oinsert,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_the__elem__def,axiom, % 183.51/184.29 ! [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))))) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one__idem_Ohom__commute,axiom, % 183.51/184.29 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.51/184.29 => ( ! [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)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.51/184.29 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => 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)) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple_Oinsert,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_finite__induct,axiom, % 183.51/184.29 ! [V_P_2,V_F_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.51/184.29 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.29 => ( ! [B_x,B_F] : % 183.51/184.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 183.51/184.29 => ( hBOOL(hAPP(V_P_2,B_F)) % 183.51/184.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 183.51/184.29 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 183.51/184.29 => 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) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_K__record__comp,axiom, % 183.51/184.29 ! [V_x_2,V_f_2,V_ca_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_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 183.51/184.29 % 183.51/184.29 fof(fact_image__eq__fold__image,axiom, % 183.51/184.29 ! [V_f_2,T_b,V_A_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple__idem_Oidem,axiom, % 183.51/184.29 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 183.51/184.29 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => 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) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_fold__image__empty,axiom, % 183.51/184.29 ! [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 ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 183.51/184.29 ! [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] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__comp,axiom, % 183.51/184.29 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__left__comp,axiom, % 183.51/184.29 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple_Oempty,axiom, % 183.51/184.29 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 183.51/184.29 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__comp_H_H,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__left__comp_H,axiom, % 183.51/184.29 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ocommute__comp_H,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Sup__fin_Oidem,axiom, % 183.51/184.29 ! [V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_o__eq__dest__lhs,axiom, % 183.51/184.29 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 183.51/184.29 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 183.51/184.29 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one_Osingleton,axiom, % 183.51/184.29 ! [V_x_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.29 => 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 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_comm__monoid__big_OF__eq,axiom, % 183.51/184.29 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 183.51/184.29 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => 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) ) % 183.51/184.29 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one_Oclosed,axiom, % 183.51/184.29 ! [V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => ( ! [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)))))) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Oremove,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => 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)) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Sup__fin_Oinsert,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => 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)) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_the__sym__eq__trivial,axiom, % 183.51/184.29 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 183.51/184.29 % 183.51/184.29 fof(fact_the__eq__trivial,axiom, % 183.51/184.29 ! [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 ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Ounion,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.29 => ( 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)) % 183.51/184.29 => 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)) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__image__simple_Oremove,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 183.51/184.29 => 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)))))) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding__one_Oremove,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.29 => ( ( 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)) % 183.51/184.29 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 183.51/184.29 & ( 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)) % 183.51/184.29 => 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)))))) ) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_folding_Oinsert__remove,axiom, % 183.51/184.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Sup__fin_Ounion__idem,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.29 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.29 => 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)) ) ) ) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf1I,axiom, % 183.51/184.29 ! [T_a,V_B_2,V_x_2,V_A_2] : % 183.51/184.29 ( hBOOL(hAPP(V_A_2,V_x_2)) % 183.51/184.29 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 183.51/184.29 => 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)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf1E,axiom, % 183.51/184.29 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.51/184.29 ( 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)) % 183.51/184.29 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 183.51/184.29 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_IntI,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_IntE,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.29 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_DiffI,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_DiffE,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.29 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_finite__Int,axiom, % 183.51/184.29 ! [V_Ga_2,V_F_2,T_a] : % 183.51/184.29 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.51/184.29 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 183.51/184.29 => 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))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_finite__Diff,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,T_a] : % 183.51/184.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.29 => 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))) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Inf__fin_Oidem,axiom, % 183.51/184.29 ! [V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__absorb,axiom, % 183.51/184.29 ! [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 ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__commute,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__left__absorb,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__left__commute,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__Int__distrib,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__idemp,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__Diff,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Int__assoc,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__Int__distrib2,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__Int2,axiom, % 183.51/184.29 ! [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) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf_Oidem,axiom, % 183.51/184.29 ! [V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__idem,axiom, % 183.51/184.29 ! [V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_fun__diff__def,axiom, % 183.51/184.29 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.29 ( class_Groups_Ominus(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__fun__def,axiom, % 183.51/184.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf_Ocommute,axiom, % 183.51/184.29 ! [V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I1_J,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__commute,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf_Oleft__idem,axiom, % 183.51/184.29 ! [V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I4_J,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__left__idem,axiom, % 183.51/184.29 ! [V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf_Oleft__commute,axiom, % 183.51/184.29 ! [V_c,V_a,V_b,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I3_J,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__left__commute,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf_Oassoc,axiom, % 183.51/184.29 ! [V_c,V_b,V_a,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__sup__aci_I2_J,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__assoc,axiom, % 183.51/184.29 ! [V_z,V_y,V_x,T_a] : % 183.51/184.29 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_minus__apply,axiom, % 183.51/184.29 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.29 ( class_Groups_Ominus(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf__apply,axiom, % 183.51/184.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 183.51/184.29 ( class_Lattices_Olattice(T_a) % 183.51/184.29 => 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)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf1D1,axiom, % 183.51/184.29 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.51/184.29 ( 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)) % 183.51/184.29 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_inf1D2,axiom, % 183.51/184.29 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.51/184.29 ( 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)) % 183.51/184.29 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__disjoint,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__triv,axiom, % 183.51/184.29 ! [V_B_2,V_A_2,T_a] : % 183.51/184.29 ( 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)) % 183.51/184.29 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__Int,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Diff__Un,axiom, % 183.51/184.29 ! [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)) ). % 183.51/184.29 % 183.51/184.29 fof(fact_Un__Diff__Int,axiom, % 183.51/184.29 ! [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 ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__Sup__absorb,axiom, % 183.51/184.30 ! [V_a_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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 ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__bot__left,axiom, % 183.51/184.30 ! [V_x,T_a] : % 183.51/184.30 ( class_Lattices_Obounded__lattice__bot(T_a) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__bot__right,axiom, % 183.51/184.30 ! [V_x,T_a] : % 183.51/184.30 ( class_Lattices_Obounded__lattice__bot(T_a) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_sup__inf__distrib2,axiom, % 183.51/184.30 ! [V_x,V_z,V_y,T_a] : % 183.51/184.30 ( class_Lattices_Odistrib__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__sup__distrib2,axiom, % 183.51/184.30 ! [V_x,V_z,V_y,T_a] : % 183.51/184.30 ( class_Lattices_Odistrib__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_sup__inf__distrib1,axiom, % 183.51/184.30 ! [V_z,V_y,V_x,T_a] : % 183.51/184.30 ( class_Lattices_Odistrib__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__sup__distrib1,axiom, % 183.51/184.30 ! [V_z,V_y,V_x,T_a] : % 183.51/184.30 ( class_Lattices_Odistrib__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_sup__inf__absorb,axiom, % 183.51/184.30 ! [V_y,V_x,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__sup__absorb,axiom, % 183.51/184.30 ! [V_y,V_x,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__iff,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.30 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_DiffD1,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_DiffD2,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__iff,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.51/184.30 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_IntD1,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_IntD2,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_empty__Diff,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__empty,axiom, % 183.51/184.30 ! [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 ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__cancel,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__Diff2,axiom, % 183.51/184.30 ! [V_A_2,V_B_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( 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))) % 183.51/184.30 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__empty__left,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__empty__right,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_disjoint__iff__not__equal,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> ! [B_x] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.30 => ! [B_xa] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 183.51/184.30 => B_x != B_xa ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__inter__insert,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Diff__cancel,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Diff__cancel2,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Diff,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__Un__distrib,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Int__distrib,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__Un__distrib2,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Int__distrib2,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Un__Int__crazy,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__Int__eq,axiom, % 183.51/184.30 ! [V_x_2,V_S_2,V_R_2,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> 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))) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__Diff__if,axiom, % 183.51/184.30 ! [V_A_2,V_B_2,V_x_2,T_a] : % 183.51/184.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.51/184.30 => 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) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__Diff1,axiom, % 183.51/184.30 ! [V_A_2,V_B_2,V_x_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oinsert__remove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ( 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)) % 183.51/184.30 => 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 ) % 183.51/184.30 & ( 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)) % 183.51/184.30 => 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)))))) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__insert,axiom, % 183.51/184.30 ! [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)))) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__insert2,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__Diff__single,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__Diff__insert,axiom, % 183.51/184.30 ! [V_B_2,V_a_2,V_A_2,T_a] : % 183.51/184.30 ( 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)))) % 183.51/184.30 <=> 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))) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__right,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__left,axiom, % 183.51/184.30 ! [V_B_2,V_C_2,V_a_2,T_a] : % 183.51/184.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 183.51/184.30 => 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)) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__right__if0,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__left__if0,axiom, % 183.51/184.30 ! [V_B_2,V_C_2,V_a_2,T_a] : % 183.51/184.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__right__if1,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__insert__left__if1,axiom, % 183.51/184.30 ! [V_B_2,V_C_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Ounion__inter,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Osingleton,axiom, % 183.51/184.30 ! [V_x_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oremove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( ( 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)) % 183.51/184.30 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 183.51/184.30 & ( 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)) % 183.51/184.30 => 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)))))) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff__insert__absorb,axiom, % 183.51/184.30 ! [V_A_2,V_x_2,T_a] : % 183.51/184.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__Diff,axiom, % 183.51/184.30 ! [V_A_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image__simple_Ounion__inter,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oin__idem,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__one_Oinsert__remove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ( 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)) % 183.51/184.30 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 183.51/184.30 & ( 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)) % 183.51/184.30 => 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)))))) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => 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)))))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding_Ounion__inter,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__one_Ounion__inter,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__one_Ounion__disjoint,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oinsert__idem,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_comm__monoid__big_Oinfinite,axiom, % 183.51/184.30 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 183.51/184.30 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oclosed,axiom, % 183.51/184.30 ! [V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( ! [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)))))) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oremove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( ( 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)) % 183.51/184.30 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 183.51/184.30 & ( 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)) % 183.51/184.30 => 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)))))) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__image,axiom, % 183.51/184.30 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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)))))) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Ohom__commute,axiom, % 183.51/184.30 ! [V_N_2,V_h_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( ! [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)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.51/184.30 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__empty__induct,axiom, % 183.51/184.30 ! [V_P_2,V_A_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 183.51/184.30 => ( ! [B_a,B_A] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 183.51/184.30 => ( hBOOL(hAPP(V_P_2,B_A)) % 183.51/184.30 => 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)))))) ) ) ) % 183.51/184.30 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Ounion__inter,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oinsert__remove,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ( 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)) % 183.51/184.30 => 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 ) % 183.51/184.30 & ( 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)) % 183.51/184.30 => 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)))))) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oinsert,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.51/184.30 => ( ! [B_x] : % 183.51/184.30 ( 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))) % 183.51/184.30 => hAPP(V_g_2,B_x) = V_z_2 ) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem__remove,axiom, % 183.51/184.30 ! [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))))) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__triv,axiom, % 183.51/184.30 ! [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 ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__idem,axiom, % 183.51/184.30 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 183.51/184.30 ( hAPP(V_f_2,V_x_2) = V_y_2 % 183.51/184.30 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__other,axiom, % 183.51/184.30 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 183.51/184.30 ( V_z_2 != V_x_2 % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__twist,axiom, % 183.51/184.30 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 183.51/184.30 ( V_a_2 != V_ca_2 % 183.51/184.30 => 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_ca_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_ca_2),V_d_2)),V_a_2),V_b_2) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__apply,axiom, % 183.51/184.30 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 183.51/184.30 ( ( V_z_2 = V_x_2 % 183.51/184.30 => 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 ) % 183.51/184.30 & ( V_z_2 != V_x_2 % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__same,axiom, % 183.51/184.30 ! [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 ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__upd,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__idem__iff,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 183.51/184.30 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 183.51/184.30 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__def,axiom, % 183.51/184.30 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 183.51/184.30 ( ( V_x_2 = V_a_2 % 183.51/184.30 => 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 ) % 183.51/184.30 & ( V_x_2 != V_a_2 % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 183.51/184.30 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__upd__comp,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem__insert,axiom, % 183.51/184.30 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem__sup,axiom, % 183.51/184.30 ! [T_a] : % 183.51/184.30 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.30 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem__inf,axiom, % 183.51/184.30 ! [T_a] : % 183.51/184.30 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.30 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 183.51/184.30 ! [V_x_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Osingleton,axiom, % 183.51/184.30 ! [V_x_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_sup__Inf__absorb,axiom, % 183.51/184.30 ! [V_a_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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 ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oin__idem,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oinsert__idem,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Ounion__idem,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oclosed,axiom, % 183.51/184.30 ! [V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => ( ! [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)))))) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Ohom__commute,axiom, % 183.51/184.30 ! [V_N_2,V_h_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( ! [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)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.51/184.30 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__diff1__ring,axiom, % 183.51/184.30 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Rings_Oring(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__diff1,axiom, % 183.51/184.30 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Groups_Oab__group__add(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 183.51/184.30 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( 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) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Diff1__fold__graph,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin__Inf,axiom, % 183.51/184.30 ! [V_A_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__Un,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.51/184.30 & 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__Inter,axiom, % 183.51/184.30 ! [V_M_2,T_a] : % 183.51/184.30 ( ? [B_x] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 183.51/184.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 183.51/184.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__empty,axiom, % 183.51/184.30 ! [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))) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__id2,axiom, % 183.51/184.30 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__commute,axiom, % 183.51/184.30 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 183.51/184.30 ( class_Groups_Ocomm__monoid__add(T_a) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__def,axiom, % 183.51/184.30 ! [V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 <=> ! [B_x] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.30 => ! [B_xa] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 183.51/184.30 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 183.51/184.30 => B_x = B_xa ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__def,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__reindex,axiom, % 183.51/184.30 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 183.51/184.30 ( class_Groups_Ocomm__monoid__add(T_c) % 183.51/184.30 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__onD,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.51/184.30 => V_x_2 = V_y_2 ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__iff,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.51/184.30 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 183.51/184.30 <=> V_x_2 = V_y_2 ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__contraD,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( V_x_2 != V_y_2 % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.51/184.30 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__Int,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__imageI2,axiom, % 183.51/184.30 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 183.51/184.30 ( 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) % 183.51/184.30 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__diff,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 183.51/184.30 ! [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) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__empty,axiom, % 183.51/184.30 ! [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 ). % 183.51/184.30 % 183.51/184.30 fof(fact_inf__Inf__fold__inf,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum_Oreindex,axiom, % 183.51/184.30 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__subtractf,axiom, % 183.51/184.30 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( class_Groups_Oab__group__add(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_Oequations_I1_J,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_OemptyI,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_empty__fold__graphE,axiom, % 183.51/184.30 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 => V_x_2 = V_z_2 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph__imp__finite,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 183.51/184.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__image__def,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__imageD,axiom, % 183.51/184.30 ! [V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 183.51/184.30 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 183.51/184.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__Un__image__eq__iff,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 => ( 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) % 183.51/184.30 <=> V_A_2 = V_B_2 ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__imageI,axiom, % 183.51/184.30 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 183.51/184.30 ( 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) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_comp__inj__on,axiom, % 183.51/184.30 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( 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)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_comp__inj__on__iff,axiom, % 183.51/184.30 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( 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)) % 183.51/184.30 <=> 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding_Oeq__fold,axiom, % 183.51/184.30 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_OinsertI,axiom, % 183.51/184.30 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 183.51/184.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 183.51/184.30 => 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))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__fun__updI,axiom, % 183.51/184.30 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_union__fold__insert,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__sup__insert,axiom, % 183.51/184.30 ! [V_a_2,V_b_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__inf__insert,axiom, % 183.51/184.30 ! [V_a_2,V_b_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 183.51/184.30 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 183.51/184.30 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 183.51/184.30 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__diff1__nat,axiom, % 183.51/184.30 ! [V_f_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) % 183.51/184.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 183.51/184.30 ! [V_a_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 183.51/184.30 ! [V_a_2,V_A_2,T_a] : % 183.51/184.30 ( class_Lattices_Olattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_minus__fold__remove,axiom, % 183.51/184.30 ! [V_B_2,V_A_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__one_Oeq__fold_H,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_inj__on__insert,axiom, % 183.51/184.30 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 183.51/184.30 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.30 & ~ 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))))))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__binary,axiom, % 183.51/184.30 ! [V_b_2,V_a_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__insert,axiom, % 183.51/184.30 ! [V_A_2,V_a_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__singleton,axiom, % 183.51/184.30 ! [V_a_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => 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 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__rec,axiom, % 183.51/184.30 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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)))))) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_InterE,axiom, % 183.51/184.30 ! [V_X_2,V_C_2,V_A_2,T_a] : % 183.51/184.30 ( 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))) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_InterD,axiom, % 183.51/184.30 ! [V_X_2,V_C_2,V_A_2,T_a] : % 183.51/184.30 ( 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))) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold1Set_Ointros,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 183.51/184.30 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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)))))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image_Oreindex,axiom, % 183.51/184.30 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 183.51/184.30 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.30 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 183.51/184.30 | ? [B_x,B_y] : % 183.51/184.30 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 183.51/184.30 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 183.51/184.30 & 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 183.51/184.30 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 183.51/184.30 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 183.51/184.30 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 183.51/184.30 => V_y_2 = V_x_2 ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold1Set__nonempty,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_f_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 183.51/184.30 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_empty__fold1SetE,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image_Odistrib,axiom, % 183.51/184.30 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 183.51/184.30 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inter__Un__distrib,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inter__insert,axiom, % 183.51/184.30 ! [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)) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Int__eq__Inter,axiom, % 183.51/184.30 ! [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))))) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__equality,axiom, % 183.51/184.30 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 183.51/184.30 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold1Set__sing,axiom, % 183.51/184.30 ! [V_b_2,V_a_2,V_f_2,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> V_a_2 = V_b_2 ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_folding__image_Oeq__fold,axiom, % 183.51/184.30 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 183.51/184.30 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 183.51/184.30 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__insert,axiom, % 183.51/184.30 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 183.51/184.30 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => ? [B_y_H] : % 183.51/184.30 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 183.51/184.30 & 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)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_the__inv__into__comp,axiom, % 183.51/184.30 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 183.51/184.30 => ( 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)))) % 183.51/184.30 => 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) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_SUPR__fold__sup,axiom, % 183.51/184.30 ! [V_f_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Inf__fold__inf,axiom, % 183.51/184.30 ! [V_A_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum_Oremove,axiom, % 183.51/184.30 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => 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)))))) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_setsum__diff1_H,axiom, % 183.51/184.30 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 183.51/184.30 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => 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)))))) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__fold__sup,axiom, % 183.51/184.30 ! [V_A_2,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.30 => 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) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_insert__fold1SetE,axiom, % 183.51/184.30 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 => ~ ! [B_a,B_A] : % 183.51/184.30 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 183.51/184.30 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fold1Set_Oequations,axiom, % 183.51/184.30 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 183.51/184.30 ( 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)) % 183.51/184.30 <=> ? [B_a,B_A] : % 183.51/184.30 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 183.51/184.30 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 183.51/184.30 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 183.51/184.30 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 183.51/184.30 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.51/184.30 => ( 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)) % 183.51/184.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.30 => ~ ! [B_y] : % 183.51/184.30 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 183.51/184.30 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_UNIV__I,axiom, % 183.51/184.30 ! [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)))) ). % 183.51/184.30 % 183.51/184.30 fof(fact_SUP1__I,axiom, % 183.51/184.30 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 183.51/184.30 => 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)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_UN__I,axiom, % 183.51/184.30 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 183.51/184.30 => 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))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_SUP2__I,axiom, % 183.51/184.30 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 183.51/184.30 => 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_ca_2)) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_UnionI,axiom, % 183.51/184.30 ! [V_A_2,V_C_2,V_X_2,T_a] : % 183.51/184.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 183.51/184.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 183.51/184.30 => 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))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_Sup__UNIV,axiom, % 183.51/184.30 ! [T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => 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) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_SUPR__apply,axiom, % 183.51/184.30 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.30 => 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)) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__Plus__UNIV__iff,axiom, % 183.51/184.30 ! [T_b,T_a] : % 183.51/184.30 ( 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)))) % 183.51/184.30 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__option__UNIV,axiom, % 183.51/184.30 ! [T_a] : % 183.51/184.30 ( 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)))) % 183.51/184.30 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__Prod__UNIV,axiom, % 183.51/184.30 ! [T_b,T_a] : % 183.51/184.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 183.51/184.30 => 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)))) ) ) ). % 183.51/184.30 % 183.51/184.30 fof(fact_finite__fun__UNIVD2,axiom, % 183.51/184.30 ! [T_b,T_a] : % 183.51/184.30 ( 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)))) % 183.51/184.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_top__apply,axiom, % 183.51/184.31 ! [V_x_2,T_b,T_a] : % 183.51/184.31 ( class_Orderings_Otop(T_a) % 183.51/184.31 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_SUP__UN__eq,axiom, % 183.51/184.31 ! [V_x_2,V_r_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_image__Union,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__Union__image,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__Union2,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__Union,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_the__inv__f__f,axiom, % 183.51/184.31 ! [V_x_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => 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 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_SUP__commute,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UN,axiom, % 183.51/184.31 ! [V_B_2,T_b,V_A_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( 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))) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__o,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__empty,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UnionD,axiom, % 183.51/184.31 ! [V_A_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__Un__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__eq__Union,axiom, % 183.51/184.31 ! [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))))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__insert,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_iso__tuple__UNIV__I,axiom, % 183.51/184.31 ! [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)))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UNIV__not__empty,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UNIV,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Finite__Set_Ofinite(T_a) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__UNIV__left,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__UNIV__right,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__UNIV__left,axiom, % 183.51/184.31 ! [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 ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__UNIV__right,axiom, % 183.51/184.31 ! [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 ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__eq,axiom, % 183.51/184.31 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 183.51/184.31 <=> V_x_2 = V_y_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_injD,axiom, % 183.51/184.31 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 183.51/184.31 => V_x_2 = V_y_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__iff,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 183.51/184.31 ( 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))) % 183.51/184.31 <=> ? [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UNION__empty__conv_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__empty2,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__constant,axiom, % 183.51/184.31 ! [V_ca_2,T_b,T_a,V_A_2] : % 183.51/184.31 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 183.51/184.31 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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_ca_2)) = V_ca_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UNION__empty__conv_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I10_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_image__UN,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I10_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__Un,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__Un__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__UN__distrib2,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I4_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__UN__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I5_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I4_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I5_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I6_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I6_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inter__empty,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__addf,axiom, % 183.51/184.31 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_range__composition,axiom, % 183.51/184.31 ! [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)))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__fun,axiom, % 183.51/184.31 ! [T_c,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_sup__top__right,axiom, % 183.51/184.31 ! [V_x,T_a] : % 183.51/184.31 ( class_Lattices_Obounded__lattice__top(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_sup__top__left,axiom, % 183.51/184.31 ! [V_x,T_a] : % 183.51/184.31 ( class_Lattices_Obounded__lattice__top(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inf__top__left,axiom, % 183.51/184.31 ! [V_x,T_a] : % 183.51/184.31 ( class_Lattices_Obounded__lattice__top(T_a) % 183.51/184.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inf__top__right,axiom, % 183.51/184.31 ! [V_x,T_a] : % 183.51/184.31 ( class_Lattices_Obounded__lattice__top(T_a) % 183.51/184.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inf__eq__top__iff,axiom, % 183.51/184.31 ! [V_y_2,V_x_2,T_a] : % 183.51/184.31 ( class_Lattices_Obounded__lattice__top(T_a) % 183.51/184.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 183.51/184.31 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 183.51/184.31 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__disjoint,axiom, % 183.51/184.31 ! [V_A_2,V_C_2,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_rangeI,axiom, % 183.51/184.31 ! [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))))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_range__eqI,axiom, % 183.51/184.31 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 183.51/184.31 ( V_b_2 = hAPP(V_f_2,V_x_2) % 183.51/184.31 => 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))))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_SUP__const,axiom, % 183.51/184.31 ! [V_M_2,T_a,V_A_2,T_b] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__insert__distrib,axiom, % 183.51/184.31 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__absorb,axiom, % 183.51/184.31 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__singleton,axiom, % 183.51/184.31 ! [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 ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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))) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Diff__UNIV,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comp__surj,axiom, % 183.51/184.31 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 183.51/184.31 ( 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)) % 183.51/184.31 => ( 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)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I3_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I3_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__insert,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__image__eq__iff,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( 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) % 183.51/184.31 <=> V_A_2 = V_B_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__comp,axiom, % 183.51/184.31 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 183.51/184.31 => 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))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inf__UNIV,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inter__UNIV,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum_Odistrib,axiom, % 183.51/184.31 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__singleton,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__range__imageI,axiom, % 183.51/184.31 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 183.51/184.31 ( 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))))) % 183.51/184.31 => 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))))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Sup__empty,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Sup__singleton,axiom, % 183.51/184.31 ! [V_a_2,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Sup__insert,axiom, % 183.51/184.31 ! [V_A_2,V_a_2,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_image__eq__UN,axiom, % 183.51/184.31 ! [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)))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_range__ex1__eq,axiom, % 183.51/184.31 ! [V_b_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( 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))))) % 183.51/184.31 <=> ? [B_x] : % 183.51/184.31 ( V_b_2 = hAPP(V_f_2,B_x) % 183.51/184.31 & ! [B_y] : % 183.51/184.31 ( V_b_2 = hAPP(V_f_2,B_y) % 183.51/184.31 => B_y = B_x ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__image__mem__iff,axiom, % 183.51/184.31 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => ( 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))) % 183.51/184.31 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UNIV__inj__surj,axiom, % 183.51/184.31 ! [V_f_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.31 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UNIV__surj__inj,axiom, % 183.51/184.31 ! [V_f_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.31 => ( 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)) % 183.51/184.31 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inf__empty,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_image__Int,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_image__set__diff,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_the__inv__into__f__eq,axiom, % 183.51/184.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_the__inv__into__f__f,axiom, % 183.51/184.31 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.31 => 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 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__on__the__inv__into,axiom, % 183.51/184.31 ! [V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_the__inv__into__onto,axiom, % 183.51/184.31 ! [V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => 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 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__insert,axiom, % 183.51/184.31 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 183.51/184.31 => 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)) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum_Oinsert,axiom, % 183.51/184.31 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.31 => 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)) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__Un__Int,axiom, % 183.51/184.31 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => 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)) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_the__inv__into__def,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Sup__binary,axiom, % 183.51/184.31 ! [V_b_2,V_a_2,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_sup__Sup__fold__sup,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Sup__fin__Sup,axiom, % 183.51/184.31 ! [V_A_2,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum_Oinsert__remove,axiom, % 183.51/184.31 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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)))))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__Un__disjoint,axiom, % 183.51/184.31 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => ( 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)) % 183.51/184.31 => 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)) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_f__the__inv__into__f,axiom, % 183.51/184.31 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 183.51/184.31 => 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 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__Un,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Oab__group__add(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => 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))) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_sup__SUPR__fold__sup,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__Un__nat,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,V_A_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => 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))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__diff__cancel,axiom, % 183.51/184.31 ! [V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Ogroup__add(T_a) % 183.51/184.31 => 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 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__add__cancel,axiom, % 183.51/184.31 ! [V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Ogroup__add(T_a) % 183.51/184.31 => 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 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INFI__fold__inf,axiom, % 183.51/184.31 ! [V_f_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__on__Inter,axiom, % 183.51/184.31 ! [V_f_2,T_b,T_a,V_S_2] : % 183.51/184.31 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 183.51/184.31 => ( ! [B_A] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 183.51/184.31 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_insert__partition,axiom, % 183.51/184.31 ! [V_F_2,V_x_2,T_a] : % 183.51/184.31 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 183.51/184.31 => ( ! [B_x] : % 183.51/184.31 ( 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))) % 183.51/184.31 => ! [B_xa] : % 183.51/184.31 ( 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))) % 183.51/184.31 => ( B_x != B_xa % 183.51/184.31 => 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)) ) ) ) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__image__reindex,axiom, % 183.51/184.31 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_c) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 183.51/184.31 => 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) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__graph__permute__diff,axiom, % 183.51/184.31 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => ( 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)) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 183.51/184.31 => 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)) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_InterI,axiom, % 183.51/184.31 ! [V_A_2,V_C_2,T_a] : % 183.51/184.31 ( ! [B_X] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__reindex__cong,axiom, % 183.51/184.31 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__add(T_c) % 183.51/184.31 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.31 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 183.51/184.31 => ( ! [B_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 183.51/184.31 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 183.51/184.31 => 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) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inf__INFI__fold__inf,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_top1I,axiom, % 183.51/184.31 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__D,axiom, % 183.51/184.31 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 183.51/184.31 ( 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))) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__E,axiom, % 183.51/184.31 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 183.51/184.31 ( 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))) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 183.51/184.31 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF1__D,axiom, % 183.51/184.31 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF1__E,axiom, % 183.51/184.31 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 183.51/184.31 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF2__D,axiom, % 183.51/184.31 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.31 ( 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_ca_2)) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF2__E,axiom, % 183.51/184.31 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.31 ( 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_ca_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 183.51/184.31 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__INT,axiom, % 183.51/184.31 ! [V_A_2,T_b,V_I_2,T_a] : % 183.51/184.31 ( ? [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 183.51/184.31 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__image__eq,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UNION__eq__Union__image,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__UNIV,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Union__def,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I8_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I8_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I9_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I9_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I8_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I8_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_ball__UN,axiom, % 183.51/184.31 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( ! [B_x] : % 183.51/184.31 ( 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))) % 183.51/184.31 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => ! [B_xa] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 183.51/184.31 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I9_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I9_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__UN__flatten,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_SUP1__iff,axiom, % 183.51/184.31 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> ? [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_SUP2__iff,axiom, % 183.51/184.31 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.31 ( 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_ca_2)) % 183.51/184.31 <=> ? [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_mult__left__idem,axiom, % 183.51/184.31 ! [V_b,V_a,T_a] : % 183.51/184.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_mult__idem,axiom, % 183.51/184.31 ! [V_x,T_a] : % 183.51/184.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_times_Oidem,axiom, % 183.51/184.31 ! [V_a,T_a] : % 183.51/184.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INFI__apply,axiom, % 183.51/184.31 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF__commute,axiom, % 183.51/184.31 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__iff,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 183.51/184.31 ( 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))) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF__INT__eq,axiom, % 183.51/184.31 ! [V_x_2,V_r_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__constant,axiom, % 183.51/184.31 ! [V_ca_2,T_b,T_a,V_A_2] : % 183.51/184.31 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 183.51/184.31 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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_ca_2)) = V_ca_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__empty,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I5_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I5_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I10_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I10_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I7_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I6_J,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I7_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__INT__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I6_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__INT__distrib2,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__Int__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__simps_I7_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_UN__extend__simps_I7_J,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fun__left__comm,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fun__left__comm__idem,axiom, % 183.51/184.31 ! [T_a] : % 183.51/184.31 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.31 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INTER__eq__Inter__image,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inter__image__eq,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Inter__def,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__product,axiom, % 183.51/184.31 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( class_Rings_Osemiring__0(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__left__distrib,axiom, % 183.51/184.31 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 183.51/184.31 ( class_Rings_Osemiring__0(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setsum__right__distrib,axiom, % 183.51/184.31 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 183.51/184.31 ( class_Rings_Osemiring__0(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__insert__distrib,axiom, % 183.51/184.31 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__absorb,axiom, % 183.51/184.31 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF__const,axiom, % 183.51/184.31 ! [V_M_2,T_a,V_A_2,T_b] : % 183.51/184.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I2_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I1_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__insert,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I3_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I3_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__extend__simps_I4_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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 ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__simps_I4_J,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 183.51/184.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) % 183.51/184.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INT__Un,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Int__Inter__image,axiom, % 183.51/184.31 ! [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))) ). % 183.51/184.31 % 183.51/184.31 fof(fact_Un__Inter,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__graph__insert__swap,axiom, % 183.51/184.31 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => ( 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)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 183.51/184.31 => 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))) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__add(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__left__cancel,axiom, % 183.51/184.31 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.51/184.31 ( class_Groups_Ocancel__semigroup__add(T_a) % 183.51/184.31 => ( 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_ca_2) % 183.51/184.31 <=> V_b_2 = V_ca_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__right__cancel,axiom, % 183.51/184.31 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 183.51/184.31 ( class_Groups_Ocancel__semigroup__add(T_a) % 183.51/184.31 => ( 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_ca_2),V_a_2) % 183.51/184.31 <=> V_b_2 = V_ca_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__left__imp__eq,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Ocancel__semigroup__add(T_a) % 183.51/184.31 => ( 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) % 183.51/184.31 => V_b = V_c ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__imp__eq,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 183.51/184.31 => ( 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) % 183.51/184.31 => V_b = V_c ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__right__imp__eq,axiom, % 183.51/184.31 ! [V_c,V_a,V_b,T_a] : % 183.51/184.31 ( class_Groups_Ocancel__semigroup__add(T_a) % 183.51/184.31 => ( 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) % 183.51/184.31 => V_b = V_c ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__eq__diff__eq,axiom, % 183.51/184.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__group__add(T_a) % 183.51/184.31 => ( 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_ca_2),V_d_2) % 183.51/184.31 => ( V_a_2 = V_b_2 % 183.51/184.31 <=> V_ca_2 = V_d_2 ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__image__insert,axiom, % 183.51/184.31 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.31 => 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)) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_eq__add__iff1,axiom, % 183.51/184.31 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.51/184.31 ( class_Rings_Oring(T_a) % 183.51/184.31 => ( 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_ca_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) % 183.51/184.31 <=> 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_ca_2) = V_d_2 ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_eq__add__iff2,axiom, % 183.51/184.31 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.51/184.31 ( class_Rings_Oring(T_a) % 183.51/184.31 => ( 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_ca_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) % 183.51/184.31 <=> V_ca_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) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__Union,axiom, % 183.51/184.31 ! [V_A_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 183.51/184.31 => ( ! [B_M] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__add__inverse2,axiom, % 183.51/184.31 ! [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 ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__add__inverse,axiom, % 183.51/184.31 ! [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 ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__diff__left,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__cancel,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__cancel2,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 183.51/184.31 ! [V_z,V_y,V_x,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF1__iff,axiom, % 183.51/184.31 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 183.51/184.31 ( 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)) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_INF2__iff,axiom, % 183.51/184.31 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 183.51/184.31 ( 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_ca_2)) % 183.51/184.31 <=> ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 183.51/184.31 ! [V_d,V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 183.51/184.31 ! [V_d,V_c,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 183.51/184.31 ! [V_d,V_c,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 183.51/184.31 ! [V_c,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 183.51/184.31 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 183.51/184.31 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 183.51/184.31 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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))) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 183.51/184.31 ! [V_rx,V_ly,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 183.51/184.31 ! [V_rx,V_ly,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 183.51/184.31 ! [V_ry,V_rx,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 183.51/184.31 ! [V_ry,V_rx,V_lx,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 183.51/184.31 ! [V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__add__commute,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__add__left__commute,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__mult__distrib2,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__add__assoc,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_add__mult__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__add__left__cancel,axiom, % 183.51/184.31 ! [V_n_2,V_m_2,V_k_2] : % 183.51/184.31 ( 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) % 183.51/184.31 <=> V_m_2 = V_n_2 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__add__right__cancel,axiom, % 183.51/184.31 ! [V_n_2,V_k_2,V_m_2] : % 183.51/184.31 ( 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) % 183.51/184.31 <=> V_m_2 = V_n_2 ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__commute,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__mult__distrib,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_diff__mult__distrib2,axiom, % 183.51/184.31 ! [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)) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__on__add__nat,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.31 fof(fact_crossproduct__eq,axiom, % 183.51/184.31 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 183.51/184.31 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 183.51/184.31 => ( 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)) % 183.51/184.31 <=> ( V_w_2 = V_x_2 % 183.51/184.31 | V_y_2 = V_z_2 ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_combine__common__factor,axiom, % 183.51/184.31 ! [V_c,V_b,V_e,V_a,T_a] : % 183.51/184.31 ( class_Rings_Osemiring(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 183.51/184.31 ! [V_b,V_m,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_comm__semiring__class_Odistrib,axiom, % 183.51/184.31 ! [V_c,V_b,V_a,T_a] : % 183.51/184.31 ( class_Rings_Ocomm__semiring(T_a) % 183.51/184.31 => 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)) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_crossproduct__noteq,axiom, % 183.51/184.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.51/184.31 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 183.51/184.31 => ( ( V_a_2 != V_b_2 % 183.51/184.31 & V_ca_2 != V_d_2 ) % 183.51/184.31 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_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_ca_2)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__Un__disjoint,axiom, % 183.51/184.31 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => ( 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)) % 183.51/184.31 => 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)) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold1__eq__fold,axiom, % 183.51/184.31 ! [V_a_2,V_A_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.31 => 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) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold1__Un,axiom, % 183.51/184.31 ! [V_B_2,V_A_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => ( 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)) % 183.51/184.31 => 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)) ) ) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_inj__on__INTER,axiom, % 183.51/184.31 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 183.51/184.31 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => ( ! [B_i] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 183.51/184.31 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 183.51/184.31 => 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)) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold1__insert,axiom, % 183.51/184.31 ! [V_x_2,V_A_2,T_a] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.31 => 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)) ) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_finite__UN__I,axiom, % 183.51/184.31 ! [V_B_2,T_b,V_A_2,T_a] : % 183.51/184.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ! [B_a] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 183.51/184.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 183.51/184.31 => 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))) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_setprod_Oremove,axiom, % 183.51/184.31 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.31 => 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)))))) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__image__Un__Int,axiom, % 183.51/184.31 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.31 => 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))) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_fold__image__cong,axiom, % 183.51/184.31 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.31 ( class_Groups_Oab__semigroup__mult(T_b) % 183.51/184.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.31 => ( ! [B_x] : % 183.51/184.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.31 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 183.51/184.31 => 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) ) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__mult__1,axiom, % 183.51/184.31 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__1__eq__mult__iff,axiom, % 183.51/184.31 ! [V_n_2,V_m_2] : % 183.51/184.31 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 183.51/184.31 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 183.51/184.31 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__mult__1__right,axiom, % 183.51/184.31 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 183.51/184.31 % 183.51/184.31 fof(fact_nat__mult__commute,axiom, % 183.51/184.31 ! [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) ). % 183.51/184.31 % 183.51/184.32 fof(fact_nat__mult__eq__1__iff,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 183.51/184.32 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 183.51/184.32 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat__mult__assoc,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__empty,axiom, % 183.51/184.32 ! [V_f_2,T_b,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oempty,axiom, % 183.51/184.32 ! [V_g_2,T_b,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__1,axiom, % 183.51/184.32 ! [V_A_2,T_b,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__eq__1__iff,axiom, % 183.51/184.32 ! [V_f_2,V_F_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.51/184.32 => ( 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) % 183.51/184.32 <=> ! [B_x] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 183.51/184.32 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_one__reorient,axiom, % 183.51/184.32 ! [V_x_2,T_a] : % 183.51/184.32 ( class_Groups_Oone(T_a) % 183.51/184.32 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 183.51/184.32 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__infinite,axiom, % 183.51/184.32 ! [V_f_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oinfinite,axiom, % 183.51/184.32 ! [V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__delta_H,axiom, % 183.51/184.32 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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) ) % 183.51/184.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__delta,axiom, % 183.51/184.32 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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) ) % 183.51/184.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_mult__1__left,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Groups_Omonoid__mult(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_mult__1,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_mult__1__right,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Groups_Omonoid__mult(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_mult_Ocomm__neutral,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 183.51/184.32 ! [V_a,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__timesf,axiom, % 183.51/184.32 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_OF__eq,axiom, % 183.51/184.32 ! [V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) % 183.51/184.32 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oeq__fold,axiom, % 183.51/184.32 ! [V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 183.51/184.32 ! [V_m,V_a,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 183.51/184.32 ! [V_a,V_m,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 183.51/184.32 ! [V_m,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Odistrib,axiom, % 183.51/184.32 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__singleton__def,axiom, % 183.51/184.32 ! [V_a_2,V_f_2,T_a,V_g_2] : % 183.51/184.32 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 183.51/184.32 => 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 ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__singleton,axiom, % 183.51/184.32 ! [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 ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__reindex,axiom, % 183.51/184.32 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_c) % 183.51/184.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__reindex__cong,axiom, % 183.51/184.32 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_c) % 183.51/184.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.32 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 183.51/184.32 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 183.51/184.32 => 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) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_folding__one_Oeq__fold,axiom, % 183.51/184.32 ! [V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.32 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__def,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__insert,axiom, % 183.51/184.32 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oinsert,axiom, % 183.51/184.32 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Ounion__inter,axiom, % 183.51/184.32 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__Un__Int,axiom, % 183.51/184.32 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold__image__distrib,axiom, % 183.51/184.32 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oreindex,axiom, % 183.51/184.32 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 183.51/184.32 => 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) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Sup__fin_OF__eq,axiom, % 183.51/184.32 ! [V_A_2,T_a] : % 183.51/184.32 ( class_Lattices_Olattice(T_a) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Inf__fin_OF__eq,axiom, % 183.51/184.32 ! [V_A_2,T_a] : % 183.51/184.32 ( class_Lattices_Olattice(T_a) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Oinsert__remove,axiom, % 183.51/184.32 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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)))))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__Un__disjoint,axiom, % 183.51/184.32 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => ( 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)) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Ounion__disjoint,axiom, % 183.51/184.32 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => ( 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)) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__insert__idem,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__Un2,axiom, % 183.51/184.32 ! [V_B_2,V_A_2,T_a] : % 183.51/184.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.32 => 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)) ) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__eq__fold__idem,axiom, % 183.51/184.32 ! [V_a_2,V_A_2,T_a] : % 183.51/184.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_semilattice__big_OF__eq,axiom, % 183.51/184.32 ! [V_A_2,V_F_2,V_f_2,T_a] : % 183.51/184.32 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold__image__Un__one,axiom, % 183.51/184.32 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.51/184.32 => ( ! [B_x] : % 183.51/184.32 ( 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))) % 183.51/184.32 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold1__in,axiom, % 183.51/184.32 ! [V_A_2,T_a] : % 183.51/184.32 ( class_Groups_Oab__semigroup__mult(T_a) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.32 => ( ! [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)))))) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod_Ounion__inter__neutral,axiom, % 183.51/184.32 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => ( ! [B_x] : % 183.51/184.32 ( 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))) % 183.51/184.32 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__Un__one,axiom, % 183.51/184.32 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.51/184.32 => ( ! [B_x] : % 183.51/184.32 ( 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))) % 183.51/184.32 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_left__add__mult__distrib,axiom, % 183.51/184.32 ! [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) ). % 183.51/184.32 % 183.51/184.32 fof(fact_hom__fold1__commute,axiom, % 183.51/184.32 ! [V_N_2,V_h_2,T_a] : % 183.51/184.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.51/184.32 => ( ! [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)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.51/184.32 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_strong__setprod__reindex__cong,axiom, % 183.51/184.32 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_c) % 183.51/184.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.32 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 183.51/184.32 => ( ! [B_x] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.51/184.32 => 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) ) % 183.51/184.32 => 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) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff__singleton__if,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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)) ) % 183.51/184.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__UNIV__unit,axiom, % 183.51/184.32 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) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__eq__setsum,axiom, % 183.51/184.32 ! [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) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 183.51/184.32 ! [V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.51/184.32 => ( 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))) % 183.51/184.32 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__image,axiom, % 183.51/184.32 ! [V_A_2,V_f_2,T_b,T_a] : % 183.51/184.32 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.32 => 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) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_inj__on__iff__eq__card,axiom, % 183.51/184.32 ! [V_f_2,T_b,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.51/184.32 <=> 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_eq__card__imp__inj__on,axiom, % 183.51/184.32 ! [V_f_2,T_b,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( 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) % 183.51/184.32 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card_Oinsert,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Un__Int,axiom, % 183.51/184.32 ! [V_B_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card_Ounion__inter,axiom, % 183.51/184.32 ! [V_B_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff__subset__Int,axiom, % 183.51/184.32 ! [V_B_2,V_A_2,T_a] : % 183.51/184.32 ( 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))) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff__insert,axiom, % 183.51/184.32 ! [V_B_2,V_a_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card_Oinsert__remove,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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)))))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Un__disjoint,axiom, % 183.51/184.32 ! [V_B_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.51/184.32 => ( 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)) % 183.51/184.32 => 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)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card_Oremove,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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)))))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff__singleton,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_setprod__gen__delta,axiom, % 183.51/184.32 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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_ca_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_ca_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)))) ) % 183.51/184.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.51/184.32 => 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_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff1__less,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff2__less,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.51/184.32 => 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))) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Suc__Diff1,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.51/184.32 => 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) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Diff1__le,axiom, % 183.51/184.32 ! [V_x_2,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__partition,axiom, % 183.51/184.32 ! [V_k_2,V_C_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 183.51/184.32 => ( ! [B_c] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 183.51/184.32 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 183.51/184.32 => ( ! [B_c1] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 183.51/184.32 => ! [B_c2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 183.51/184.32 => ( B_c1 != B_c2 % 183.51/184.32 => 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)) ) ) ) % 183.51/184.32 => 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)) ) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_fold__image__1,axiom, % 183.51/184.32 ! [V_f_2,V_S_2,T_a,T_b] : % 183.51/184.32 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.51/184.32 => ( ! [B_x] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.51/184.32 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.51/184.32 => 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) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_card__Plus,axiom, % 183.51/184.32 ! [V_B_2,T_b,V_A_2,T_a] : % 183.51/184.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.51/184.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__refl,axiom, % 183.51/184.32 ! [V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__mono,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_lessI,axiom, % 183.51/184.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__iff__Suc__add,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__add__Suc2,axiom, % 183.51/184.32 ! [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)))) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__add__Suc1,axiom, % 183.51/184.32 ! [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)))) ). % 183.51/184.32 % 183.51/184.32 fof(fact_INF__subset,axiom, % 183.51/184.32 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__less__Suc,axiom, % 183.51/184.32 ! [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))) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__diff__le,axiom, % 183.51/184.32 ! [V_m,V_n] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__less__mono,axiom, % 183.51/184.32 ! [V_c,V_b,V_a] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__diff__iff,axiom, % 183.51/184.32 ! [V_n_2,V_m_2,V_k_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 183.51/184.32 => ( 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))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat__less__cases,axiom, % 183.51/184.32 ! [V_P_2,V_n_2,V_m_2] : % 183.51/184.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 183.51/184.32 => ( ( V_m_2 = V_n_2 % 183.51/184.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 183.51/184.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 183.51/184.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 183.51/184.32 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__or__eq__imp__le,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 | V_m = V_n ) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__less__SucD,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__inject,axiom, % 183.51/184.32 ! [V_y,V_x] : % 183.51/184.32 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 183.51/184.32 => V_x = V_y ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__leD,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__le__lessD,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__lessD,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__SucE,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__SucE,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => V_m = V_n ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__trans__Suc,axiom, % 183.51/184.32 ! [V_k,V_j,V_i] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__antisym,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.51/184.32 => V_m = V_n ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__trans,axiom, % 183.51/184.32 ! [V_k,V_j,V_i] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__lessI,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__neq__implies__less,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => ( V_m != V_n % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__less__Suc__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 183.51/184.32 <=> V_n_2 = V_m_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__leI,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__SucI,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__imp__less__Suc,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__SucI,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__imp__le__nat,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_eq__imp__le,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( V_m = V_n % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__not__refl3,axiom, % 183.51/184.32 ! [V_t,V_s] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 183.51/184.32 => V_s != V_t ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__not__refl2,axiom, % 183.51/184.32 ! [V_m,V_n] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 183.51/184.32 => V_m != V_n ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__irrefl__nat,axiom, % 183.51/184.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__neqE__linordered__idom,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Rings_Olinordered__idom(T_a) % 183.51/184.32 => ( V_x != V_y % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__neqE__nat,axiom, % 183.51/184.32 ! [V_y,V_x] : % 183.51/184.32 ( V_x != V_y % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__antisym,axiom, % 183.51/184.32 ! [V_m,V_n] : % 183.51/184.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 183.51/184.32 => V_m = V_n ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_not__less__less__Suc__eq,axiom, % 183.51/184.32 ! [V_m_2,V_n_2] : % 183.51/184.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 183.51/184.32 <=> V_n_2 = V_m_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__eq__Suc__le__raw,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__le__mono,axiom, % 183.51/184.32 ! [V_m_2,V_n_2] : % 183.51/184.32 ( 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))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__less__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( 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))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat_Oinject,axiom, % 183.51/184.32 ! [V_nat_H_2,V_nat_2] : % 183.51/184.32 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 183.51/184.32 <=> V_nat_2 = V_nat_H_2 ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__le__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__Suc__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__Suc__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 | V_m_2 = V_n_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__Suc__eq__le,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__eq__less__or__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 | V_m_2 = V_n_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat__less__le,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 & V_m_2 != V_n_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__eq__Suc__le,axiom, % 183.51/184.32 ! [V_m_2,V_n_2] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat__le__linear,axiom, % 183.51/184.32 ! [V_n,V_m] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_nat__neq__iff,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( V_m_2 != V_n_2 % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_not__less__eq__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_not__less__eq,axiom, % 183.51/184.32 ! [V_n_2,V_m_2] : % 183.51/184.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__refl,axiom, % 183.51/184.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__n__not__le__n,axiom, % 183.51/184.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__n__not__n,axiom, % 183.51/184.32 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 183.51/184.32 % 183.51/184.32 fof(fact_n__not__Suc__n,axiom, % 183.51/184.32 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__not__refl,axiom, % 183.51/184.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__cases,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ( V_x != V_y % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__le__cases,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__funE,axiom, % 183.51/184.32 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 183.51/184.32 ( class_Orderings_Oord(T_b) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__asym,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I6_J,axiom, % 183.51/184.32 ! [V_z,V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I5_J,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => V_x = V_y ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I8_J,axiom, % 183.51/184.32 ! [V_z,V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__trans,axiom, % 183.51/184.32 ! [V_z,V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__antisym,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => V_x = V_y ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__le__less__trans,axiom, % 183.51/184.32 ! [V_z,V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I4_J,axiom, % 183.51/184.32 ! [V_c,V_a,V_b,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.51/184.32 => ( V_b = V_c % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_ord__le__eq__trans,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oord(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => ( V_b = V_c % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I7_J,axiom, % 183.51/184.32 ! [V_z,V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I10_J,axiom, % 183.51/184.32 ! [V_z,V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__le__trans,axiom, % 183.51/184.32 ! [V_z,V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__trans,axiom, % 183.51/184.32 ! [V_z,V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I2_J,axiom, % 183.51/184.32 ! [V_c,V_a,V_b,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.51/184.32 => ( V_b = V_c % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_ord__less__eq__trans,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oord(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => ( V_b = V_c % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I3_J,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( V_a = V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_ord__eq__le__trans,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oord(T_a) % 183.51/184.32 => ( V_a = V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I1_J,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( V_a = V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_ord__eq__less__trans,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oord(T_a) % 183.51/184.32 => ( V_a = V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I9_J,axiom, % 183.51/184.32 ! [V_a,V_b,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__asym_H,axiom, % 183.51/184.32 ! [V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I11_J,axiom, % 183.51/184.32 ! [V_a,V_b,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.51/184.32 => ( V_a != V_b % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__le__neq__trans,axiom, % 183.51/184.32 ! [V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => ( V_a != V_b % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__antisym__conv,axiom, % 183.51/184.32 ! [V_x_2,V_y_2,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__le__imp__less__or__eq,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 | V_x = V_y ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__imp__not__eq2,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => V_y != V_x ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__imp__not__eq,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => V_x != V_y ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__funD,axiom, % 183.51/184.32 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 183.51/184.32 ( class_Orderings_Oord(T_b) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__antisym__conv2,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__imp__not__less,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__imp__le,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__eq__refl,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( V_x = V_y % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_leD,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__not__sym,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__imp__neq,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => V_x != V_y ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__neqE,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( V_x != V_y % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_xt1_I12_J,axiom, % 183.51/184.32 ! [V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( V_a != V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__neq__le__trans,axiom, % 183.51/184.32 ! [V_b,V_a,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( V_a != V_b % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__antisym__conv1,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__antisym__conv3,axiom, % 183.51/184.32 ! [V_x_2,V_y_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_not__leE,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_leI,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__less__linear,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.51/184.32 | V_x = V_y % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__le__less,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 | V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__eq__iff,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( V_x_2 = V_y_2 % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__le__not__le,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__le,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Oorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 & V_x_2 != V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__linear,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__le__less__linear,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__fun__def,axiom, % 183.51/184.32 ! [V_g_2,V_f_2,T_a,T_b] : % 183.51/184.32 ( class_Orderings_Oord(T_b) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.51/184.32 <=> ! [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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_not__less__iff__gr__or__eq,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 183.51/184.32 | V_x_2 = V_y_2 ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__neq__iff,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( V_x_2 != V_y_2 % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__not__le,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_linorder__not__less,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Orderings_Olinorder(T_a) % 183.51/184.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_order__less__irrefl,axiom, % 183.51/184.32 ! [V_x,T_a] : % 183.51/184.32 ( class_Orderings_Opreorder(T_a) % 183.51/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__less__le__mono,axiom, % 183.51/184.32 ! [V_d,V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 183.51/184.32 => 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))) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__le__less__mono,axiom, % 183.51/184.32 ! [V_d,V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 183.51/184.32 => 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))) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_SUP__subset,axiom, % 183.51/184.32 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.51/184.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__mult__le__cancel1,axiom, % 183.51/184.32 ! [V_n_2,V_m_2,V_k_2] : % 183.51/184.32 ( 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))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_Suc__mult__less__cancel1,axiom, % 183.51/184.32 ! [V_n_2,V_m_2,V_k_2] : % 183.51/184.32 ( 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))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 183.51/184.32 ! [V_q,V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 183.51/184.32 ! [V_q,V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 183.51/184.32 ! [V_q,V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__Suc__diff__eq1,axiom, % 183.51/184.32 ! [V_m,V_j,V_k] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__Suc__diff__eq2,axiom, % 183.51/184.32 ! [V_m,V_j,V_k] : % 183.51/184.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 183.51/184.32 ! [V_q,V_y,V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 183.51/184.32 ! [V_q,V_p,V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => 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)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__less__cancel__right,axiom, % 183.51/184.32 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__less__cancel__left,axiom, % 183.51/184.32 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__strict__right__mono,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__strict__left__mono,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__strict__mono,axiom, % 183.51/184.32 ! [V_d,V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 183.51/184.32 => 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))) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__less__imp__less__right,axiom, % 183.51/184.32 ! [V_b,V_c,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( 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))) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__less__imp__less__left,axiom, % 183.51/184.32 ! [V_b,V_a,V_c,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( 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))) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__le__cancel__right,axiom, % 183.51/184.32 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__le__cancel__left,axiom, % 183.51/184.32 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__right__mono,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__left__mono,axiom, % 183.51/184.32 ! [V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__mono,axiom, % 183.51/184.32 ! [V_d,V_c,V_b,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 183.51/184.32 => 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))) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__le__imp__le__right,axiom, % 183.51/184.32 ! [V_b,V_c,V_a,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( 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))) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__le__imp__le__left,axiom, % 183.51/184.32 ! [V_b,V_a,V_c,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.51/184.32 => ( 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))) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__eq__diff__less,axiom, % 183.51/184.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__group__add(T_a) % 183.51/184.32 => ( 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_ca_2),V_d_2) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_bot__least,axiom, % 183.51/184.32 ! [V_x,T_a] : % 183.51/184.32 ( class_Orderings_Obot(T_a) % 183.51/184.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__Suc__shift,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__Suc,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_add__Suc__right,axiom, % 183.51/184.32 ! [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)) ). % 183.51/184.32 % 183.51/184.32 fof(fact_diff__eq__diff__less__eq,axiom, % 183.51/184.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.51/184.32 ( class_Groups_Oordered__ab__group__add(T_a) % 183.51/184.32 => ( 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_ca_2),V_d_2) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 183.51/184.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__supI1,axiom, % 183.51/184.32 ! [V_b,V_a,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__supI2,axiom, % 183.51/184.32 ! [V_a,V_b,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 183.51/184.32 ! [V_x,T_a] : % 183.51/184.32 ( class_Rings_Ocomm__semiring__1(T_a) % 183.51/184.32 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__infI2,axiom, % 183.51/184.32 ! [V_a,V_x,V_b,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_less__infI1,axiom, % 183.51/184.32 ! [V_b,V_x,V_a,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 183.51/184.32 => 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)) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_inf__sup__ord_I3_J,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Olattice(T_a) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_sup__ge1,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_inf__sup__ord_I4_J,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Lattices_Olattice(T_a) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_sup__ge2,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => 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))) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__iff__sup,axiom, % 183.51/184.32 ! [V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.51/184.32 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__sup__iff,axiom, % 183.51/184.32 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( 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)) % 183.51/184.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 183.51/184.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__supI1,axiom, % 183.51/184.32 ! [V_b,V_a,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_le__supI2,axiom, % 183.51/184.32 ! [V_a,V_b,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 183.51/184.32 => 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))) ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_sup__absorb2,axiom, % 183.51/184.32 ! [V_y,V_x,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.51/184.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 183.51/184.32 % 183.51/184.32 fof(fact_sup__absorb1,axiom, % 183.51/184.32 ! [V_x,V_y,T_a] : % 183.51/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.51/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.51/184.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_le__supI,axiom, % 183.66/184.32 ! [V_b,V_x,V_a,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 183.66/184.32 => 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)) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_sup__least,axiom, % 183.66/184.32 ! [V_z,V_x,V_y,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 183.66/184.32 => 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)) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_sup__mono,axiom, % 183.66/184.32 ! [V_d,V_b,V_c,V_a,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 183.66/184.32 => 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))) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_le__supE,axiom, % 183.66/184.32 ! [V_x,V_b,V_a,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__sup(T_a) % 183.66/184.32 => ( 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)) % 183.66/184.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.66/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_le__infE,axiom, % 183.66/184.32 ! [V_b,V_a,V_x,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( 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))) % 183.66/184.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.66/184.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_inf__mono,axiom, % 183.66/184.32 ! [V_d,V_b,V_c,V_a,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 183.66/184.32 => 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))) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_inf__greatest,axiom, % 183.66/184.32 ! [V_z,V_y,V_x,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 183.66/184.32 => 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))) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_le__infI,axiom, % 183.66/184.32 ! [V_b,V_a,V_x,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 183.66/184.32 => 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))) ) ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_inf__absorb2,axiom, % 183.66/184.32 ! [V_x,V_y,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.66/184.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_inf__absorb1,axiom, % 183.66/184.32 ! [V_y,V_x,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.66/184.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 183.66/184.32 % 183.66/184.32 fof(fact_le__infI2,axiom, % 183.66/184.32 ! [V_a,V_x,V_b,T_a] : % 183.66/184.32 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__infI1,axiom, % 183.66/184.33 ! [V_b,V_x,V_a,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__inf__iff,axiom, % 183.66/184.33 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__iff__inf,axiom, % 183.66/184.33 ! [V_y_2,V_x_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.66/184.33 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inf__le2,axiom, % 183.66/184.33 ! [V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inf__sup__ord_I2_J,axiom, % 183.66/184.33 ! [V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inf__le1,axiom, % 183.66/184.33 ! [V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inf__sup__ord_I1_J,axiom, % 183.66/184.33 ! [V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_top__greatest,axiom, % 183.66/184.33 ! [V_x,T_a] : % 183.66/184.33 ( class_Orderings_Otop(T_a) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__Suc__Suc,axiom, % 183.66/184.33 ! [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) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__diff__diff,axiom, % 183.66/184.33 ! [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) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__mult__cancel1,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( 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) % 183.66/184.33 <=> V_m_2 = V_n_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__lessD1,axiom, % 183.66/184.33 ! [V_k,V_j,V_i] : % 183.66/184.33 ( 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)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__add__eq__less,axiom, % 183.66/184.33 ! [V_n,V_m,V_l,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 183.66/184.33 => ( 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) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__less__mono,axiom, % 183.66/184.33 ! [V_l,V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__less__mono1,axiom, % 183.66/184.33 ! [V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_trans__less__add2,axiom, % 183.66/184.33 ! [V_m,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_trans__less__add1,axiom, % 183.66/184.33 ! [V_m,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__add__left__cancel__less,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_not__add__less2,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_not__add__less1,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__leE,axiom, % 183.66/184.33 ! [V_n,V_k,V_m] : % 183.66/184.33 ( 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)) % 183.66/184.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__leD1,axiom, % 183.66/184.33 ! [V_n,V_k,V_m] : % 183.66/184.33 ( 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)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__leD2,axiom, % 183.66/184.33 ! [V_n,V_k,V_m] : % 183.66/184.33 ( 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)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__le__mono,axiom, % 183.66/184.33 ! [V_l,V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__le__mono1,axiom, % 183.66/184.33 ! [V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_trans__le__add2,axiom, % 183.66/184.33 ! [V_m,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_trans__le__add1,axiom, % 183.66/184.33 ! [V_m,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__add__left__cancel__le,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__iff__add,axiom, % 183.66/184.33 ! [V_n_2,V_m_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.66/184.33 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add1,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add2,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__imp__diff__less,axiom, % 183.66/184.33 ! [V_n,V_k,V_j] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__less__mono2,axiom, % 183.66/184.33 ! [V_l,V_n,V_m] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__le__self,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__le__mono2,axiom, % 183.66/184.33 ! [V_l,V_n,V_m] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__le__mono,axiom, % 183.66/184.33 ! [V_l,V_n,V_m] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__diff__cancel,axiom, % 183.66/184.33 ! [V_n,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 183.66/184.33 => 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 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_eq__diff__iff,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 183.66/184.33 => ( 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) % 183.66/184.33 <=> V_m_2 = V_n_2 ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Nat_Odiff__diff__eq,axiom, % 183.66/184.33 ! [V_n,V_m,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 183.66/184.33 => 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) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__diff__iff,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__square,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__cube,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__le__mono1,axiom, % 183.66/184.33 ! [V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__le__mono2,axiom, % 183.66/184.33 ! [V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__le__mono,axiom, % 183.66/184.33 ! [V_l,V_k,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__Sup__iff,axiom, % 183.66/184.33 ! [V_S_2,V_a_2,T_a] : % 183.66/184.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 & class_Orderings_Olinorder(T_a) ) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 183.66/184.33 <=> ? [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Sup__le__iff,axiom, % 183.66/184.33 ! [V_b_2,V_A_2,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( 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)) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inf__less__iff,axiom, % 183.66/184.33 ! [V_a_2,V_S_2,T_a] : % 183.66/184.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 & class_Orderings_Olinorder(T_a) ) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 183.66/184.33 <=> ? [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__Inf__iff,axiom, % 183.66/184.33 ! [V_A_2,V_b_2,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__less__add__iff2,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__less__add__iff1,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__SUP__iff,axiom, % 183.66/184.33 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 183.66/184.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 & class_Orderings_Olinorder(T_a) ) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> ? [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_SUP__le__iff,axiom, % 183.66/184.33 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( 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)) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_INF__less__iff,axiom, % 183.66/184.33 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 & class_Orderings_Olinorder(T_a) ) % 183.66/184.33 => ( 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)) % 183.66/184.33 <=> ? [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__INF__iff,axiom, % 183.66/184.33 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__Suc,axiom, % 183.66/184.33 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 183.66/184.33 % 183.66/184.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 183.66/184.33 ! [V_q,V_p,V_x,T_a] : % 183.66/184.33 ( class_Rings_Ocomm__semiring__1(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__add__one,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => 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)))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__1__mult,axiom, % 183.66/184.33 ! [V_n,V_m,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_distrib__inf__le,axiom, % 183.66/184.33 ! [V_z,V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => 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)))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_distrib__sup__le,axiom, % 183.66/184.33 ! [V_z,V_y,V_x,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => 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)))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__Suc,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__Suc__right,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Sup__upper,axiom, % 183.66/184.33 ! [V_A_2,V_x_2,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__Suc__1,axiom, % 183.66/184.33 ! [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 ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__diff__inverse,axiom, % 183.66/184.33 ! [V_n,V_m] : % 183.66/184.33 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => 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 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__diff__conv,axiom, % 183.66/184.33 ! [V_k_2,V_j_2,V_i_2] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__add__assoc2,axiom, % 183.66/184.33 ! [V_i,V_j,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__diff__assoc2,axiom, % 183.66/184.33 ! [V_i,V_j,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__add__assoc,axiom, % 183.66/184.33 ! [V_i,V_j,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__imp__diff__is__add,axiom, % 183.66/184.33 ! [V_k_2,V_j_2,V_i_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 183.66/184.33 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 183.66/184.33 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add__diff__inverse2,axiom, % 183.66/184.33 ! [V_m,V_n] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.66/184.33 => 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 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__diff__conv2,axiom, % 183.66/184.33 ! [V_i_2,V_j_2,V_k_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__diff__assoc,axiom, % 183.66/184.33 ! [V_i,V_j,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add__diff__inverse,axiom, % 183.66/184.33 ! [V_m,V_n] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.66/184.33 => 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 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add__diff,axiom, % 183.66/184.33 ! [V_m,V_n,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__diff__conv,axiom, % 183.66/184.33 ! [V_i_2,V_k_2,V_j_2] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__diff__right,axiom, % 183.66/184.33 ! [V_i,V_j,V_k] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inf__lower,axiom, % 183.66/184.33 ! [V_A_2,V_x_2,T_a] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__SUPI,axiom, % 183.66/184.33 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_INF__leI,axiom, % 183.66/184.33 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 183.66/184.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__add__iff1,axiom, % 183.66/184.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Oordered__ring(T_a) % 183.66/184.33 => ( 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_ca_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))) % 183.66/184.33 <=> 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_ca_2)),V_d_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__add__iff2,axiom, % 183.66/184.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Oordered__ring(T_a) % 183.66/184.33 => ( 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_ca_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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add__iff1,axiom, % 183.66/184.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Oordered__ring(T_a) % 183.66/184.33 => ( 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_ca_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))) % 183.66/184.33 <=> 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_ca_2)),V_d_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__add__iff2,axiom, % 183.66/184.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Oordered__ring(T_a) % 183.66/184.33 => ( 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_ca_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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__insert__le,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => 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)))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__image__le,axiom, % 183.66/184.33 ! [V_f_2,T_b,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__eq__add__iff2,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 183.66/184.33 => ( 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) % 183.66/184.33 <=> 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) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__diff__add__eq2,axiom, % 183.66/184.33 ! [V_n,V_m,V_u,V_j,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__le__add__iff2,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__eq__add__iff1,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 183.66/184.33 => ( 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) % 183.66/184.33 <=> 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 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__diff__add__eq1,axiom, % 183.66/184.33 ! [V_n,V_m,V_u,V_i,V_j] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__le__add__iff1,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_pigeonhole,axiom, % 183.66/184.33 ! [V_A_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_setprod__constant,axiom, % 183.66/184.33 ! [V_y_2,V_A_2,T_a,T_b] : % 183.66/184.33 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__insert__disjoint,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__insert__if,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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) ) % 183.66/184.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_sup__le__fold__sup,axiom, % 183.66/184.33 ! [V_b_2,V_a_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__sup(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_fold__inf__le__inf,axiom, % 183.66/184.33 ! [V_b_2,V_a_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_fold1__belowI,axiom, % 183.66/184.33 ! [V_a_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_below__fold1__iff,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Osemilattice__inf(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__card__le__card__Diff,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => 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)))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inf__le__Sup,axiom, % 183.66/184.33 ! [V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__Plus__iff,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__Plus,axiom, % 183.66/184.33 ! [V_B_2,T_b,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__PlusD_I1_J,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__PlusD_I2_J,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__insert,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => 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)))))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__increasing__iff,axiom, % 183.66/184.33 ! [V_y_2,V_x_2,V_b_2,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__le__imp__le__exp,axiom, % 183.66/184.33 ! [V_n,V_m,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_UNIV__Plus__UNIV,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__increasing,axiom, % 183.66/184.33 ! [V_a,V_N,V_n,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__strict__increasing__iff,axiom, % 183.66/184.33 ! [V_y_2,V_x_2,V_b_2,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__less__imp__less__exp,axiom, % 183.66/184.33 ! [V_n,V_m,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__strict__increasing,axiom, % 183.66/184.33 ! [V_a,V_N,V_n,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__gt1,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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)))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_equalityI,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => V_A_2 = V_B_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subsetD,axiom, % 183.66/184.33 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_empty__subsetI,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_predicate1D,axiom, % 183.66/184.33 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 183.66/184.33 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.66/184.33 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_rev__predicate1D,axiom, % 183.66/184.33 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 183.66/184.33 ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 183.66/184.33 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_equalityE,axiom, % 183.66/184.33 ! [T_a,V_B_2,V_A_2] : % 183.66/184.33 ( V_A_2 = V_B_2 % 183.66/184.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__trans,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__psubset__trans,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__subset__trans,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__imp__subset,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_equalityD2,axiom, % 183.66/184.33 ! [T_a,V_B_2,V_A_2] : % 183.66/184.33 ( V_A_2 = V_B_2 % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_equalityD1,axiom, % 183.66/184.33 ! [T_a,V_B_2,V_A_2] : % 183.66/184.33 ( V_A_2 = V_B_2 % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__iff__psubset__eq,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 | V_A_2 = V_B_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_set__eq__subset,axiom, % 183.66/184.33 ! [T_a,V_B_2,V_A_2] : % 183.66/184.33 ( V_A_2 = V_B_2 % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__eq,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 & V_A_2 != V_B_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__refl,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__fun__def,axiom, % 183.66/184.33 ! [V_g_2,V_f_2,T_a,T_b] : % 183.66/184.33 ( class_Orderings_Oord(T_b) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.66/184.33 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Union__mono,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inter__anti__mono,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubsetD,axiom, % 183.66/184.33 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_in__mono,axiom, % 183.66/184.33 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_set__rev__mp,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_x_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_set__mp,axiom, % 183.66/184.33 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_not__psubset__empty,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__empty,axiom, % 183.66/184.33 ! [V_A_2,T_a] : % 183.66/184.33 ( 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)))) % 183.66/184.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__subset,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_rev__finite__subset,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__insertI,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__insertI2,axiom, % 183.66/184.33 ! [V_b_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_insert__mono,axiom, % 183.66/184.33 ! [V_a_2,V_D_2,V_C_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__UNIV,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__image__iff,axiom, % 183.66/184.33 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ? [B_AA] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 183.66/184.33 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_image__mono,axiom, % 183.66/184.33 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__upper1,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__upper2,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__Un__eq,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__absorb1,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__absorb2,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__least,axiom, % 183.66/184.33 ! [V_B_2,V_C_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__mono,axiom, % 183.66/184.33 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__lower1,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__lower2,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__absorb2,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__absorb1,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__greatest,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_C_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Int__mono,axiom, % 183.66/184.33 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Diff__subset,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Diff__mono,axiom, % 183.66/184.33 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_double__diff,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => 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 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__inj__on,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_asm,axiom, % 183.66/184.33 ! [V_Ga_2,V_ts_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_weaken,axiom, % 183.66/184.33 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 183.66/184.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 183.66/184.33 => ( 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)) % 183.66/184.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_thin,axiom, % 183.66/184.33 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 183.66/184.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 183.66/184.33 => ( 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)) % 183.66/184.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__psubset,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_pred__subset__eq,axiom, % 183.66/184.33 ! [V_S_2,V_R_2,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_UN__subset__iff,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_INT__subset__iff,axiom, % 183.66/184.33 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__insert__iff,axiom, % 183.66/184.33 ! [V_B_2,V_x_2,V_A_2,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 183.66/184.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.66/184.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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)) ) % 183.66/184.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_insert__subset,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_x_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 183.66/184.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__insert,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_x_2,T_a] : % 183.66/184.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__singletonD,axiom, % 183.66/184.33 ! [V_x_2,V_A_2,T_a] : % 183.66/184.33 ( 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))))) % 183.66/184.33 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 | 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__surj,axiom, % 183.66/184.33 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__on__strict__subset,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_image__Int__subset,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Un__Int__assoc__eq,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_image__diff__subset,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Diff__subset__conv,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Diff__partition,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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 ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Union__Int__subset,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Union__upper,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inter__Un__subset,axiom, % 183.66/184.33 ! [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)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inter__lower,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_UN__upper,axiom, % 183.66/184.33 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_INT__lower,axiom, % 183.66/184.33 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.66/184.33 => 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))) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__card__mono,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__surj__inj,axiom, % 183.66/184.33 ! [V_f_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_endo__inj__surj,axiom, % 183.66/184.33 ! [V_f_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( 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)) % 183.66/184.33 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 183.66/184.33 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__mono,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__seteq,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => V_A_2 = V_B_2 ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__image__subset__iff,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.66/184.33 => ( 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))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__on__image__Int,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__on__image__set__diff,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_folding__one__idem_Osubset__idem,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 183.66/184.33 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_subset__insert__iff,axiom, % 183.66/184.33 ! [V_B_2,V_x_2,V_A_2,T_a] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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)) ) % 183.66/184.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__single__insert,axiom, % 183.66/184.33 ! [V_B_2,V_x_2,V_A_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_setsum__diff,axiom, % 183.66/184.33 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.66/184.33 ( class_Groups_Oab__group__add(T_b) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__bij__eq,axiom, % 183.66/184.33 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.66/184.33 => ( 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)) % 183.66/184.33 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 183.66/184.33 => ( 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)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.66/184.33 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__Diff__subset,axiom, % 183.66/184.33 ! [V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Sup__fin_Osubset__idem,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Inf__fin_Osubset__idem,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_a] : % 183.66/184.33 ( class_Lattices_Olattice(T_a) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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) ) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_setsum__diff__nat,axiom, % 183.66/184.33 ! [V_f_2,V_A_2,V_B_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.66/184.33 => 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)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_the__inv__into__into,axiom, % 183.66/184.33 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => 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)) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_card__inj__on__le,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.66/184.33 => ( 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)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.66/184.33 => 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__mult__distrib,axiom, % 183.66/184.33 ! [V_n,V_b,V_a,T_a] : % 183.66/184.33 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__commutes,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__one,axiom, % 183.66/184.33 ! [V_n,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__mult,axiom, % 183.66/184.33 ! [V_n,V_m,V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__one__right,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Plus__eq__empty__conv,axiom, % 183.66/184.33 ! [V_B_2,V_A_2,T_b,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_one__le__power,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__inject__exp,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 183.66/184.33 => ( 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) % 183.66/184.33 <=> V_m_2 = V_n_2 ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__Suc2,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__Suc,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Power_Opower(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__add,axiom, % 183.66/184.33 ! [V_n,V_m,V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__mult(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__gt1__lemma,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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)))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__less__power__Suc,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.66/184.33 => 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)))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__on__iff__card__le,axiom, % 183.66/184.33 ! [V_B_2,T_b,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.66/184.33 => ( ? [B_f] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 183.66/184.33 & 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)) ) % 183.66/184.33 <=> 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))) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_inj__on__iff__surj,axiom, % 183.66/184.33 ! [V_A_H_2,T_b,T_a,V_A_2] : % 183.66/184.33 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.66/184.33 => ( ? [B_f] : % 183.66/184.33 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 183.66/184.33 & 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)) ) % 183.66/184.33 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__Suc__eq__diff__pred,axiom, % 183.66/184.33 ! [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) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__eq__plus1__left,axiom, % 183.66/184.33 ! [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) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__eq__plus1,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Body__triple__valid__Suc,axiom, % 183.66/184.33 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_psubset__trans,axiom, % 183.66/184.33 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.66/184.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_triple__valid__Suc,axiom, % 183.66/184.33 ! [V_t,V_n,T_a] : % 183.66/184.33 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 183.66/184.33 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__nat__set__iff__bounded,axiom, % 183.66/184.33 ! [V_N_2] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 183.66/184.33 <=> ? [B_m] : % 183.66/184.33 ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 183.66/184.33 ! [V_N_2] : % 183.66/184.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 183.66/184.33 <=> ? [B_m] : % 183.66/184.33 ! [B_x] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_flat__lub__def,axiom, % 183.66/184.33 ! [V_b_2,V_A_2,T_a] : % 183.66/184.33 ( ( 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))))) % 183.66/184.33 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 183.66/184.33 & ( ~ 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))))) % 183.66/184.33 => 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)))))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__power__power,axiom, % 183.66/184.33 ! [T_a] : % 183.66/184.33 ( class_Power_Opower(T_a) % 183.66/184.33 => 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)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_finite__fun__UNIVD1,axiom, % 183.66/184.33 ! [T_b,T_a] : % 183.66/184.33 ( 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)))) % 183.66/184.33 => ( 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)) % 183.66/184.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_ord_OatMost__iff,axiom, % 183.66/184.33 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_ord_OatLeast__iff,axiom, % 183.66/184.33 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_ord_OlessThan__iff,axiom, % 183.66/184.33 ! [V_k_2,V_less_2,V_i_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_ord_OgreaterThan__iff,axiom, % 183.66/184.33 ! [V_k_2,V_less_2,V_i_2,T_a] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__zeroE,axiom, % 183.66/184.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le0,axiom, % 183.66/184.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_zero__less__Suc,axiom, % 183.66/184.33 ! [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))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_bot__nat__def,axiom, % 183.66/184.33 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.66/184.33 % 183.66/184.33 fof(fact_infinite__UNIV__nat,axiom, % 183.66/184.33 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_zero__reorient,axiom, % 183.66/184.33 ! [V_x_2,T_a] : % 183.66/184.33 ( class_Groups_Ozero(T_a) % 183.66/184.33 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 183.66/184.33 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power_Opower_Opower__0,axiom, % 183.66/184.33 ! [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 ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__eq__0__iff,axiom, % 183.66/184.33 ! [V_n_2,V_a_2,T_a] : % 183.66/184.33 ( ( class_Power_Opower(T_a) % 183.66/184.33 & class_Rings_Omult__zero(T_a) % 183.66/184.33 & class_Rings_Ono__zero__divisors(T_a) % 183.66/184.33 & class_Rings_Ozero__neq__one(T_a) ) % 183.66/184.33 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__0__left,axiom, % 183.66/184.33 ! [V_n,T_a] : % 183.66/184.33 ( ( class_Power_Opower(T_a) % 183.66/184.33 & class_Rings_Osemiring__0(T_a) ) % 183.66/184.33 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 => 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) ) % 183.66/184.33 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 => 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) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__0__iff,axiom, % 183.66/184.33 ! [V_a_2,V_b_2,T_a] : % 183.66/184.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 183.66/184.33 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 183.66/184.33 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Ocomm__semiring__1(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Ocomm__semiring__1(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add_Ocomm__neutral,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Ocomm__monoid__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__0__right,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_double__zero__sym,axiom, % 183.66/184.33 ! [V_a_2,T_a] : % 183.66/184.33 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.66/184.33 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 183.66/184.33 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__0,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Ocomm__monoid__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__0__left,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Omonoid__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_divisors__zero,axiom, % 183.66/184.33 ! [V_b,V_a,T_a] : % 183.66/184.33 ( class_Rings_Ono__zero__divisors(T_a) % 183.66/184.33 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_no__zero__divisors,axiom, % 183.66/184.33 ! [V_b,V_a,T_a] : % 183.66/184.33 ( class_Rings_Ono__zero__divisors(T_a) % 183.66/184.33 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__eq__0__iff,axiom, % 183.66/184.33 ! [V_b_2,V_a_2,T_a] : % 183.66/184.33 ( class_Rings_Oring__no__zero__divisors(T_a) % 183.66/184.33 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Ocomm__semiring__1(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__zero__right,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Omult__zero(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Ocomm__semiring__1(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__zero__left,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Rings_Omult__zero(T_a) % 183.66/184.33 => 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) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_right__minus__eq,axiom, % 183.66/184.33 ! [V_b_2,V_a_2,T_a] : % 183.66/184.33 ( class_Groups_Ogroup__add(T_a) % 183.66/184.33 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 <=> V_a_2 = V_b_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_eq__iff__diff__eq__0,axiom, % 183.66/184.33 ! [V_b_2,V_a_2,T_a] : % 183.66/184.33 ( class_Groups_Oab__group__add(T_a) % 183.66/184.33 => ( V_a_2 = V_b_2 % 183.66/184.33 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__self,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Ogroup__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__0__right,axiom, % 183.66/184.33 ! [V_a,T_a] : % 183.66/184.33 ( class_Groups_Ogroup__add(T_a) % 183.66/184.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_one__neq__zero,axiom, % 183.66/184.33 ! [T_a] : % 183.66/184.33 ( class_Rings_Ozero__neq__one(T_a) % 183.66/184.33 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_zero__neq__one,axiom, % 183.66/184.33 ! [T_a] : % 183.66/184.33 ( class_Rings_Ozero__neq__one(T_a) % 183.66/184.33 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_power__Suc__0,axiom, % 183.66/184.33 ! [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)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 183.66/184.33 ! [V_m_2,V_x_2] : % 183.66/184.33 ( 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)) % 183.66/184.33 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Zero__not__Suc,axiom, % 183.66/184.33 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat_Osimps_I2_J,axiom, % 183.66/184.33 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__not__Zero,axiom, % 183.66/184.33 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat_Osimps_I3_J,axiom, % 183.66/184.33 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Zero__neq__Suc,axiom, % 183.66/184.33 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 183.66/184.33 % 183.66/184.33 fof(fact_Suc__neq__Zero,axiom, % 183.66/184.33 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.66/184.33 % 183.66/184.33 fof(fact_field__power__not__zero,axiom, % 183.66/184.33 ! [V_n,V_a,T_a] : % 183.66/184.33 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 183.66/184.33 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.33 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__zero__less__power__iff,axiom, % 183.66/184.33 ! [V_n_2,V_x_2] : % 183.66/184.33 ( 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))) % 183.66/184.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 183.66/184.33 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__power__less__imp__less,axiom, % 183.66/184.33 ! [V_n,V_m,V_i] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 183.66/184.33 => ( 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))) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_not__less0,axiom, % 183.66/184.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_neq0__conv,axiom, % 183.66/184.33 ! [V_n_2] : % 183.66/184.33 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__nat__zero__code,axiom, % 183.66/184.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 183.66/184.33 % 183.66/184.33 fof(fact_gr__implies__not0,axiom, % 183.66/184.33 ! [V_n,V_m] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.66/184.33 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_gr0I,axiom, % 183.66/184.33 ! [V_n] : % 183.66/184.33 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_plus__nat_Oadd__0,axiom, % 183.66/184.33 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 183.66/184.33 % 183.66/184.33 fof(fact_Nat_Oadd__0__right,axiom, % 183.66/184.33 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__is__0,axiom, % 183.66/184.33 ! [V_n_2,V_m_2] : % 183.66/184.33 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_add__eq__self__zero,axiom, % 183.66/184.33 ! [V_n,V_m] : % 183.66/184.33 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 183.66/184.33 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 183.66/184.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 183.66/184.33 % 183.66/184.33 fof(fact_le__0__eq,axiom, % 183.66/184.33 ! [V_n_2] : % 183.66/184.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 183.66/184.33 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diffs0__imp__equal,axiom, % 183.66/184.33 ! [V_n,V_m] : % 183.66/184.33 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 => V_m = V_n ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__self__eq__0,axiom, % 183.66/184.33 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.66/184.33 % 183.66/184.33 fof(fact_minus__nat_Odiff__0,axiom, % 183.66/184.33 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 183.66/184.33 % 183.66/184.33 fof(fact_diff__0__eq__0,axiom, % 183.66/184.33 ! [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) ). % 183.66/184.33 % 183.66/184.33 fof(fact_nat__mult__eq__cancel__disj,axiom, % 183.66/184.33 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.33 ( 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) % 183.66/184.33 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.33 | V_m_2 = V_n_2 ) ) ). % 183.66/184.33 % 183.66/184.33 fof(fact_mult__cancel2,axiom, % 183.66/184.33 ! [V_n_2,V_k_2,V_m_2] : % 183.66/184.34 ( 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) % 183.66/184.34 <=> ( V_m_2 = V_n_2 % 183.66/184.34 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__cancel1,axiom, % 183.66/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.66/184.34 ( 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) % 183.66/184.34 <=> ( V_m_2 = V_n_2 % 183.66/184.34 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__is__0,axiom, % 183.66/184.34 ! [V_n_2,V_m_2] : % 183.66/184.34 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.66/184.34 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__0__right,axiom, % 183.66/184.34 ! [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) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__0,axiom, % 183.66/184.34 ! [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) ). % 183.66/184.34 % 183.66/184.34 fof(fact_power__eq__imp__eq__base,axiom, % 183.66/184.34 ! [V_b,V_n,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( 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) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.66/184.34 => V_a = V_b ) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setsum__0,axiom, % 183.66/184.34 ! [V_A_2,T_b,T_a] : % 183.66/184.34 ( class_Groups_Ocomm__monoid__add(T_a) % 183.66/184.34 => 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) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_power__strict__mono,axiom, % 183.66/184.34 ! [V_n,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.66/184.34 => 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))) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__nonpos__nonpos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__increasing2,axiom, % 183.66/184.34 ! [V_a,V_b,V_c,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__increasing,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__nonneg__eq__0__iff,axiom, % 183.66/184.34 ! [V_y_2,V_x_2,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 183.66/184.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__nonneg__nonneg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 183.66/184.34 ! [V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 183.66/184.34 ! [V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__le__square,axiom, % 183.66/184.34 ! [V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring(T_a) % 183.66/184.34 => 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))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__le__mult__iff,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__le__0__iff,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__nonneg__nonneg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__cancel__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__nonneg__nonpos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__cancel__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__nonneg__nonpos2,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__cancel__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__nonpos__nonneg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__cancel__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__nonpos__nonpos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__ring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__right__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__left__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_comm__mult__left__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__comm__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__right__mono__neg,axiom, % 183.66/184.34 ! [V_c,V_a,V_b,T_a] : % 183.66/184.34 ( class_Rings_Oordered__ring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__left__mono__neg,axiom, % 183.66/184.34 ! [V_c,V_a,V_b,T_a] : % 183.66/184.34 ( class_Rings_Oordered__ring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__mono_H,axiom, % 183.66/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__mono,axiom, % 183.66/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__semiring(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_split__mult__pos__le,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__ring(T_a) % 183.66/184.34 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 183.66/184.34 => 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_split__mult__neg__le,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Oordered__cancel__semiring(T_a) % 183.66/184.34 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 183.66/184.34 => 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__neg__neg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__pos__pos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 183.66/184.34 ! [V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 183.66/184.34 ! [V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_pos__add__strict,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_not__square__less__zero,axiom, % 183.66/184.34 ! [V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring(T_a) % 183.66/184.34 => ~ 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))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__less__cancel__right__disj,axiom, % 183.66/184.34 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))) % 183.66/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__less__cancel__left__disj,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 183.66/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 183.66/184.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__less__cancel__left__pos,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__pos__pos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__pos__neg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__pos__neg2,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__less__mult__pos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__less__mult__pos2,axiom, % 183.66/184.34 ! [V_a,V_b,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( 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))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__less__cancel__left__neg,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 183.66/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__neg__pos,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__neg__neg,axiom, % 183.66/184.34 ! [V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__strict__right__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__strict__left__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_comm__mult__strict__left__mono,axiom, % 183.66/184.34 ! [V_c,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__strict__right__mono__neg,axiom, % 183.66/184.34 ! [V_c,V_a,V_b,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_mult__strict__left__mono__neg,axiom, % 183.66/184.34 ! [V_c,V_a,V_b,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_le__iff__diff__le__0,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Oordered__ab__group__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 183.66/184.34 <=> 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_less__iff__diff__less__0,axiom, % 183.66/184.34 ! [V_b_2,V_a_2,T_a] : % 183.66/184.34 ( class_Groups_Oordered__ab__group__add(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.66/184.34 <=> 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_add__scale__eq__noteq,axiom, % 183.66/184.34 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 183.66/184.34 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 183.66/184.34 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.34 => ( ( V_a = V_b % 183.66/184.34 & V_c != V_d ) % 183.66/184.34 => 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)) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_sum__squares__eq__zero__iff,axiom, % 183.66/184.34 ! [V_y_2,V_x_2,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.66/184.34 => ( 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) % 183.66/184.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.66/184.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_not__one__le__zero,axiom, % 183.66/184.34 ! [T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ~ 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))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__le__one,axiom, % 183.66/184.34 ! [T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => 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))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_not__one__less__zero,axiom, % 183.66/184.34 ! [T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__less__one,axiom, % 183.66/184.34 ! [T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_power__mono,axiom, % 183.66/184.34 ! [V_n,V_b,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => 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))) ) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__le__power,axiom, % 183.66/184.34 ! [V_n,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_zero__less__power,axiom, % 183.66/184.34 ! [V_n,V_a,T_a] : % 183.66/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.66/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.66/184.34 => 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))) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setsum__empty,axiom, % 183.66/184.34 ! [V_f_2,T_b,T_a] : % 183.66/184.34 ( class_Groups_Ocomm__monoid__add(T_a) % 183.66/184.34 => 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) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setsum_Oempty,axiom, % 183.66/184.34 ! [V_g_2,T_b,T_a] : % 183.66/184.34 ( class_Groups_Ocomm__monoid__add(T_a) % 183.66/184.34 => 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) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setsum__infinite,axiom, % 183.66/184.34 ! [V_f_2,V_A_2,T_a,T_b] : % 183.66/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.66/184.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.34 => 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) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setsum_Oinfinite,axiom, % 183.66/184.34 ! [V_g_2,V_A_2,T_a,T_b] : % 183.66/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.66/184.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.34 => 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) ) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_power__0__Suc,axiom, % 183.66/184.34 ! [V_n,T_a] : % 183.66/184.34 ( ( class_Power_Opower(T_a) % 183.66/184.34 & class_Rings_Osemiring__0(T_a) ) % 183.66/184.34 => 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) ) ). % 183.66/184.34 % 183.66/184.34 fof(fact_setprod__zero,axiom, % 183.66/184.34 ! [V_f_2,V_A_2,T_a,T_b] : % 183.66/184.34 ( class_Rings_Ocomm__semiring__1(T_b) % 183.66/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.66/184.34 => ( ? [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.34 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.34 => 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) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setprod__zero__iff,axiom, % 183.72/184.34 ! [V_f_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( ( class_Rings_Ocomm__semiring__1(T_b) % 183.72/184.34 & class_Rings_Ono__zero__divisors(T_b) ) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => ( 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) % 183.72/184.34 <=> ? [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.34 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_gr0__conv__Suc,axiom, % 183.72/184.34 ! [V_n_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 183.72/184.34 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_less__Suc0,axiom, % 183.72/184.34 ! [V_n_2] : % 183.72/184.34 ( 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)))) % 183.72/184.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_less__Suc__eq__0__disj,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 183.72/184.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 | ? [B_j] : % 183.72/184.34 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 183.72/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_one__is__add,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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) % 183.72/184.34 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.34 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.34 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__is__1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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)) % 183.72/184.34 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.34 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.34 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__gr__0,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 183.72/184.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__one__le__power,axiom, % 183.72/184.34 ! [V_n,V_i] : % 183.72/184.34 ( 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)) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__0,axiom, % 183.72/184.34 ! [V_a,T_a] : % 183.72/184.34 ( class_Power_Opower(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 183.72/184.34 ! [V_x,T_a] : % 183.72/184.34 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card_Oempty,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__infinite,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__eq__1__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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)) % 183.72/184.34 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_diff__less,axiom, % 183.72/184.34 ! [V_m,V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 183.72/184.34 => 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)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zero__less__diff,axiom, % 183.72/184.34 ! [V_m_2,V_n_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__0__less__mult__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 183.72/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__cancel1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__cancel2,axiom, % 183.72/184.34 ! [V_n_2,V_k_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__mono1,axiom, % 183.72/184.34 ! [V_k,V_j,V_i] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__mono2,axiom, % 183.72/184.34 ! [V_k,V_j,V_i] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__mult__eq__cancel1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 => ( 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) % 183.72/184.34 <=> V_m_2 = V_n_2 ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__mult__less__cancel1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_diff__add__0,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_diff__is__0__eq_H,axiom, % 183.72/184.34 ! [V_n,V_m] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.72/184.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_diff__is__0__eq,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_One__nat__def,axiom, % 183.72/184.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__eq__self__implies__10,axiom, % 183.72/184.34 ! [V_n,V_m] : % 183.72/184.34 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 183.72/184.34 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 183.72/184.34 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__eq__0__iff,axiom, % 183.72/184.34 ! [V_f_2,V_F_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.72/184.34 => ( 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) % 183.72/184.34 <=> ! [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 183.72/184.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power_Opower_Opower__Suc,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__nonpos__neg,axiom, % 183.72/184.34 ! [V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__neg__nonpos,axiom, % 183.72/184.34 ! [V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__strict__increasing2,axiom, % 183.72/184.34 ! [V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__strict__increasing,axiom, % 183.72/184.34 ! [V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__nonneg__pos,axiom, % 183.72/184.34 ! [V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__pos__nonneg,axiom, % 183.72/184.34 ! [V_b,V_a,T_a] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__le__cancel__left__pos,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__le__cancel__left__neg,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__strict__mono,axiom, % 183.72/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => 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))) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__strict__mono_H,axiom, % 183.72/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => 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))) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__le__imp__less,axiom, % 183.72/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => 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))) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__le__less__imp__less,axiom, % 183.72/184.34 ! [V_d,V_c,V_b,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => 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))) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__right__less__imp__less,axiom, % 183.72/184.34 ! [V_b,V_c,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__imp__less__right,axiom, % 183.72/184.34 ! [V_b,V_c,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__left__less__imp__less,axiom, % 183.72/184.34 ! [V_b,V_a,V_c,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__less__imp__less__left,axiom, % 183.72/184.34 ! [V_b,V_a,V_c,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__right__le__imp__le,axiom, % 183.72/184.34 ! [V_b,V_c,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__left__le__imp__le,axiom, % 183.72/184.34 ! [V_b,V_a,V_c,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__strict(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_sum__squares__ge__zero,axiom, % 183.72/184.34 ! [V_y,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring(T_a) % 183.72/184.34 => 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)))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_sum__squares__le__zero__iff,axiom, % 183.72/184.34 ! [V_y_2,V_x_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_not__sum__squares__lt__zero,axiom, % 183.72/184.34 ! [V_y,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring(T_a) % 183.72/184.34 => ~ 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_sum__squares__gt__zero__iff,axiom, % 183.72/184.34 ! [V_y_2,V_x_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__ring__strict(T_a) % 183.72/184.34 => ( 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)))) % 183.72/184.34 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.34 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__left__le__one__le,axiom, % 183.72/184.34 ! [V_y,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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)) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__right__le__one__le,axiom, % 183.72/184.34 ! [V_y,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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)) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zero__less__two,axiom, % 183.72/184.34 ! [T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => 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)))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__less__imp__less__base,axiom, % 183.72/184.34 ! [V_b,V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__inject__base,axiom, % 183.72/184.34 ! [V_b,V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => V_a = V_b ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__le__imp__le__base,axiom, % 183.72/184.34 ! [V_b,V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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)))) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__eq__0__iff,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.34 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__ge__0__finite,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( 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))) % 183.72/184.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_diff__Suc__less,axiom, % 183.72/184.34 ! [V_i,V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Suc__pred,axiom, % 183.72/184.34 ! [V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => 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 ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_n__less__m__mult__n,axiom, % 183.72/184.34 ! [V_m,V_n] : % 183.72/184.34 ( 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)) % 183.72/184.34 => ( 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)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_n__less__n__mult__m,axiom, % 183.72/184.34 ! [V_m,V_n] : % 183.72/184.34 ( 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)) % 183.72/184.34 => ( 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)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_one__less__mult,axiom, % 183.72/184.34 ! [V_m,V_n] : % 183.72/184.34 ( 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)) % 183.72/184.34 => ( 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)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__diff__split,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_P_2] : % 183.72/184.34 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 183.72/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.34 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 183.72/184.34 & ! [B_d] : % 183.72/184.34 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 183.72/184.34 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__diff__split__asm,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_P_2] : % 183.72/184.34 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 183.72/184.34 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.34 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 183.72/184.34 | ? [B_d] : % 183.72/184.34 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 183.72/184.34 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_one__le__mult__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( 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)) % 183.72/184.34 & 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)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__le__cancel1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__le__cancel2,axiom, % 183.72/184.34 ! [V_n_2,V_k_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_nat__mult__le__cancel1,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,V_k_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__eq__if,axiom, % 183.72/184.34 ! [V_p,V_m] : % 183.72/184.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 183.72/184.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => 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)))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__eq__Suc0__iff,axiom, % 183.72/184.34 ! [V_f_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => ( 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)) % 183.72/184.34 <=> ? [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.34 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.34 & ! [B_xa] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 183.72/184.34 => ( B_x != B_xa % 183.72/184.34 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__eq__1__iff,axiom, % 183.72/184.34 ! [V_f_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => ( 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) % 183.72/184.34 <=> ? [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.34 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 183.72/184.34 & ! [B_xa] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 183.72/184.34 => ( B_x != B_xa % 183.72/184.34 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__delta,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.72/184.34 => 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) ) % 183.72/184.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.72/184.34 => 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) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__delta_H,axiom, % 183.72/184.34 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.72/184.34 => 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) ) % 183.72/184.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 183.72/184.34 => 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) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setprod__pos__nat__iff,axiom, % 183.72/184.34 ! [V_f_2,V_S_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> ! [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Body__triple__valid__0,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_convex__bound__le,axiom, % 183.72/184.34 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__1(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 183.72/184.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.34 => 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)) ) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__Suc__less,axiom, % 183.72/184.34 ! [V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__Suc__less__one,axiom, % 183.72/184.34 ! [V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__strict__decreasing,axiom, % 183.72/184.34 ! [V_a,V_N,V_n,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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))) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_power__decreasing,axiom, % 183.72/184.34 ! [V_a,V_N,V_n,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.34 => 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))) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_one__less__power,axiom, % 183.72/184.34 ! [V_n,V_a,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => 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))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__gt__0__iff,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_finite__UNIV__card__ge__0,axiom, % 183.72/184.34 ! [T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.72/184.34 => 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))))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum_Oeq__fold,axiom, % 183.72/184.34 ! [V_g_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum_OF__eq,axiom, % 183.72/184.34 ! [V_g_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) % 183.72/184.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Suc__diff__1,axiom, % 183.72/184.34 ! [V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => 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 ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Suc__pred_H,axiom, % 183.72/184.34 ! [V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add__eq__if,axiom, % 183.72/184.34 ! [V_n,V_m] : % 183.72/184.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 183.72/184.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => 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)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_mult__eq__if,axiom, % 183.72/184.34 ! [V_n,V_m] : % 183.72/184.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => 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)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__restrict__set,axiom, % 183.72/184.34 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__def,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) % 183.72/184.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card_Oeq__fold__g,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_convex__bound__lt,axiom, % 183.72/184.34 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 183.72/184.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.34 => 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)) ) ) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__Plus__conv__if,axiom, % 183.72/184.34 ! [V_B_2,T_b,V_A_2,T_a] : % 183.72/184.34 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 183.72/184.34 => 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)) ) % 183.72/184.34 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 183.72/184.34 => 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) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_triple_Osize_I1_J,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_even__less__0__iff,axiom, % 183.72/184.34 ! [V_a_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_triple_Osize_I2_J,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card_Ounion__inter__neutral,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.34 => ( ( ? [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))) % 183.72/184.34 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.34 => 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)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__mono2,axiom, % 183.72/184.34 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Oordered__comm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 => ( ! [B_b] : % 183.72/184.34 ( 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))) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 183.72/184.34 => 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))) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_arith__series__nat,axiom, % 183.72/184.34 ! [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)))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__Un__zero,axiom, % 183.72/184.34 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.72/184.34 => ( ! [B_x] : % 183.72/184.34 ( 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))) % 183.72/184.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.34 => 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)) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_finite__lessThan,axiom, % 183.72/184.34 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__lessThan,axiom, % 183.72/184.34 ! [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 ). % 183.72/184.34 % 183.72/184.34 fof(fact_UN__lessThan__UNIV,axiom, % 183.72/184.34 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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__eq__iff,axiom, % 183.72/184.34 ! [V_y_2,V_x_2,T_a] : % 183.72/184.34 ( class_Orderings_Olinorder(T_a) % 183.72/184.34 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 183.72/184.34 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__0,axiom, % 183.72/184.34 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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__Suc,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__lessThan__Suc,axiom, % 183.72/184.34 ! [V_n_2,V_f_2,T_a] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__iff,axiom, % 183.72/184.34 ! [V_k_2,V_i_2,T_a] : % 183.72/184.34 ( class_Orderings_Oord(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__subset__iff,axiom, % 183.72/184.34 ! [V_y_2,V_x_2,T_a] : % 183.72/184.34 ( class_Orderings_Olinorder(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_lessThan__strict__subset__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,T_a] : % 183.72/184.34 ( class_Orderings_Olinorder(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zpower__zadd__distrib,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zpower__zpower,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_single__Diff__lessThan,axiom, % 183.72/184.34 ! [V_k_2,T_a] : % 183.72/184.34 ( class_Orderings_Oorder(T_a) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_double__eq__0__iff,axiom, % 183.72/184.34 ! [V_a_2,T_a] : % 183.72/184.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__Pow,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_arith__series__general,axiom, % 183.72/184.34 ! [V_n_2,V_d_2,V_a_2,T_a] : % 183.72/184.34 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.34 => 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)))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum_Ounion__inter__neutral,axiom, % 183.72/184.34 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.34 => ( ! [B_x] : % 183.72/184.34 ( 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))) % 183.72/184.34 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.34 => 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)) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_card__Suc__eq,axiom, % 183.72/184.34 ! [V_k_2,V_A_2,T_a] : % 183.72/184.34 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 183.72/184.34 <=> ? [B_b,B_B] : % 183.72/184.34 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 183.72/184.34 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 183.72/184.34 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 183.72/184.34 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.34 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__mono3,axiom, % 183.72/184.34 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 183.72/184.34 ( ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.34 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 => ( ! [B_x] : % 183.72/184.34 ( 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))) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 183.72/184.34 => 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))) ) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__reindex__nonzero,axiom, % 183.72/184.34 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 183.72/184.34 ( class_Groups_Ocomm__monoid__add(T_c) % 183.72/184.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.34 => ( ! [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.72/184.34 => ! [B_y] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 183.72/184.34 => ( B_x != B_y % 183.72/184.34 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 183.72/184.34 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 183.72/184.34 => 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) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_PowI,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_pos__zmult__eq__1__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 183.72/184.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.34 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.34 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__zless__mono2,axiom, % 183.72/184.34 ! [V_k,V_j,V_i] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__1__right,axiom, % 183.72/184.34 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__1,axiom, % 183.72/184.34 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 183.72/184.34 % 183.72/184.34 fof(fact_zadd__zmult__distrib,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zadd__zmult__distrib2,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__commute,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__assoc,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zdiff__zmult__distrib,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zdiff__zmult__distrib2,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__eq__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,T_a] : % 183.72/184.34 ( class_Nat_Osemiring__char__0(T_a) % 183.72/184.34 => ( 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) % 183.72/184.34 <=> V_m_2 = V_n_2 ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__0,axiom, % 183.72/184.34 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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__eq__0__conv,axiom, % 183.72/184.34 ! [V_n_2] : % 183.72/184.34 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__le__0__conv,axiom, % 183.72/184.34 ! [V_n_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zless__iff__Suc__zadd,axiom, % 183.72/184.34 ! [V_z_2,V_w_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 183.72/184.34 <=> ? [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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__Suc,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zless__int,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zadd__int__left,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zadd__int,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zle__int,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__int,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__mult,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__1,axiom, % 183.72/184.34 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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_inj__int,axiom, % 183.72/184.34 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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__power,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zpower__int,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_image__Pow__surj,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 183.72/184.34 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__top,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Union__Pow__eq,axiom, % 183.72/184.34 ! [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 ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__setsum,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Cantors__paradox,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ~ ? [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__not__empty,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__INT__eq,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__setprod,axiom, % 183.72/184.34 ! [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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__Suc0__eq__1,axiom, % 183.72/184.34 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) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zmult__zless__mono2__lemma,axiom, % 183.72/184.34 ! [V_k,V_j,V_i] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zero__less__int__conv,axiom, % 183.72/184.34 ! [V_n_2] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__0__le__iff,axiom, % 183.72/184.34 ! [V_n,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zero__le__imp__of__nat,axiom, % 183.72/184.34 ! [V_m,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zdiff__int,axiom, % 183.72/184.34 ! [V_m,V_n] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__less__0__iff,axiom, % 183.72/184.34 ! [V_m,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ~ 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__0,axiom, % 183.72/184.34 ! [T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__less__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_less__imp__of__nat__less,axiom, % 183.72/184.34 ! [V_n,V_m,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__less__imp__less,axiom, % 183.72/184.34 ! [V_n,V_m,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__le__iff,axiom, % 183.72/184.34 ! [V_n_2,V_m_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__add,axiom, % 183.72/184.34 ! [V_n,V_m,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__mult,axiom, % 183.72/184.34 ! [V_n,V_m,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__1,axiom, % 183.72/184.34 ! [T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__power,axiom, % 183.72/184.34 ! [V_n,V_m,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__bottom,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__iff,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_PowD,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__setsum,axiom, % 183.72/184.34 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_inj__of__nat,axiom, % 183.72/184.34 ! [T_a] : % 183.72/184.34 ( class_Nat_Osemiring__char__0(T_a) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__mono,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_finite__Pow__iff,axiom, % 183.72/184.34 ! [V_A_2,T_a] : % 183.72/184.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 183.72/184.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_subset__Pow__Union,axiom, % 183.72/184.34 ! [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)))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__setprod,axiom, % 183.72/184.34 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.34 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 183.72/184.34 & class_Rings_Osemiring__1(T_a) ) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__Suc,axiom, % 183.72/184.34 ! [V_m,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__insert,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__UNIV,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__diff,axiom, % 183.72/184.34 ! [V_m,V_n,T_a] : % 183.72/184.34 ( class_Rings_Oring__1(T_a) % 183.72/184.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.34 => 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)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_UN__Pow__subset,axiom, % 183.72/184.34 ! [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)))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__Int__eq,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__constant,axiom, % 183.72/184.34 ! [V_A_2,V_y_2,T_b,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_image__Pow__mono,axiom, % 183.72/184.34 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 183.72/184.34 ( 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)) % 183.72/184.34 => 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_of__nat__0__less__iff,axiom, % 183.72/184.34 ! [V_n_2,T_a] : % 183.72/184.34 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.34 => ( 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))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Pow__empty,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Un__Pow__subset,axiom, % 183.72/184.34 ! [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)))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 183.72/184.34 ! [V_n_2,T_a] : % 183.72/184.34 ( class_Rings_Osemiring__1(T_a) % 183.72/184.34 => 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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zdiff__int__split,axiom, % 183.72/184.34 ! [V_y_2,V_x_2,V_P_2] : % 183.72/184.34 ( 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)))) % 183.72/184.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 183.72/184.34 => 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)))) ) % 183.72/184.34 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 183.72/184.34 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Powp__Pow__eq,axiom, % 183.72/184.34 ! [V_x_2,V_A_2,T_a] : % 183.72/184.34 ( 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)) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 183.72/184.34 ! [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)) ). % 183.72/184.34 % 183.72/184.34 fof(fact_setsum__bounded,axiom, % 183.72/184.34 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.34 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 183.72/184.34 & class_Rings_Osemiring__1(T_b) ) % 183.72/184.34 => ( ! [B_i] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 183.72/184.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 183.72/184.34 => 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))) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 183.72/184.34 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 183.72/184.34 ( 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))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 183.72/184.34 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__less__0__conv,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zero__zle__int,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 183.72/184.34 ! [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))) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 183.72/184.34 ! [V_P_2] : % 183.72/184.34 ( ? [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.34 & hBOOL(hAPP(V_P_2,B_x)) ) % 183.72/184.34 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 183.72/184.34 ! [V_P_2] : % 183.72/184.34 ( ! [B_x] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.34 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.72/184.34 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_int__int__eq,axiom, % 183.72/184.34 ! [V_n_2,V_m_2] : % 183.72/184.34 ( 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) % 183.72/184.34 <=> V_m_2 = V_n_2 ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zle__iff__zadd,axiom, % 183.72/184.34 ! [V_z_2,V_w_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 183.72/184.34 <=> ? [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)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 183.72/184.34 ! [V_B_2,V_A_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 <=> 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 183.72/184.34 ! [V_B_2,V_A_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.34 <=> 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 183.72/184.34 ! [V_B_2,V_A_2] : % 183.72/184.34 ( V_A_2 = V_B_2 % 183.72/184.34 <=> 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) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 183.72/184.34 ! [V_A_2,V_x_2] : % 183.72/184.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 183.72/184.34 <=> 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))) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 183.72/184.34 ! [V_y_2,V_x_2] : % 183.72/184.34 ( 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) % 183.72/184.34 <=> V_x_2 = V_y_2 ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zle__diff1__eq,axiom, % 183.72/184.34 ! [V_z_2,V_w_2] : % 183.72/184.34 ( 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)))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zle__add1__eq__le,axiom, % 183.72/184.34 ! [V_z_2,V_w_2] : % 183.72/184.34 ( 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)))) % 183.72/184.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_zless__add1__eq,axiom, % 183.72/184.34 ! [V_z_2,V_w_2] : % 183.72/184.34 ( 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)))) % 183.72/184.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 183.72/184.34 | V_w_2 = V_z_2 ) ) ). % 183.72/184.34 % 183.72/184.34 fof(fact_add1__zle__eq,axiom, % 183.72/184.35 ! [V_z_2,V_w_2] : % 183.72/184.35 ( 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)) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zless__imp__add1__zle,axiom, % 183.72/184.35 ! [V_z,V_w] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zle__refl,axiom, % 183.72/184.35 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zle__linear,axiom, % 183.72/184.35 ! [V_w,V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 183.72/184.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zless__le,axiom, % 183.72/184.35 ! [V_w_2,V_z_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 183.72/184.35 & V_z_2 != V_w_2 ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zless__linear,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 183.72/184.35 | V_x = V_y % 183.72/184.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zle__trans,axiom, % 183.72/184.35 ! [V_k,V_j,V_i] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zle__antisym,axiom, % 183.72/184.35 ! [V_w,V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 183.72/184.35 => V_z = V_w ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__strict__right__mono,axiom, % 183.72/184.35 ! [V_k,V_j,V_i] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__left__mono,axiom, % 183.72/184.35 ! [V_k,V_j,V_i] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__zless__mono,axiom, % 183.72/184.35 ! [V_z,V_z_H,V_w,V_w_H] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__assoc,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__left__commute,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__commute,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__0__neq__1,axiom, % 183.72/184.35 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 183.72/184.35 % 183.72/184.35 fof(fact_odd__nonzero,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__0,axiom, % 183.72/184.35 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 183.72/184.35 % 183.72/184.35 fof(fact_zadd__0__right,axiom, % 183.72/184.35 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_less__bin__lemma,axiom, % 183.72/184.35 ! [V_l_2,V_k_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 183.72/184.35 <=> 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_le__imp__0__less,axiom, % 183.72/184.35 ! [V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_odd__less__0,axiom, % 183.72/184.35 ! [V_z_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__one__le__iff__zero__less,axiom, % 183.72/184.35 ! [V_z_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__0__less__1,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 183.72/184.35 ! [V_i_2,V_inc_2,T_a] : % 183.72/184.35 ( class_Rings_Osemiring__1(T_a) % 183.72/184.35 => 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 ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 183.72/184.35 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 183.72/184.35 ( class_Rings_Osemiring__1(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 183.72/184.35 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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 183.72/184.35 ! [V_y_2,V_x_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 183.72/184.35 ! [V_y_2,V_x_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 183.72/184.35 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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 183.72/184.35 ! [V_n,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 183.72/184.35 ! [V_A_2] : % 183.72/184.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 183.72/184.35 <=> 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Powp__mono,axiom, % 183.72/184.35 ! [V_B_2,V_A_2,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_self__quotient__aux1,axiom, % 183.72/184.35 ! [V_q,V_r,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.35 => ( 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)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_self__quotient__aux2,axiom, % 183.72/184.35 ! [V_q,V_r,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.35 => ( 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)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_q__pos__lemma,axiom, % 183.72/184.35 ! [V_r_H,V_q_H,V_b_H] : % 183.72/184.35 ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_q__neg__lemma,axiom, % 183.72/184.35 ! [V_r_H,V_q_H,V_b_H] : % 183.72/184.35 ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_unique__quotient__lemma,axiom, % 183.72/184.35 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 183.72/184.35 ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono2__lemma,axiom, % 183.72/184.35 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 183.72/184.35 ( 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) % 183.72/184.35 => ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_infinite__UNIV__int,axiom, % 183.72/184.35 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono2__neg__lemma,axiom, % 183.72/184.35 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 183.72/184.35 ( 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) % 183.72/184.35 => ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_unique__quotient__lemma__neg,axiom, % 183.72/184.35 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 183.72/184.35 ( 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))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ord_OatLeastLessThan__iff,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ord_OatLeastAtMost__iff,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_tsub__def,axiom, % 183.72/184.35 ! [V_x,V_y] : % 183.72/184.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 183.72/184.35 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 183.72/184.35 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_termination__basic__simps_I4_J,axiom, % 183.72/184.35 ! [V_y,V_z,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_termination__basic__simps_I3_J,axiom, % 183.72/184.35 ! [V_z,V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_comp__cong,axiom, % 183.72/184.35 ! [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] : % 183.72/184.35 ( 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)) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_tsub__eq,axiom, % 183.72/184.35 ! [V_x,V_y] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 183.72/184.35 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_termination__basic__simps_I1_J,axiom, % 183.72/184.35 ! [V_z,V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_termination__basic__simps_I2_J,axiom, % 183.72/184.35 ! [V_y,V_z,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_termination__basic__simps_I5_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 183.72/184.35 ! [V_x_2,V_y_2,V_ca_2] : % 183.72/184.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 183.72/184.35 => 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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 183.72/184.35 => 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_ca_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))) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 183.72/184.35 => 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_ca_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)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__odd__less__0,axiom, % 183.72/184.35 ! [V_a_2,T_a] : % 183.72/184.35 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__power__div__base,axiom, % 183.72/184.35 ! [V_k,V_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 183.72/184.35 => 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)))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__INT,axiom, % 183.72/184.35 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 183.72/184.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 183.72/184.35 => ( ! [B_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 183.72/184.35 => 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)) ) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I4_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I5_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__atLeastLessThan,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__zero,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__0,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__by__0,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__by__1,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 183.72/184.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 183.72/184.35 => V_b_2 = V_d_2 ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 183.72/184.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 183.72/184.35 => V_a_2 = V_ca_2 ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__eq__iff,axiom, % 183.72/184.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 183.72/184.35 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 183.72/184.35 <=> ( V_a_2 = V_ca_2 % 183.72/184.35 & V_b_2 = V_d_2 ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 183.72/184.35 ! [V_a_2,V_b_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 183.72/184.35 ! [V_a_2,V_b_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__neg__pos__less0,axiom, % 183.72/184.35 ! [V_b,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__add__Un,axiom, % 183.72/184.35 ! [V_k_2,V_j_2,V_i_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__self,axiom, % 183.72/184.35 ! [V_a] : % 183.72/184.35 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan0,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeast0LessThan,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__mult1,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__mult2,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self1__is__id,axiom, % 183.72/184.35 ! [V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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 ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self2__is__id,axiom, % 183.72/184.35 ! [V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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 ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__mult1__if,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) % 183.72/184.35 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__self,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__atLeastLessThan,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__Suc__atLeastLessThan,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__empty,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__empty__iff2,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( 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) % 183.72/184.35 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__empty__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( 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)) % 183.72/184.35 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__subset__iff,axiom, % 183.72/184.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( 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_ca_2),V_d_2))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 183.72/184.35 ! [V_n_2,V_m_2,V_f_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I17_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.35 => 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 183.72/184.35 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__diff,axiom, % 183.72/184.35 ! [V_m_2,V_n_2,V_i_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I11_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__add__atLeastLessThan,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__0,axiom, % 183.72/184.35 ! [T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__eq__0__iff,axiom, % 183.72/184.35 ! [V_k_2,V_i_2] : % 183.72/184.35 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.35 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 183.72/184.35 ! [V_a_2,V_b_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 183.72/184.35 ! [V_i_2,V_k_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono2,axiom, % 183.72/184.35 ! [V_b,V_b_H,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__nonneg__neg__le0,axiom, % 183.72/184.35 ! [V_b,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__pos__pos__trivial,axiom, % 183.72/184.35 ! [V_b,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 183.72/184.35 ! [V_a_2,V_b_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__nonpos__pos__le0,axiom, % 183.72/184.35 ! [V_b,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono2__neg,axiom, % 183.72/184.35 ! [V_b,V_b_H,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__neg__neg__trivial,axiom, % 183.72/184.35 ! [V_b,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono1,axiom, % 183.72/184.35 ! [V_b,V_a_H,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__mono1__neg,axiom, % 183.72/184.35 ! [V_b,V_a_H,V_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__add,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__mult,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__diff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__div__less__self,axiom, % 183.72/184.35 ! [V_k,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__zmult2__eq,axiom, % 183.72/184.35 ! [V_b,V_a,V_c] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__1,axiom, % 183.72/184.35 ! [T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__of__nat,axiom, % 183.72/184.35 ! [V_n_2,T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__power,axiom, % 183.72/184.35 ! [V_n_2,V_a_2,T_a] : % 183.72/184.35 ( class_Rings_Oring__1(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__add__nat__ivl,axiom, % 183.72/184.35 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__diff__nat__ivl,axiom, % 183.72/184.35 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 183.72/184.35 ( class_Groups_Oab__group__add(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self1,axiom, % 183.72/184.35 ! [V_c,V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self2,axiom, % 183.72/184.35 ! [V_c,V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__add__self2,axiom, % 183.72/184.35 ! [V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__add__self1,axiom, % 183.72/184.35 ! [V_a,V_b,T_a] : % 183.72/184.35 ( class_Divides_Osemiring__div(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThan__singleton,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I7_J,axiom, % 183.72/184.35 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.35 % 183.72/184.35 fof(fact_UN__UN__finite__eq,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I1_J,axiom, % 183.72/184.35 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I8_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_subset__card__intvl__is__intvl,axiom, % 183.72/184.35 ! [V_k_2,V_A_2] : % 183.72/184.35 ( 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))))) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I2_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 183.72/184.35 ! [V_k_2,V_f_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__head__upt__Suc,axiom, % 183.72/184.35 ! [V_f_2,V_n_2,V_m_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__double__eq__0__iff,axiom, % 183.72/184.35 ! [V_a_2,T_a] : % 183.72/184.35 ( class_Int_Oring__char__0(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastLessThanSuc,axiom, % 183.72/184.35 ! [V_n_2,V_m_2] : % 183.72/184.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.35 => 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)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__op__ivl__Suc,axiom, % 183.72/184.35 ! [V_f_2,V_m_2,V_n_2,T_a] : % 183.72/184.35 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 183.72/184.35 => 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) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_split__zdiv,axiom, % 183.72/184.35 ! [V_k_2,V_n_2,V_P_2] : % 183.72/184.35 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 183.72/184.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.35 => ! [B_i] : % 183.72/184.35 ( ? [B_j] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 183.72/184.35 & 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) ) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 183.72/184.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => ! [B_i] : % 183.72/184.35 ( ? [B_j] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 & 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) ) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divmod__int__rel__div__eq,axiom, % 183.72/184.35 ! [V_r_1,V_y,V_b_1,V_a_1] : % 183.72/184.35 ( 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) % 183.72/184.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 183.72/184.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Ints__odd__nonzero,axiom, % 183.72/184.35 ! [V_a_2,T_a] : % 183.72/184.35 ( class_Int_Oring__char__0(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I6_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ex__nat__less__eq,axiom, % 183.72/184.35 ! [V_P_2,V_n_2] : % 183.72/184.35 ( ? [B_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 183.72/184.35 & hBOOL(hAPP(V_P_2,B_m)) ) % 183.72/184.35 <=> ? [B_x] : % 183.72/184.35 ( 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))) % 183.72/184.35 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_all__nat__less__eq,axiom, % 183.72/184.35 ! [V_P_2,V_n_2] : % 183.72/184.35 ( ! [B_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_m)) ) % 183.72/184.35 <=> ! [B_x] : % 183.72/184.35 ( 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))) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_UN__finite2__subset,axiom, % 183.72/184.35 ! [V_B_2,V_k_2,V_A_2,T_a] : % 183.72/184.35 ( ! [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))) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_UN__finite2__eq,axiom, % 183.72/184.35 ! [V_B_2,V_k_2,V_A_2,T_a] : % 183.72/184.35 ( ! [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) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_UN__finite__subset,axiom, % 183.72/184.35 ! [V_C_2,V_A_2,T_a] : % 183.72/184.35 ( ! [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)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I3_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__greaterThanLessThan,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__atLeastLessThan__int,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__greaterThanLessThan__int,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__le__dividend,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__le__mono,axiom, % 183.72/184.35 ! [V_k,V_n,V_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult2__eq,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__1,axiom, % 183.72/184.35 ! [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 ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__less,axiom, % 183.72/184.35 ! [V_n,V_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__mult__div__cancel__disj,axiom, % 183.72/184.35 ! [V_n,V_m,V_k] : % 183.72/184.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 => 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) ) % 183.72/184.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zdiv__int,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThanLessThan__empty,axiom, % 183.72/184.35 ! [V_k_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__le__mono2,axiom, % 183.72/184.35 ! [V_k,V_n,V_m] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__mult__div__cancel1,axiom, % 183.72/184.35 ! [V_n,V_m,V_k] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self__is__m,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.35 => 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 ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__mult__self1__is__m,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.35 => 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 ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__less__dividend,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__geq,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_div__if,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_split__div,axiom, % 183.72/184.35 ! [V_k_2,V_n_2,V_P_2] : % 183.72/184.35 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 183.72/184.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 183.72/184.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 => ! [B_i,B_j] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 183.72/184.35 => ( 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) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__add__int__atLeastLessThan,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I9_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__greaterThanLessThan,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_le__div__geq,axiom, % 183.72/184.35 ! [V_m,V_n] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_split__div_H,axiom, % 183.72/184.35 ! [V_n_2,V_m_2,V_P_2] : % 183.72/184.35 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 183.72/184.35 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 183.72/184.35 | ? [B_q] : % 183.72/184.35 ( 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)) % 183.72/184.35 & 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)))) % 183.72/184.35 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_split__div__lemma,axiom, % 183.72/184.35 ! [V_m_2,V_q_2,V_n_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 183.72/184.35 => ( ( 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)) % 183.72/184.35 & 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)))) ) % 183.72/184.35 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I15_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.35 => 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I4_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I12_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I13_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setprod__diff1,axiom, % 183.72/184.35 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.35 ( class_Fields_Ofield(T_b) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.35 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.35 => 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)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.35 => 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) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I14_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__greaterThanAtMost,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_finite__greaterThanAtMost__int,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__zero,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__zero__left,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_add__divide__distrib,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_times__divide__eq__right,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_diff__divide__distrib,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__1,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_power__divide,axiom, % 183.72/184.35 ! [V_n,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__divide__distrib,axiom, % 183.72/184.35 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nonzero__eq__divide__eq,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 183.72/184.35 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nonzero__divide__eq__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 183.72/184.35 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__eq__imp,axiom, % 183.72/184.35 ! [V_a,V_b,V_c,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 183.72/184.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_eq__divide__imp,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 183.72/184.35 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__self__if,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 183.72/184.35 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 183.72/184.35 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__self,axiom, % 183.72/184.35 ! [V_a,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_right__inverse__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,T_a] : % 183.72/184.35 ( class_Rings_Odivision__ring(T_a) % 183.72/184.35 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.35 <=> V_a_2 = V_b_2 ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nonzero__power__divide,axiom, % 183.72/184.35 ! [V_n,V_a,V_b,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_power__one__over,axiom, % 183.72/184.35 ! [V_n,V_a,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setprod__dividef,axiom, % 183.72/184.35 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_b) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThanAtMost__empty,axiom, % 183.72/184.35 ! [V_k_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 183.72/184.35 ! [V_l_2,V_k_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( 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) % 183.72/184.35 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThanAtMost__empty__iff,axiom, % 183.72/184.35 ! [V_l_2,V_k_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => ( 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)) % 183.72/184.35 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I20_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.35 => 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I14_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__greaterThanAtMost,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I15_J,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_com_Osize_I9_J,axiom, % 183.72/184.35 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.35 % 183.72/184.35 fof(fact_power__diff,axiom, % 183.72/184.35 ! [V_m,V_n,V_a,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I10_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I16_J,axiom, % 183.72/184.35 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 183.72/184.35 => 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_geometric__sum,axiom, % 183.72/184.35 ! [V_n_2,V_x_2,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__left__mono__neg,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__left__mono,axiom, % 183.72/184.35 ! [V_c,V_a,V_b,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__divide__le__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__le__divide__eq,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> 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_ca_2))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__imp__le__div__pos,axiom, % 183.72/184.35 ! [V_x,V_z,V_y,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => ( 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)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_times__divide__times__eq,axiom, % 183.72/184.35 ! [V_w,V_z,V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__right__mono__neg,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__right__mono,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__le__0__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zero__le__divide__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__strict__right__mono__neg,axiom, % 183.72/184.35 ! [V_c,V_a,V_b,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__strict__right__mono,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__neg__neg,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__neg__pos,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__pos__neg,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__pos__pos,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__less__0__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zero__less__divide__iff,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 183.72/184.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_eq__divide__eq,axiom, % 183.72/184.35 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 183.72/184.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 183.72/184.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__eq__eq,axiom, % 183.72/184.35 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 183.72/184.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 183.72/184.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__divide__mult__cancel__right,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__divide__mult__cancel__left,axiom, % 183.72/184.35 ! [V_b,V_a,V_c,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_frac__eq__eq,axiom, % 183.72/184.35 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( 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) % 183.72/184.35 <=> 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) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__nonpos__neg,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__nonpos__pos,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_frac__le,axiom, % 183.72/184.35 ! [V_z,V_w,V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 183.72/184.35 => 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))) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_frac__less,axiom, % 183.72/184.35 ! [V_z,V_w,V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 183.72/184.35 => 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))) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_frac__less2,axiom, % 183.72/184.35 ! [V_z,V_w,V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 183.72/184.35 => 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))) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__nonneg__neg,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__nonneg__pos,axiom, % 183.72/184.35 ! [V_y,V_x,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__strict__left__mono__neg,axiom, % 183.72/184.35 ! [V_c,V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__strict__left__mono,axiom, % 183.72/184.35 ! [V_c,V_a,V_b,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__divide__less__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_neg__less__divide__eq,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> 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_ca_2))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__imp__less__div__pos,axiom, % 183.72/184.35 ! [V_x,V_z,V_y,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => ( 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)) % 183.72/184.35 => 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))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__imp__div__pos__less,axiom, % 183.72/184.35 ! [V_z,V_x,V_y,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__divide__less__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> 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_ca_2))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__less__divide__eq,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__less__eq,axiom, % 183.72/184.35 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => 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_ca_2))) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_less__divide__eq,axiom, % 183.72/184.35 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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_ca_2))) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_add__num__frac,axiom, % 183.72/184.35 ! [V_x,V_z,V_y,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_add__divide__eq__iff,axiom, % 183.72/184.35 ! [V_y,V_x,V_z,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_add__frac__num,axiom, % 183.72/184.35 ! [V_z,V_x,V_y,T_a] : % 183.72/184.35 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__add__eq__iff,axiom, % 183.72/184.35 ! [V_y,V_x,V_z,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_add__frac__eq,axiom, % 183.72/184.35 ! [V_w,V_x,V_z,V_y,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_diff__divide__eq__iff,axiom, % 183.72/184.35 ! [V_y,V_x,V_z,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__diff__eq__iff,axiom, % 183.72/184.35 ! [V_y,V_x,V_z,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_diff__frac__eq,axiom, % 183.72/184.35 ! [V_w,V_x,V_z,V_y,T_a] : % 183.72/184.35 ( class_Fields_Ofield(T_a) % 183.72/184.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_less__half__sum,axiom, % 183.72/184.35 ! [V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.35 => 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))))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_gt__half__sum,axiom, % 183.72/184.35 ! [V_b,V_a,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_le__divide__eq,axiom, % 183.72/184.35 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => 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_ca_2))) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_divide__le__eq,axiom, % 183.72/184.35 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => 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_ca_2))) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__le__divide__eq,axiom, % 183.72/184.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( 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_ca_2))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_pos__divide__le__eq,axiom, % 183.72/184.35 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 183.72/184.35 <=> 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_ca_2))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_mult__imp__div__pos__le,axiom, % 183.72/184.35 ! [V_z,V_x,V_y,T_a] : % 183.72/184.35 ( class_Fields_Olinordered__field(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.35 => ( 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))) % 183.72/184.35 => 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)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setprod__Un,axiom, % 183.72/184.35 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 183.72/184.35 ( class_Fields_Ofield(T_b) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.35 => ( ! [B_x] : % 183.72/184.35 ( 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))) % 183.72/184.35 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.35 => 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))) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__atLeastZeroLessThan__int,axiom, % 183.72/184.35 ! [V_u_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__nonneg__leq__bound,axiom, % 183.72/184.35 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 183.72/184.35 ( class_Groups_Oordered__ab__group__add(T_b) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 183.72/184.35 => ( ! [B_i] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 183.72/184.35 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_setsum__nonneg__0,axiom, % 183.72/184.35 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 183.72/184.35 ( class_Groups_Oordered__ab__group__add(T_b) % 183.72/184.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 183.72/184.35 => ( ! [B_i] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 183.72/184.35 => ( 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) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 183.72/184.35 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThan__0,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThan__eq__iff,axiom, % 183.72/184.35 ! [V_y_2,V_x_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 183.72/184.35 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__int,axiom, % 183.72/184.35 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__0,axiom, % 183.72/184.35 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 183.72/184.35 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ex__nat,axiom, % 183.72/184.35 ! [V_P_2] : % 183.72/184.35 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.35 <=> ? [B_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.35 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_all__nat,axiom, % 183.72/184.35 ! [V_P_2] : % 183.72/184.35 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.35 <=> ! [B_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.35 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 183.72/184.35 ! [V_y_2,V_x_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 183.72/184.35 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 183.72/184.35 <=> V_x_2 = V_y_2 ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_eq__nat__nat__iff,axiom, % 183.72/184.35 ! [V_z_H_2,V_z_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 183.72/184.35 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 183.72/184.35 <=> V_z_2 = V_z_H_2 ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 183.72/184.35 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__set__return__embed,axiom, % 183.72/184.35 ! [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 ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 183.72/184.35 ! [V_A_2,V_f_2,T_a] : % 183.72/184.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__le__0,axiom, % 183.72/184.35 ! [V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__0__iff,axiom, % 183.72/184.35 ! [V_i_2] : % 183.72/184.35 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__mono__iff,axiom, % 183.72/184.35 ! [V_w_2,V_z_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zless__nat__conj,axiom, % 183.72/184.35 ! [V_z_2,V_w_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 183.72/184.35 ! [V_y_2,V_x_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__1,axiom, % 183.72/184.35 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__0__le,axiom, % 183.72/184.35 ! [V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__eq__iff,axiom, % 183.72/184.35 ! [V_z_2,V_m_2] : % 183.72/184.35 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 183.72/184.35 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 183.72/184.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_int__nat__eq,axiom, % 183.72/184.35 ! [V_z] : % 183.72/184.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zless__nat__eq__int__zless,axiom, % 183.72/184.35 ! [V_z_2,V_m_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 183.72/184.35 <=> 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThan__iff,axiom, % 183.72/184.35 ! [V_k_2,V_i_2,T_a] : % 183.72/184.35 ( class_Orderings_Oord(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThan__subset__iff,axiom, % 183.72/184.35 ! [V_y_2,V_x_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 183.72/184.35 ! [V_A_2,V_f_2,T_a] : % 183.72/184.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__atLeastZeroLessThan__int,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__atLeastLessThan__int,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_zero__less__nat__eq,axiom, % 183.72/184.35 ! [V_z_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__less__eq__zless,axiom, % 183.72/184.35 ! [V_z_2,V_w_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 183.72/184.35 ! [V_y_2,V_x_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__eq__iff2,axiom, % 183.72/184.35 ! [V_w_2,V_m_2] : % 183.72/184.35 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__eq__iff,axiom, % 183.72/184.35 ! [V_m_2,V_w_2] : % 183.72/184.35 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 183.72/184.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 183.72/184.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__le__eq__zle,axiom, % 183.72/184.35 ! [V_z_2,V_w_2] : % 183.72/184.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 183.72/184.35 => ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_split__nat,axiom, % 183.72/184.35 ! [V_i_2,V_P_2] : % 183.72/184.35 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 183.72/184.35 <=> ( ! [B_n] : % 183.72/184.35 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 183.72/184.35 => hBOOL(hAPP(V_P_2,B_n)) ) % 183.72/184.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.35 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__add__distrib,axiom, % 183.72/184.35 ! [V_z_H,V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__mult__distrib,axiom, % 183.72/184.35 ! [V_z_H,V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 183.72/184.35 ! [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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__diff__distrib,axiom, % 183.72/184.35 ! [V_z,V_z_H] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_INT__greaterThan__UNIV,axiom, % 183.72/184.35 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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__div__distrib,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__greaterThanAtMost__int,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 183.72/184.35 ! [V_n,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__power__eq,axiom, % 183.72/184.35 ! [V_n,V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => 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) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 183.72/184.35 ! [V_y,V_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_one__less__nat__eq,axiom, % 183.72/184.35 ! [V_z_2] : % 183.72/184.35 ( 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))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__less__iff,axiom, % 183.72/184.35 ! [V_m_2,V_w_2] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 183.72/184.35 <=> 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 183.72/184.35 ! [V_z] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__un_I11_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Olinorder(T_a) % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.35 => 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) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_ivl__disj__int_I5_J,axiom, % 183.72/184.35 ! [V_u_2,V_l_2,T_a] : % 183.72/184.35 ( class_Orderings_Oorder(T_a) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_greaterThan__Suc,axiom, % 183.72/184.35 ! [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)))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_card__greaterThanLessThan__int,axiom, % 183.72/184.35 ! [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)))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__aux__def,axiom, % 183.72/184.35 ! [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) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__morphism__nat__int,axiom, % 183.72/184.35 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))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 183.72/184.35 ! [V_B_2,V_A_2] : % 183.72/184.35 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.35 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.35 => 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))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_inj__vimage__singleton,axiom, % 183.72/184.35 ! [V_a_2,V_f_2,T_b,T_a] : % 183.72/184.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.35 => 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))))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_sum__diff__distrib,axiom, % 183.72/184.35 ! [V_n_2,V_P_2,V_Q_2] : % 183.72/184.35 ( ! [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))) % 183.72/184.35 => 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)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimageI,axiom, % 183.72/184.35 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 183.72/184.35 ( hAPP(V_f_2,V_a_2) = V_b_2 % 183.72/184.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__empty,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__code,axiom, % 183.72/184.35 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 183.72/184.35 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__ident,axiom, % 183.72/184.35 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 183.72/184.35 ! [V_B_2,V_A_2] : % 183.72/184.35 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.35 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 183.72/184.35 ! [V_B_2,V_A_2] : % 183.72/184.35 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.35 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.35 => 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)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__eq,axiom, % 183.72/184.35 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 183.72/184.35 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimageD,axiom, % 183.72/184.35 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimageI2,axiom, % 183.72/184.35 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__mono,axiom, % 183.72/184.35 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.35 => 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))) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__UNIV,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__Un,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__Int,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__compose,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__Diff,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__UN,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 183.72/184.35 ! [V_B_2,V_A_2] : % 183.72/184.35 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.35 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.35 => ( V_A_2 = V_B_2 % 183.72/184.35 <=> 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) ) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__INT,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_image__vimage__subset,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_surj__image__vimage__eq,axiom, % 183.72/184.35 ! [V_A_2,V_f_2,T_a,T_b] : % 183.72/184.35 ( 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)) % 183.72/184.35 => 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 ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 183.72/184.35 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 183.72/184.35 % 183.72/184.35 fof(fact_nat__set__def,axiom, % 183.72/184.35 ! [V_S_2] : % 183.72/184.35 ( c_Nat__Transfer_Onat__set(V_S_2) % 183.72/184.35 <=> ! [B_x] : % 183.72/184.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 183.72/184.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__Union,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__singleton__eq,axiom, % 183.72/184.35 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 183.72/184.35 ( 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)))))) % 183.72/184.35 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 183.72/184.35 % 183.72/184.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 183.72/184.35 ! [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)) ). % 183.72/184.35 % 183.72/184.35 fof(fact_vimage__insert,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__vimageD,axiom, % 183.72/184.36 ! [V_F_2,V_h_2,T_b,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 183.72/184.36 => ( 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)) % 183.72/184.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__subsetD,axiom, % 183.72/184.36 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 183.72/184.36 ( 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)) % 183.72/184.36 => ( 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)) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_image__vimage__eq,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__vimageI,axiom, % 183.72/184.36 ! [V_h_2,T_b,V_F_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.72/184.36 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 183.72/184.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_inj__vimage__image__eq,axiom, % 183.72/184.36 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 183.72/184.36 ! [V_f_2,V_A_2,T_a] : % 183.72/184.36 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__const,axiom, % 183.72/184.36 ! [T_b,V_A_2,V_ca_2,T_a] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.72/184.36 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.72/184.36 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__eq__UN,axiom, % 183.72/184.36 ! [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))))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__subsetI,axiom, % 183.72/184.36 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.36 => ( 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))) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__nat__int__set__return__embed,axiom, % 183.72/184.36 ! [V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 183.72/184.36 ! [V_B_2,V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 183.72/184.36 ! [V_x_2,V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 183.72/184.36 ! [V_f_2,V_A_2,T_a] : % 183.72/184.36 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 183.72/184.36 ! [V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 183.72/184.36 <=> 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 183.72/184.36 ! [V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 183.72/184.36 ! [V_B_2,V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.36 <=> 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 183.72/184.36 ! [V_B_2,V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.36 <=> 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 183.72/184.36 ! [V_A_2,V_x_2] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x_2) % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 183.72/184.36 <=> 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__Suc,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__natinterval__difff,axiom, % 183.72/184.36 ! [V_f_2,V_n_2,V_m_2,T_a] : % 183.72/184.36 ( class_Groups_Oab__group__add(T_a) % 183.72/184.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.36 => 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)))) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_gauss__sum,axiom, % 183.72/184.36 ! [V_n_2,T_a] : % 183.72/184.36 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I12_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__atLeastAtMost,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__eq__iff,axiom, % 183.72/184.36 ! [V_y_2,V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 183.72/184.36 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 183.72/184.36 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_y) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 183.72/184.36 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 183.72/184.36 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_y) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_y) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 183.72/184.36 ! [V_n,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I13_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ex__nat__less,axiom, % 183.72/184.36 ! [V_P_2,V_n_2] : % 183.72/184.36 ( ? [B_m] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 183.72/184.36 & hBOOL(hAPP(V_P_2,B_m)) ) % 183.72/184.36 <=> ? [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_all__nat__less,axiom, % 183.72/184.36 ! [V_P_2,V_n_2] : % 183.72/184.36 ( ! [B_m] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 183.72/184.36 => hBOOL(hAPP(V_P_2,B_m)) ) % 183.72/184.36 <=> ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_y) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastatMost__empty__iff2,axiom, % 183.72/184.36 ! [V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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) % 183.72/184.36 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastatMost__empty__iff,axiom, % 183.72/184.36 ! [V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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)) % 183.72/184.36 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastatMost__empty,axiom, % 183.72/184.36 ! [V_a_2,V_b_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastatMost__subset__iff,axiom, % 183.72/184.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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_ca_2,V_d_2))) % 183.72/184.36 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 183.72/184.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastAtMost__singleton,axiom, % 183.72/184.36 ! [V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastAtMost__singleton__iff,axiom, % 183.72/184.36 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.36 <=> ( V_a_2 = V_b_2 % 183.72/184.36 & V_b_2 = V_ca_2 ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastAtMost__singleton_H,axiom, % 183.72/184.36 ! [V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( V_a_2 = V_b_2 % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_image__Suc__atLeastAtMost,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 183.72/184.36 ! [V_n_2,V_m_2,V_f_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 183.72/184.36 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_is__nat__def,axiom, % 183.72/184.36 ! [V_x_2] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x_2) % 183.72/184.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_image__add__atLeastAtMost,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__iff,axiom, % 183.72/184.36 ! [V_k_2,V_i_2,T_a] : % 183.72/184.36 ( class_Orderings_Oord(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 183.72/184.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__subset__iff,axiom, % 183.72/184.36 ! [V_y_2,V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__0,axiom, % 183.72/184.36 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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__atLeastAtMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastAtMostSuc__conv,axiom, % 183.72/184.36 ! [V_n_2,V_m_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 183.72/184.36 ! [V_x_2,V_A_2] : % 183.72/184.36 ( c_Nat__Transfer_Onat__set(V_A_2) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 183.72/184.36 ! [V_k_2,V_f_2] : % 183.72/184.36 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast__Suc__greaterThan,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I21_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I15_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastatMost__psubset__iff,axiom, % 183.72/184.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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_ca_2,V_d_2))) % 183.72/184.36 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 183.72/184.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 183.72/184.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 183.72/184.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I22_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I4_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I16_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I13_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I12_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I7_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__head__Suc,axiom, % 183.72/184.36 ! [V_f_2,V_n_2,V_m_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I14_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I8_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_UN__atLeast__UNIV,axiom, % 183.72/184.36 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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I6_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__cl__ivl__Suc,axiom, % 183.72/184.36 ! [V_f_2,V_m_2,V_n_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 183.72/184.36 => 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) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__head,axiom, % 183.72/184.36 ! [V_P_2,V_n_2,V_m_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__ub__add__nat,axiom, % 183.72/184.36 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => ( 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)))) % 183.72/184.36 => 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)))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I6_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I5_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I18_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I1_J,axiom, % 183.72/184.36 ! [V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I19_J,axiom, % 183.72/184.36 ! [V_u_2,V_m_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 183.72/184.36 ! [V_f_2,V_A_2,T_a] : % 183.72/184.36 ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 183.72/184.36 ! [V_f_2,V_A_2,T_a] : % 183.72/184.36 ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_UN__le__eq__Un0,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_decr__mult__lemma,axiom, % 183.72/184.36 ! [V_k_2,V_P_2,V_d_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.36 => 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)))) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_incr__mult__lemma,axiom, % 183.72/184.36 ! [V_k_2,V_P_2,V_d_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.36 => 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)))) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__atLeastAtMost__int,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__atMost,axiom, % 183.72/184.36 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__eq__iff,axiom, % 183.72/184.36 ! [V_y_2,V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 183.72/184.36 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 183.72/184.36 ! [V_y_2,V_x_2] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x_2) % 183.72/184.36 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeast0AtMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_lessThan__Suc__atMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__atMost,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__Suc,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__iff,axiom, % 183.72/184.36 ! [V_k_2,V_i_2,T_a] : % 183.72/184.36 ( class_Orderings_Oord(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 183.72/184.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__subset__iff,axiom, % 183.72/184.36 ! [V_y_2,V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 183.72/184.36 ! [V_y_2,V_x_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 183.72/184.36 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_UN__atMost__UNIV,axiom, % 183.72/184.36 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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__atMost__Suc,axiom, % 183.72/184.36 ! [V_n_2,V_f_2,T_a] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__0,axiom, % 183.72/184.36 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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_simp__from__to,axiom, % 183.72/184.36 ! [V_i_2,V_j_2] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 183.72/184.36 => 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)) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I9_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_UN__le__add__shift,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I3_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__int_I1_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__atLeastAtMost__int,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 183.72/184.36 ! [V_n_2,V_m_2] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_m_2) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I2_J,axiom, % 183.72/184.36 ! [V_u_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I10_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_atMost__Int__atLeast,axiom, % 183.72/184.36 ! [V_n_2,T_a] : % 183.72/184.36 ( class_Orderings_Oorder(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ivl__disj__un_I7_J,axiom, % 183.72/184.36 ! [V_u_2,V_l_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I8_J,axiom, % 183.72/184.36 ! [V_B_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 183.72/184.36 => 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))) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I6_J,axiom, % 183.72/184.36 ! [V_A_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 183.72/184.36 => 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)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I4_J,axiom, % 183.72/184.36 ! [V_A_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( B_x != V_t_2 % 183.72/184.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I4_J,axiom, % 183.72/184.36 ! [V_B_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( B_x != V_t_2 % 183.72/184.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I7_J,axiom, % 183.72/184.36 ! [V_B_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 183.72/184.36 => 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))) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I3_J,axiom, % 183.72/184.36 ! [V_B_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xa] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 183.72/184.36 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 183.72/184.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I3_J,axiom, % 183.72/184.36 ! [V_A_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xa] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 183.72/184.36 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 183.72/184.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I5_J,axiom, % 183.72/184.36 ! [V_A_2,V_t_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 183.72/184.36 => 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)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I6_J,axiom, % 183.72/184.36 ! [V_t_2,V_B_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 183.72/184.36 => 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)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I8_J,axiom, % 183.72/184.36 ! [V_t_2,V_A_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_periodic__finite__ex,axiom, % 183.72/184.36 ! [V_P_2,V_d_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 183.72/184.36 => ( ! [B_x,B_k] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.36 <=> 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)))) ) % 183.72/184.36 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.36 <=> ? [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_aset_I7_J,axiom, % 183.72/184.36 ! [V_t_2,V_A_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_bset_I5_J,axiom, % 183.72/184.36 ! [V_t_2,V_B_2,V_D_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 183.72/184.36 => ! [B_x] : % 183.72/184.36 ( ! [B_xa] : % 183.72/184.36 ( 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))) % 183.72/184.36 => ! [B_xb] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 183.72/184.36 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 183.72/184.36 => 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)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_ex__least__nat__less,axiom, % 183.72/184.36 ! [V_n_2,V_P_2] : % 183.72/184.36 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 183.72/184.36 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 183.72/184.36 => ? [B_k] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 183.72/184.36 & ! [B_i] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 183.72/184.36 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 183.72/184.36 & 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)))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setprod__mono__one__right,axiom, % 183.72/184.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setprod__mono__one__left,axiom, % 183.72/184.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zero__less__imp__eq__int,axiom, % 183.72/184.36 ! [V_k] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 183.72/184.36 => ? [B_n] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 183.72/184.36 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__mono__zero__left,axiom, % 183.72/184.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__mono__zero__right,axiom, % 183.72/184.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__subset__induct,axiom, % 183.72/184.36 ! [V_P_2,V_A_2,V_F_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 183.72/184.36 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 183.72/184.36 => ( ! [B_a,B_F] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 183.72/184.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 183.72/184.36 => ( hBOOL(hAPP(V_P_2,B_F)) % 183.72/184.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 183.72/184.36 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__strict__mono,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.36 ( ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.36 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 183.72/184.36 => 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))) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_field__le__mult__one__interval,axiom, % 183.72/184.36 ! [V_y,V_x,T_a] : % 183.72/184.36 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.36 => ( ! [B_z] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 183.72/184.36 => 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)) ) ) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 183.72/184.36 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.36 => ( V_A_2 = V_B_2 % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.36 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_split__neg__lemma,axiom, % 183.72/184.36 ! [V_n_2,V_P_2,V_k_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> ! [B_i,B_j] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 & 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) ) % 183.72/184.36 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_split__pos__lemma,axiom, % 183.72/184.36 ! [V_n_2,V_P_2,V_k_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> ! [B_i,B_j] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 183.72/184.36 & 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) ) % 183.72/184.36 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__diff__cong,axiom, % 183.72/184.36 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Oring__div(T_a) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__diff__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Oring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__diff__left__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Oring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__diff__right__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Oring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__simps_I3_J,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zmult1__eq,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__cong,axiom, % 183.72/184.36 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__simps_I1_J,axiom, % 183.72/184.36 ! [V_b,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__simps_I2_J,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__left__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__right__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__self1,axiom, % 183.72/184.36 ! [V_a,V_b,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__add__self2,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__cong,axiom, % 183.72/184.36 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 183.72/184.36 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__simps_I4_J,axiom, % 183.72/184.36 ! [V_b,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__mult2,axiom, % 183.72/184.36 ! [V_b,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__mult1,axiom, % 183.72/184.36 ! [V_b,V_a,V_c,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__left__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__right__eq,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mod__trivial,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__self,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__by__0,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__0,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__self,axiom, % 183.72/184.36 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zero,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiff__zmod__right,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiff__zmod__left,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( c_Nat__Transfer_Ois__nat(V_x) % 183.72/184.36 => ( c_Nat__Transfer_Ois__nat(V_y) % 183.72/184.36 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zpower__zmod,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self1__is__0,axiom, % 183.72/184.36 ! [V_a,V_b,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self2__is__0,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self2,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self1,axiom, % 183.72/184.36 ! [V_b,V_c,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__by__1,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__div__trivial,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__le__nonneg__dividend,axiom, % 183.72/184.36 ! [V_k,V_m] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_pos__mod__bound,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_neg__mod__bound,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__eq__0__iff,axiom, % 183.72/184.36 ! [V_d_2,V_m_2] : % 183.72/184.36 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.36 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zdiv__trivial,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_DIVISION__BY__ZERO,axiom, % 183.72/184.36 ! [V_a] : % 183.72/184.36 ( 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) % 183.72/184.36 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiv__zadd1__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__div__equality2,axiom, % 183.72/184.36 ! [V_a,V_b,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__div__equality,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_div__mod__equality2,axiom, % 183.72/184.36 ! [V_c,V_a,V_b,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_div__mod__equality,axiom, % 183.72/184.36 ! [V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Divides_Osemiring__div(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_pos__mod__sign,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_pos__mod__conj,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.36 => ( 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))) % 183.72/184.36 & 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__pos__pos__trivial,axiom, % 183.72/184.36 ! [V_b,V_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_neg__mod__sign,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_neg__mod__conj,axiom, % 183.72/184.36 ! [V_a,V_b] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => ( 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))) % 183.72/184.36 & 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__neg__neg__trivial,axiom, % 183.72/184.36 ! [V_b,V_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiv__zmod__equality2,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiv__zmod__equality,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zdiv__zmult1__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zdiv__equality,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmult__div__cancel,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zdiv__equality_H,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__pos__neg__trivial,axiom, % 183.72/184.36 ! [V_b,V_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.36 => ( 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))) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_split__zmod,axiom, % 183.72/184.36 ! [V_k_2,V_n_2,V_P_2] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 183.72/184.36 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.36 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 183.72/184.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 183.72/184.36 => ! [B_i,B_j] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 183.72/184.36 & 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) ) % 183.72/184.36 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 183.72/184.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => ! [B_i,B_j] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 & 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) ) % 183.72/184.36 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmult2__lemma__aux3,axiom, % 183.72/184.36 ! [V_q,V_b,V_r,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmult2__lemma__aux4,axiom, % 183.72/184.36 ! [V_q,V_b,V_r,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmult2__lemma__aux1,axiom, % 183.72/184.36 ! [V_q,V_r,V_b,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmult2__lemma__aux2,axiom, % 183.72/184.36 ! [V_q,V_r,V_b,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_divmod__int__rel__mod__eq,axiom, % 183.72/184.36 ! [V_y,V_q_1,V_b_1,V_a_1] : % 183.72/184.36 ( 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) % 183.72/184.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 183.72/184.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 183.72/184.36 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__zmult2__eq,axiom, % 183.72/184.36 ! [V_b,V_a,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_incr__lemma,axiom, % 183.72/184.36 ! [V_x,V_z,V_d] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_decr__lemma,axiom, % 183.72/184.36 ! [V_z,V_x,V_d] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 183.72/184.36 ( ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.36 & class_Groups_Ocomm__monoid__mult(T_a) ) % 183.72/184.36 => ( V_A_2 = V_B_2 % 183.72/184.36 => ( c_Nat__Transfer_Onat__set(V_B_2) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.36 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 183.72/184.36 => 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) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_diff__Suc,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Inter__subset,axiom, % 183.72/184.36 ! [V_B_2,V_A_2,T_a] : % 183.72/184.36 ( ! [B_X] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__abs,axiom, % 183.72/184.36 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__abs__ge__zero,axiom, % 183.72/184.36 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__distrib,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__distrib2,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__less__eq__dividend,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__less,axiom, % 183.72/184.36 ! [V_n,V_m] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__divide,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__ge__self,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__le__D1,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__idempotent,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__one,axiom, % 183.72/184.36 ! [T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__mult,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__mult__self,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__add__abs,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__zero,axiom, % 183.72/184.36 ! [T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__eq__0,axiom, % 183.72/184.36 ! [V_a_2,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.36 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__of__nat,axiom, % 183.72/184.36 ! [V_n,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_power__abs,axiom, % 183.72/184.36 ! [V_n,V_a,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__int__eq,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__minus__commute,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__setsum__abs,axiom, % 183.72/184.36 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__setprod,axiom, % 183.72/184.36 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.36 ( class_Fields_Olinordered__field(T_a) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__ge__zero,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__le__zero__iff,axiom, % 183.72/184.36 ! [V_a_2,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__of__nonneg,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__not__less__zero,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ~ 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zero__less__abs__iff,axiom, % 183.72/184.36 ! [V_a_2,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( 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))) % 183.72/184.36 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__of__pos,axiom, % 183.72/184.36 ! [V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__triangle__ineq,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__mult__less,axiom, % 183.72/184.36 ! [V_d,V_b,V_c,V_a,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__triangle__ineq3,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__triangle__ineq2,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__triangle__ineq2__sym,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nonzero__abs__divide,axiom, % 183.72/184.36 ! [V_a,V_b,T_a] : % 183.72/184.36 ( class_Fields_Olinordered__field(T_a) % 183.72/184.36 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__Suc,axiom, % 183.72/184.36 ! [V_n,V_m] : % 183.72/184.36 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.36 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__1,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__less__divisor,axiom, % 183.72/184.36 ! [V_m,V_n] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__eq__0__iff,axiom, % 183.72/184.36 ! [V_d_2,V_m_2] : % 183.72/184.36 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__geq,axiom, % 183.72/184.36 ! [V_n,V_m] : % 183.72/184.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__if,axiom, % 183.72/184.36 ! [V_n,V_m] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.36 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self3,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_le__mod__geq,axiom, % 183.72/184.36 ! [V_m,V_n] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__zmult__eq__1,axiom, % 183.72/184.36 ! [V_n,V_m] : % 183.72/184.36 ( 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) % 183.72/184.36 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zmod__int,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_div__add1__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__case__0,axiom, % 183.72/184.36 ! [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 ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__case__Suc,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__eq__mult,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Rings_Oordered__ring__abs(T_a) % 183.72/184.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 183.72/184.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 183.72/184.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__mult__pos,axiom, % 183.72/184.36 ! [V_y,V_x,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__diff__triangle__ineq,axiom, % 183.72/184.36 ! [V_d,V_c,V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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))))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__triangle__ineq4,axiom, % 183.72/184.36 ! [V_b,V_a,T_a] : % 183.72/184.36 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zero__le__power__abs,axiom, % 183.72/184.36 ! [V_n,V_a,T_a] : % 183.72/184.36 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.36 => 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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_abs__div__pos,axiom, % 183.72/184.36 ! [V_x,V_y,T_a] : % 183.72/184.36 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__le__divisor,axiom, % 183.72/184.36 ! [V_m,V_n] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zabs__less__one__iff,axiom, % 183.72/184.36 ! [V_z_2] : % 183.72/184.36 ( 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))) % 183.72/184.36 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult__self4,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__abs__mult__distrib,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_div__mult1__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__mult2__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zero__le__zpower__abs,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_div__mod__equality_H,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mult__div__cancel,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Omod__div__equality_H,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mod__lemma,axiom, % 183.72/184.36 ! [V_q,V_b,V_r,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_split__mod,axiom, % 183.72/184.36 ! [V_k_2,V_n_2,V_P_2] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 183.72/184.36 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 183.72/184.36 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 => ! [B_i,B_j] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 183.72/184.36 => ( 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) % 183.72/184.36 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Suc__times__mod__eq,axiom, % 183.72/184.36 ! [V_m,V_k] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__mod__distrib,axiom, % 183.72/184.36 ! [V_y,V_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_zero__less__zpower__abs__iff,axiom, % 183.72/184.36 ! [V_n_2,V_x_2] : % 183.72/184.36 ( 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))) % 183.72/184.36 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.36 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nitpick_Oint__lcm__def,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OBody,axiom, % 183.72/184.36 ! [V_s1,V_n,V_s0,V_pn] : % 183.72/184.36 ( 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)) % 183.72/184.36 => 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_int__val__lemma,axiom, % 183.72/184.36 ! [V_k_2,V_f_2,V_n_2] : % 183.72/184.36 ( ! [B_i] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 183.72/184.36 => 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))) ) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 183.72/184.36 => ? [B_i] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 183.72/184.36 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat0__intermed__int__val,axiom, % 183.72/184.36 ! [V_k_2,V_f_2,V_n_2] : % 183.72/184.36 ( ! [B_i] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 183.72/184.36 => 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))) ) % 183.72/184.36 => ( 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)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 183.72/184.36 => ? [B_i] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 183.72/184.36 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setprod__pos__nat,axiom, % 183.72/184.36 ! [V_f_2,V_S_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 183.72/184.36 => 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))) ) % 183.72/184.36 => 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))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OWhileFalse,axiom, % 183.72/184.36 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 183.72/184.36 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OWhileTrue,axiom, % 183.72/184.36 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 183.72/184.36 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OIfFalse,axiom, % 183.72/184.36 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 183.72/184.36 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OIfTrue,axiom, % 183.72/184.36 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 183.72/184.36 ( hBOOL(hAPP(V_b_2,V_s_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__elim__cases_I5_J,axiom, % 183.72/184.36 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 183.72/184.36 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 183.72/184.36 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 183.72/184.36 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OSemi,axiom, % 183.72/184.36 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_OSkip,axiom, % 183.72/184.36 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__elim__cases_I1_J,axiom, % 183.72/184.36 ! [V_t,V_n,V_s] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 183.72/184.36 => V_t = V_s ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__evalc,axiom, % 183.72/184.36 ! [V_t,V_n,V_s,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_eval__eq,axiom, % 183.72/184.36 ! [V_t_2,V_s_2,V_ca_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 183.72/184.36 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__Suc,axiom, % 183.72/184.36 ! [V_s_H,V_n,V_s,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 183.72/184.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__nonstrict,axiom, % 183.72/184.36 ! [V_m,V_t,V_n,V_s,V_c] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I7_J,axiom, % 183.72/184.36 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 => ? [B_s1] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 183.72/184.36 & 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)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I8_J,axiom, % 183.72/184.36 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> ( ( V_a6_2 = V_a2_2 % 183.72/184.36 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 183.72/184.36 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 & ? [B_s1] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 183.72/184.36 & 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)) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I5_J,axiom, % 183.72/184.36 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 183.72/184.36 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I6_J,axiom, % 183.72/184.36 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 183.72/184.36 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 183.72/184.36 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I4_J,axiom, % 183.72/184.36 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> ? [B_s1] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 183.72/184.36 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I1_J,axiom, % 183.72/184.36 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_triple__valid__def2,axiom, % 183.72/184.36 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 183.72/184.36 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)) % 183.72/184.36 <=> ! [B_Z,B_s] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 183.72/184.36 => ! [B_s_H] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 183.72/184.36 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_triple__valid__def,axiom, % 183.72/184.36 ! [V_t_2,V_n_2,T_a] : % 183.72/184.36 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 183.72/184.36 <=> 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln_Oequations_I9_J,axiom, % 183.72/184.36 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 183.72/184.36 ( 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)) % 183.72/184.36 <=> 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 183.72/184.36 ! [V_n_2,V_m_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 183.72/184.36 <=> 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)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nitpick_Onat__lcm__def,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_evaln__elim__cases_I6_J,axiom, % 183.72/184.36 ! [V_s1,V_n,V_s,V_P] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 183.72/184.36 => ~ ! [B_n] : % 183.72/184.36 ( V_n = hAPP(c_Nat_OSuc,B_n) % 183.72/184.36 => ~ 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__less__Suc,axiom, % 183.72/184.36 ! [V_i_2,V_M_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 183.72/184.36 => 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))))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__less,axiom, % 183.72/184.36 ! [V_i_2,V_M_2] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_CollectI,axiom, % 183.72/184.36 ! [T_a,V_a_2,V_P_2] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,V_a_2)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__conjI,axiom, % 183.72/184.36 ! [V_Q_2,V_P_2,T_a] : % 183.72/184.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__less__nat,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__le__nat,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__def,axiom, % 183.72/184.36 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 183.72/184.36 % 183.72/184.36 fof(fact_empty__Collect__eq,axiom, % 183.72/184.36 ! [V_P_2,T_a] : % 183.72/184.36 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 183.72/184.36 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__empty__eq,axiom, % 183.72/184.36 ! [V_P_2,T_a] : % 183.72/184.36 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_CollectE,axiom, % 183.72/184.36 ! [V_P_2,V_a_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_CollectD,axiom, % 183.72/184.36 ! [V_P_2,V_a_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_mem__Collect__eq,axiom, % 183.72/184.36 ! [V_P_2,V_a_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__mem__eq,axiom, % 183.72/184.36 ! [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 ). % 183.72/184.36 % 183.72/184.36 fof(fact_empty__def,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__disjI,axiom, % 183.72/184.36 ! [V_Q_2,V_P_2,T_a] : % 183.72/184.36 ( 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)))) % 183.72/184.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_insert__Collect,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_UNIV__def,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__disj__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__conj__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__Collect__eq,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_insert__compr__raw,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_insert__compr,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Un__def,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Int__Collect,axiom, % 183.72/184.36 ! [V_P_2,V_A_2,V_x_2,T_a] : % 183.72/184.36 ( 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)))) % 183.72/184.36 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.36 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Int__def,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__conv__if,axiom, % 183.72/184.36 ! [T_a,V_a_2,V_P_2] : % 183.72/184.36 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 183.72/184.36 => 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))) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__conv__if2,axiom, % 183.72/184.36 ! [T_a,V_a_2,V_P_2] : % 183.72/184.36 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 183.72/184.36 => 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))) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_singleton__conv,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_singleton__conv2,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_set__diff__eq,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__not,axiom, % 183.72/184.36 ! [V_P_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 => ( 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)))) % 183.72/184.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_insert__def,axiom, % 183.72/184.36 ! [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) ). % 183.72/184.36 % 183.72/184.36 fof(fact_vimage__def,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__M__bounded__by__nat,axiom, % 183.72/184.36 ! [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))))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__setsum__restrict,axiom, % 183.72/184.36 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_c) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_if__image__distrib,axiom, % 183.72/184.36 ! [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))))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Collect__all__eq,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__seg__image__imp__finite,axiom, % 183.72/184.36 ! [V_n_2,V_f_2,T_a,V_A_2] : % 183.72/184.36 ( 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))) % 183.72/184.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__restrict__set_H,axiom, % 183.72/184.36 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__image__gen,axiom, % 183.72/184.36 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 183.72/184.36 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_nat__gcd_Osimps,axiom, % 183.72/184.36 ! [V_x,V_y] : % 183.72/184.36 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 183.72/184.36 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.36 => 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)) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_card__less__Suc2,axiom, % 183.72/184.36 ! [V_i_2,V_M_2] : % 183.72/184.36 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 183.72/184.36 => 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))))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_dom__if,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nitpick_Oint__gcd__def,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_dom__override__on,axiom, % 183.72/184.36 ! [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))))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__multicount,axiom, % 183.72/184.36 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 183.72/184.36 => 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 ) % 183.72/184.36 => 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)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__subsets,axiom, % 183.72/184.36 ! [V_A_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => 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)))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Pow__def,axiom, % 183.72/184.36 ! [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)) ). % 183.72/184.36 % 183.72/184.36 fof(fact_override__on__apply__in,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_override__on__apply__notin,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 183.72/184.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.36 => 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) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_override__on__emptyset,axiom, % 183.72/184.36 ! [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 ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 183.72/184.36 ! [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))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_override__on__def,axiom, % 183.72/184.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 183.72/184.36 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.36 => 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) ) % 183.72/184.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.36 => 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) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 183.72/184.36 ! [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)))) ). % 183.72/184.36 % 183.72/184.36 fof(fact_setsum__multicount__gen,axiom, % 183.72/184.36 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 183.72/184.36 => ( ! [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 183.72/184.36 => 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) ) % 183.72/184.36 => 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) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_inf__Sup1__distrib,axiom, % 183.72/184.36 ! [V_x_2,V_A_2,T_a] : % 183.72/184.36 ( class_Lattices_Odistrib__lattice(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_inf__Sup2__distrib,axiom, % 183.72/184.36 ! [V_B_2,V_A_2,T_a] : % 183.72/184.36 ( class_Lattices_Odistrib__lattice(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))))) ) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_sup__Inf2__distrib,axiom, % 183.72/184.36 ! [V_B_2,V_A_2,T_a] : % 183.72/184.36 ( class_Lattices_Odistrib__lattice(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))))) ) ) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__Collect__bounded__ex,axiom, % 183.72/184.36 ! [V_Q_2,T_b,V_P_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 => ( 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))))) % 183.72/184.36 <=> ! [B_y] : % 183.72/184.36 ( hBOOL(hAPP(V_P_2,B_y)) % 183.72/184.36 => 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)))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__image__set,axiom, % 183.72/184.36 ! [V_f_2,T_b,V_P_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 183.72/184.36 => 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))))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_sup__Inf1__distrib,axiom, % 183.72/184.36 ! [V_x_2,V_A_2,T_a] : % 183.72/184.36 ( class_Lattices_Odistrib__lattice(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_add__Min__commute,axiom, % 183.72/184.36 ! [V_k_2,V_N_2,T_a] : % 183.72/184.36 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_add__Max__commute,axiom, % 183.72/184.36 ! [V_k_2,V_N_2,T_a] : % 183.72/184.36 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => 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))))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_finite__conv__nat__seg__image,axiom, % 183.72/184.36 ! [V_A_2,T_a] : % 183.72/184.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 <=> ? [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))) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_pigeonhole__infinite,axiom, % 183.72/184.36 ! [V_f_2,T_b,V_A_2,T_a] : % 183.72/184.36 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 183.72/184.36 => ? [B_x] : % 183.72/184.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.36 & ~ 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)))))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Max_Osingleton,axiom, % 183.72/184.36 ! [V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Min_Osingleton,axiom, % 183.72/184.36 ! [V_x_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => 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 ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Min__le,axiom, % 183.72/184.36 ! [V_x_2,V_A_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.36 => 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)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Max__ge,axiom, % 183.72/184.36 ! [V_x_2,V_A_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.36 => 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))) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Max__in,axiom, % 183.72/184.36 ! [V_A_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 183.72/184.36 % 183.72/184.36 fof(fact_Min__in,axiom, % 183.72/184.36 ! [V_A_2,T_a] : % 183.72/184.36 ( class_Orderings_Olinorder(T_a) % 183.72/184.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min__antimono,axiom, % 183.72/184.37 ! [V_N_2,V_M_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 183.72/184.37 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => 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))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max__mono,axiom, % 183.72/184.37 ! [V_N_2,V_M_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 183.72/184.37 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => 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))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oremove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oremove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_card__quotient__disjoint,axiom, % 183.72/184.37 ! [V_r_2,V_A_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( 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) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inj__on__diff__nat,axiom, % 183.72/184.37 ! [V_k_2,V_N_2] : % 183.72/184.37 ( ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastAtMost,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__0L,axiom, % 183.72/184.37 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__0R,axiom, % 183.72/184.37 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__0L,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__0R,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__Suc__Suc,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__Suc__Suc,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_less__max__iff__disj,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,V_z_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 183.72/184.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__less__iff__conj,axiom, % 183.72/184.37 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oless__supI1,axiom, % 183.72/184.37 ! [V_b,V_a,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oless__supI2,axiom, % 183.72/184.37 ! [V_a,V_b,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__less__iff__conj,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,V_z_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__less__iff__disj,axiom, % 183.72/184.37 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 183.72/184.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oless__infI1,axiom, % 183.72/184.37 ! [V_b,V_x,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oless__infI2,axiom, % 183.72/184.37 ! [V_a,V_x,V_b,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__add__distrib__left,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Odistrib__sup__le,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Odistrib__inf__le,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 183.72/184.37 ! [V_x,V_z,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__inf__distrib2,axiom, % 183.72/184.37 ! [V_x,V_z,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__assoc,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf_Oassoc,axiom, % 183.72/184.37 ! [V_c,V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__assoc,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup_Oassoc,axiom, % 183.72/184.37 ! [V_c,V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__inf__distrib1,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__left__commute,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 183.72/184.37 ! [V_c,V_a,V_b,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__left__commute,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup_Oleft__commute,axiom, % 183.72/184.37 ! [V_c,V_a,V_b,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__left__idem,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__left__idem,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup_Oleft__idem,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__sup__absorb,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__inf__absorb,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__commute,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf_Ocommute,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__commute,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup_Ocommute,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf_Oidem,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup_Oidem,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oidem,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oidem,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__le__iff__disj,axiom, % 183.72/184.37 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 183.72/184.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__le1,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__le2,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__iff__inf,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.72/184.37 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__inf__iff,axiom, % 183.72/184.37 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__infI1,axiom, % 183.72/184.37 ! [V_b,V_x,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__infI2,axiom, % 183.72/184.37 ! [V_a,V_x,V_b,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__absorb1,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__absorb2,axiom, % 183.72/184.37 ! [V_x,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__infI,axiom, % 183.72/184.37 ! [V_b,V_a,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__greatest,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__mono,axiom, % 183.72/184.37 ! [V_d,V_b,V_c,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__infE,axiom, % 183.72/184.37 ! [V_b,V_a,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.72/184.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__max__iff__disj,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,V_z_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 183.72/184.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__maxI1,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__maxI2,axiom, % 183.72/184.37 ! [V_x,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__iff__sup,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.72/184.37 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__sup__iff,axiom, % 183.72/184.37 ! [V_z_2,V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__supI1,axiom, % 183.72/184.37 ! [V_b,V_a,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__supI2,axiom, % 183.72/184.37 ! [V_a,V_b,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__absorb2,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__absorb1,axiom, % 183.72/184.37 ! [V_x,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.72/184.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__supI,axiom, % 183.72/184.37 ! [V_b,V_x,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__least,axiom, % 183.72/184.37 ! [V_z,V_x,V_y,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__mono,axiom, % 183.72/184.37 ! [V_d,V_b,V_c,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ole__supE,axiom, % 183.72/184.37 ! [V_x,V_b,V_a,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 183.72/184.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__add__distrib__left,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__diff,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__greaterThanAtMost,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__diff__distrib__left,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__diff__distrib__left,axiom, % 183.72/184.37 ! [V_z,V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__greaterThanLessThan,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastLessThan,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_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_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inf__min,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( ( class_Lattices_Osemilattice__inf(T_a) % 183.72/184.37 & class_Orderings_Olinorder(T_a) ) % 183.72/184.37 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sup__max,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( ( class_Lattices_Osemilattice__sup(T_a) % 183.72/184.37 & class_Orderings_Olinorder(T_a) ) % 183.72/184.37 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__is__empty,axiom, % 183.72/184.37 ! [V_r_2,V_A_2,T_a] : % 183.72/184.37 ( 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)) % 183.72/184.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__is__empty2,axiom, % 183.72/184.37 ! [V_r_2,V_A_2,T_a] : % 183.72/184.37 ( 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) % 183.72/184.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__empty,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nat__minus__add__max,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__Suc2,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__Suc1,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofold__sup__insert,axiom, % 183.72/184.37 ! [V_a_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofold__inf__insert,axiom, % 183.72/184.37 ! [V_a_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oin__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oin__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastAtMostR1,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastAtMostL1,axiom, % 183.72/184.37 ! [V_d_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastAtMostR2,axiom, % 183.72/184.37 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_d_2) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Int__atLeastAtMostL2,axiom, % 183.72/184.37 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_b_2) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_OF__eq,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_OF__eq,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__diff1,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,V_r_2,T_a] : % 183.72/184.37 ( 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) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__Suc2,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__Suc1,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__le__fold__sup,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofold1__belowI,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Obelow__fold1__iff,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_fold1__below__iff,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ? [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_strict__below__fold1__iff,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_fold1__strict__below__iff,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ? [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max__insert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min__insert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Osubset__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Osubset__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max__Un,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min__Un,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oeq__fold__idem_H,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oeq__fold__idem_H,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oinsert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oinsert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_fold1__antimono,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => 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))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oinsert__remove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Ounion__inter,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Ounion__disjoint,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oinsert__remove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Ounion__inter,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Ounion__disjoint,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oeq__fold_H,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oeq__fold_H,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_dual__min,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_dual__max,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_max__ord__max,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Oord(T_a) % 183.72/184.37 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__ord__min,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Orderings_Oord(T_a) % 183.72/184.37 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sup__nat__def,axiom, % 183.72/184.37 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inf__nat__def,axiom, % 183.72/184.37 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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))))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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))))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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))))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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))))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__le__Sup,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Osup__Inf__absorb,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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 ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.37 => 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 ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 183.72/184.37 ! [V_a_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => 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 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => 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 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 183.72/184.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( 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)) % 183.72/184.37 => 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)) ) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oremove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oremove,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => ( ( 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)) % 183.72/184.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 183.72/184.37 & ( 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)) % 183.72/184.37 => 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)))))) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__def,axiom, % 183.72/184.37 ! [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)))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( ! [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)))))) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( ! [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)))))) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Oclosed,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( ! [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)))))) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotientI,axiom, % 183.72/184.37 ! [V_r_2,V_A_2,V_x_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_singleton__quotient,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__eq__UN,axiom, % 183.72/184.37 ! [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))))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__INT__subset,axiom, % 183.72/184.37 ! [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)))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__Int__subset,axiom, % 183.72/184.37 ! [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)))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__UN,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__empty,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__mono,axiom, % 183.72/184.37 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 183.72/184.37 ( 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)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Image__Un,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Un__Image,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotientE,axiom, % 183.72/184.37 ! [V_r_2,V_A_2,V_X_2,T_a] : % 183.72/184.37 ( 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))) % 183.72/184.37 => ~ ! [B_x] : % 183.72/184.37 ( 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)))) % 183.72/184.37 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Oclosed,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => ( ! [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)))))) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 183.72/184.37 ! [V_N_2,V_h_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( ! [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)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 183.72/184.37 ! [V_N_2,V_h_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( ! [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)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_less__by__empty,axiom, % 183.72/184.37 ! [V_B_2,T_a,V_A_2] : % 183.72/184.37 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max_Ohom__commute,axiom, % 183.72/184.37 ! [V_N_2,V_h_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( ! [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)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min_Ohom__commute,axiom, % 183.72/184.37 ! [V_N_2,V_h_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( ! [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)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 183.72/184.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__nat__eq__if,axiom, % 183.72/184.37 ! [V_z_2,V_z_H_2] : % 183.72/184.37 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 183.72/184.37 => 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) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_setsum__SucD,axiom, % 183.72/184.37 ! [V_n_2,V_A_2,V_f_2,T_a] : % 183.72/184.37 ( 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) % 183.72/184.37 => ? [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 & 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__neg__int,axiom, % 183.72/184.37 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__neg__1,axiom, % 183.72/184.37 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__neg__0,axiom, % 183.72/184.37 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__neg__eq__ge__0,axiom, % 183.72/184.37 ! [V_x_2] : % 183.72/184.37 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__def,axiom, % 183.72/184.37 ! [V_Z_2] : % 183.72/184.37 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__nat,axiom, % 183.72/184.37 ! [V_z] : % 183.72/184.37 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 183.72/184.37 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__neg__nat,axiom, % 183.72/184.37 ! [V_z] : % 183.72/184.37 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 183.72/184.37 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_setsum__cases,axiom, % 183.72/184.37 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 183.72/184.37 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => 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))))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nat__mod__eq__lemma,axiom, % 183.72/184.37 ! [V_y,V_n,V_x] : % 183.72/184.37 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 183.72/184.37 => ? [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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zdiv__zminus1__eq__if,axiom, % 183.72/184.37 ! [V_a,V_b] : % 183.72/184.37 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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)) ) % 183.72/184.37 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zdiv__zminus2__eq__if,axiom, % 183.72/184.37 ! [V_a,V_b] : % 183.72/184.37 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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)) ) % 183.72/184.37 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inj__uminus,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_ComplI,axiom, % 183.72/184.37 ! [V_A_2,V_ca_2,T_a] : % 183.72/184.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negative__zle,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negative__zless,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_fun__Compl__def,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_b,T_a] : % 183.72/184.37 ( class_Groups_Ouminus(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_vimage__Compl,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zdiv__zminus__zminus,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zdiv__zminus2,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zminus__0,axiom, % 183.72/184.37 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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__divide__divide,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__divide__right,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__divide__left,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Odivision__ring(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_ComplE,axiom, % 183.72/184.37 ! [V_A_2,V_ca_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 183.72/184.37 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_ComplD,axiom, % 183.72/184.37 ! [V_A_2,V_ca_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 183.72/184.37 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__iff,axiom, % 183.72/184.37 ! [V_A_2,V_ca_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 183.72/184.37 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zminus__zminus,axiom, % 183.72/184.37 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__minus,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_equation__minus__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 183.72/184.37 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__equation__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 183.72/184.37 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__equal__iff__equal,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 183.72/184.37 <=> V_a_2 = V_b_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_double__complement,axiom, % 183.72/184.37 ! [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 ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__eq__Compl__iff,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( 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) % 183.72/184.37 <=> V_A_2 = V_B_2 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_double__compl,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_uminus__apply,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_b,T_a] : % 183.72/184.37 ( class_Groups_Ouminus(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__eq__compl__iff,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 183.72/184.37 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_square__eq__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Oidom(T_a) % 183.72/184.37 => ( 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) % 183.72/184.37 <=> ( V_a_2 = V_b_2 % 183.72/184.37 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__mult__minus,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Oring(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__mult__commute,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Oring(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__mult__left,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Oring(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__mult__right,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Oring(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__add__distrib,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__add,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_add__minus__cancel,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__add__cancel,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__less__iff__less,axiom, % 183.72/184.37 ! [V_a_2,V_b_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__less__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_less__minus__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__equal__zero,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 183.72/184.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__equal__0__iff__equal,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_equal__neg__zero,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 183.72/184.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__0__equal__iff__equal,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 183.72/184.37 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__zero,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmult__zminus,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zminus__zadd__distrib,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__minus__cancel,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_mod__minus__cong,axiom, % 183.72/184.37 ! [V_a_H,V_b,V_a,T_a] : % 183.72/184.37 ( class_Divides_Oring__div(T_a) % 183.72/184.37 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zminus__zmod,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus__zminus,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_mod__minus__eq,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Divides_Oring__div(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus2,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__diff__eq,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oab__group__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Collect__neg__eq,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_setsum__negf,axiom, % 183.72/184.37 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.37 ( class_Groups_Oab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__minus__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__le__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__le__iff__le,axiom, % 183.72/184.37 ! [V_a_2,V_b_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__imp__neg__le,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__le__compl__iff,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__mono,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__anti__mono,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__subset__Compl__iff,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__le__self__iff,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__le__0__iff__le,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_le__minus__self__iff,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__0__le__iff__le,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_less__minus__self__iff,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__less__nonneg,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__less__0__iff__less,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__0__less__iff__less,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__unique,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_ab__left__minus,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oab__group__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_left__minus,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_eq__neg__iff__add__eq__0,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 183.72/184.37 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_right__minus,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__0,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Rings_Ocomm__ring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__def,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_ab__diff__minus,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__minus__eq__add,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Ogroup__add(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_square__eq__1__iff,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 183.72/184.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.37 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 183.72/184.37 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Rings_Ocomm__ring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__inf__bot,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inf__compl__bot,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__eq,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__top__eq,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__bot__eq,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__inf,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__sup,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sup__compl__top,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__sup__top,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nonzero__minus__divide__divide,axiom, % 183.72/184.37 ! [V_a,V_b,T_a] : % 183.72/184.37 ( class_Rings_Odivision__ring(T_a) % 183.72/184.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nonzero__minus__divide__right,axiom, % 183.72/184.37 ! [V_a,V_b,T_a] : % 183.72/184.37 ( class_Rings_Odivision__ring(T_a) % 183.72/184.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__le__D2,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__leI,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__le__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 183.72/184.37 & 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__ge__minus__self,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__less__iff,axiom, % 183.72/184.37 ! [V_b_2,V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 183.72/184.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 183.72/184.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_subset__Compl__self__eq,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( 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))) % 183.72/184.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__UNIV__eq,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__empty__eq,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_finite__compl,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 183.72/184.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__disjoint,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__disjoint2,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__partition2,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__partition,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__Int,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__Un,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__max__eq__min,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__min__eq__max,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__atLeastAtMost,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__eq__Diff__UNIV,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__power__minus,axiom, % 183.72/184.37 ! [V_n,V_a,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zadd__zminus__inverse2,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__Diff__eq,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Diff__eq,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Diff__Compl,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negative__eq__positive,axiom, % 183.72/184.37 ! [V_m_2,V_n_2] : % 183.72/184.37 ( 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) % 183.72/184.37 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.37 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__int__zless__negative,axiom, % 183.72/184.37 ! [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)))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus1__not__zero,axiom, % 183.72/184.37 ! [V_l,V_k] : % 183.72/184.37 ( 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) % 183.72/184.37 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus2__not__zero,axiom, % 183.72/184.37 ! [V_l,V_k] : % 183.72/184.37 ( 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) % 183.72/184.37 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__int__def__symmetric,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_diff__int__def,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Ints__minus,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__greaterThanLessThan,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__eq,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__atLeast,axiom, % 183.72/184.37 ! [V_k_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__lessThan,axiom, % 183.72/184.37 ! [V_k_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Collect__imp__eq,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__atMost,axiom, % 183.72/184.37 ! [V_k_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__greaterThan,axiom, % 183.72/184.37 ! [V_k_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__UN,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Compl__INT,axiom, % 183.72/184.37 ! [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)) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__minus__le__zero,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__of__nonpos,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__if,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oabs__if(T_a) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__of__neg,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_power__minus,axiom, % 183.72/184.37 ! [V_n,V_a,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_disjoint__eq__subset__Compl,axiom, % 183.72/184.37 ! [V_B_2,V_A_2,T_a] : % 183.72/184.37 ( 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)) % 183.72/184.37 <=> 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_surj__Compl__image__subset,axiom, % 183.72/184.37 ! [V_A_2,V_f_2,T_a,T_b] : % 183.72/184.37 ( 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)) % 183.72/184.37 => 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)))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_int__zle__neg,axiom, % 183.72/184.37 ! [V_m_2,V_n_2] : % 183.72/184.37 ( 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)))) % 183.72/184.37 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.37 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negative__zle__0,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nat__zminus__int,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus1__eq__if,axiom, % 183.72/184.37 ! [V_b,V_a] : % 183.72/184.37 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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) ) % 183.72/184.37 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zmod__zminus2__eq__if,axiom, % 183.72/184.37 ! [V_b,V_a] : % 183.72/184.37 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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) ) % 183.72/184.37 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zabs__def,axiom, % 183.72/184.37 ! [V_i] : % 183.72/184.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__atLeastLessThan,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__greaterThanAtMost,axiom, % 183.72/184.37 ! [V_y_2,V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_neg__zminus__int,axiom, % 183.72/184.37 ! [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))))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__greaterThan,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__lessThan,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__atMost,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_image__uminus__atLeast,axiom, % 183.72/184.37 ! [V_x_2,T_a] : % 183.72/184.37 ( class_Groups_Oordered__ab__group__add(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Pow__Compl,axiom, % 183.72/184.37 ! [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))))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_compl__unique,axiom, % 183.72/184.37 ! [V_y,V_x,T_a] : % 183.72/184.37 ( class_Lattices_Oboolean__algebra(T_a) % 183.72/184.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 183.72/184.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 183.72/184.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inj__image__Compl__subset,axiom, % 183.72/184.37 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.37 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.37 => 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)))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_not__zle__0__negative,axiom, % 183.72/184.37 ! [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))))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negative__zless__0,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_vimage__if,axiom, % 183.72/184.37 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 183.72/184.37 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 183.72/184.37 => 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_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 183.72/184.37 => 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_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 183.72/184.37 => 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_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 183.72/184.37 => 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_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_nat__mult__distrib__neg,axiom, % 183.72/184.37 ! [V_z_H,V_z] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__Min__eq__Max,axiom, % 183.72/184.37 ! [V_S_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.37 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_minus__Max__eq__Min,axiom, % 183.72/184.37 ! [V_S_2,T_a] : % 183.72/184.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 183.72/184.37 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_z3div__def,axiom, % 183.72/184.37 ! [V_k,V_l] : % 183.72/184.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.37 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.37 => 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))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_z3mod__def,axiom, % 183.72/184.37 ! [V_k,V_l] : % 183.72/184.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.37 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.37 => 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)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__of__nat,axiom, % 183.72/184.37 ! [V_k,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => 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)))) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => 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)) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_negD,axiom, % 183.72/184.37 ! [V_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.37 => ? [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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__int__eq,axiom, % 183.72/184.37 ! [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) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__eq__iff,axiom, % 183.72/184.37 ! [V_z_2,V_w_2,T_a] : % 183.72/184.37 ( class_Int_Oring__char__0(T_a) % 183.72/184.37 => ( 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) % 183.72/184.37 <=> V_w_2 = V_z_2 ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__eq__0__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Int_Oring__char__0(T_a) % 183.72/184.37 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__0__eq__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Int_Oring__char__0(T_a) % 183.72/184.37 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 183.72/184.37 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__0,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__le__iff,axiom, % 183.72/184.37 ! [V_z_2,V_w_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__less__iff,axiom, % 183.72/184.37 ! [V_z_2,V_w_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__add,axiom, % 183.72/184.37 ! [V_z,V_w,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__mult,axiom, % 183.72/184.37 ! [V_z,V_w,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__1,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__diff,axiom, % 183.72/184.37 ! [V_z,V_w,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__of__nat__eq,axiom, % 183.72/184.37 ! [V_n,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__minus,axiom, % 183.72/184.37 ! [V_z,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Ints__of__int,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__power,axiom, % 183.72/184.37 ! [V_n,V_z,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__setsum,axiom, % 183.72/184.37 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__setprod,axiom, % 183.72/184.37 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.37 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 183.72/184.37 & class_Rings_Oring__1(T_a) ) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__le__0__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__0__le__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__less__0__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__0__less__iff,axiom, % 183.72/184.37 ! [V_z_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__nat__nat,axiom, % 183.72/184.37 ! [V_z,T_a] : % 183.72/184.37 ( class_Rings_Oring__1(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 183.72/184.37 => 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) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__neg,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__1__neg,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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)) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__if,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Groups_Osgn__if(T_a) % 183.72/184.37 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 183.72/184.37 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_zsgn__def,axiom, % 183.72/184.37 ! [V_i] : % 183.72/184.37 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.37 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 183.72/184.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 183.72/184.37 => 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__sgn,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn0,axiom, % 183.72/184.37 ! [T_a] : % 183.72/184.37 ( class_Groups_Osgn__if(T_a) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__0__0,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__times,axiom, % 183.72/184.37 ! [V_b,V_a,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__less,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__greater,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( 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))) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_mult__sgn__abs,axiom, % 183.72/184.37 ! [V_x,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => 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 ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_abs__sgn,axiom, % 183.72/184.37 ! [V_k,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => 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)) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__1__pos,axiom, % 183.72/184.37 ! [V_a_2,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_sgn__pos,axiom, % 183.72/184.37 ! [V_a,T_a] : % 183.72/184.37 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 183.72/184.37 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_card_Oneutral,axiom, % 183.72/184.37 ! [V_A_2,T_a] : % 183.72/184.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 183.72/184.37 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 183.72/184.37 => 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_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_ca_2))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 183.72/184.37 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_mod__induct__0,axiom, % 183.72/184.37 ! [V_i_2,V_P_2,V_p_2] : % 183.72/184.37 ( ! [B_i] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 183.72/184.37 => ( hBOOL(hAPP(V_P_2,B_i)) % 183.72/184.37 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 183.72/184.37 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 183.72/184.37 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Min__eqI,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_y] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_Max__eqI,axiom, % 183.72/184.37 ! [V_x_2,V_A_2,T_a] : % 183.72/184.37 ( class_Orderings_Olinorder(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_y] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 183.72/184.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.37 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_inf__le__fold__inf,axiom, % 183.72/184.37 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Lattices_Osemilattice__inf(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 183.72/184.37 => 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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_fold__sup__le__sup,axiom, % 183.72/184.37 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 183.72/184.37 ( class_Lattices_Osemilattice__sup(T_a) % 183.72/184.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.37 => ( ! [B_x] : % 183.72/184.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 183.72/184.37 => 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_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_ca_2))) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_expand__Suc,axiom, % 183.72/184.37 ! [V_v] : % 183.72/184.37 ( 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))) % 183.72/184.37 => 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))) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_quotient__disj,axiom, % 183.72/184.37 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 183.72/184.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.37 => ( 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))) % 183.72/184.37 => ( 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))) % 183.72/184.37 => ( V_X_2 = V_Y_2 % 183.72/184.37 | 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)) ) ) ) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_com_Osize_I11_J,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_com_Osize_I3_J,axiom, % 183.72/184.37 ! [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))) ). % 183.72/184.37 % 183.72/184.37 fof(fact_of__int__number__of__eq,axiom, % 183.72/184.37 ! [V_v,T_a] : % 183.72/184.37 ( class_Int_Onumber__ring(T_a) % 183.72/184.37 => 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) ) ). % 183.72/184.37 % 183.72/184.37 fof(fact_number__of__eq,axiom, % 183.72/184.37 ! [V_k,T_a] : % 183.72/184.37 ( class_Int_Onumber__ring(T_a) % 183.72/184.37 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__nat__number__of__lemma,axiom, % 183.72/184.38 ! [V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I2_J,axiom, % 183.72/184.38 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 183.72/184.38 ( 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) % 183.72/184.38 <=> ( V_loc_2 = V_loc_H_2 % 183.72/184.38 & V_fun_2 = V_fun_H_2 % 183.72/184.38 & V_com_2 = V_com_H_2 ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__number__of,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Int_Oring__char__0(T_a) ) % 183.72/184.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 183.72/184.38 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__reorient,axiom, % 183.72/184.38 ! [V_x_2,V_w_2,T_a] : % 183.72/184.38 ( class_Int_Onumber(T_a) % 183.72/184.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 183.72/184.38 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__nat__number__of__eq,axiom, % 183.72/184.38 ! [V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I10_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I11_J,axiom, % 183.72/184.38 ! [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 ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I35_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I34_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I37_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I36_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I39_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I38_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I41_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_com_Osimps_I40_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__number__of__eq__not__less,axiom, % 183.72/184.38 ! [V_w_2,V_v_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber(T_a) % 183.72/184.38 & class_Orderings_Olinorder(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> ~ 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_left__distrib__number__of,axiom, % 183.72/184.38 ! [V_v,V_b,V_a,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Rings_Osemiring(T_b) ) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_right__distrib__number__of,axiom, % 183.72/184.38 ! [V_c,V_b,V_v,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Rings_Osemiring(T_b) ) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_left__diff__distrib__number__of,axiom, % 183.72/184.38 ! [V_v,V_b,V_a,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Rings_Oring(T_b) ) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_right__diff__distrib__number__of,axiom, % 183.72/184.38 ! [V_c,V_b,V_v,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Rings_Oring(T_b) ) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__number__of,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__number__of,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_min__number__of,axiom, % 183.72/184.38 ! [V_v,V_u,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Orderings_Oord(T_b) ) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_max__number__of,axiom, % 183.72/184.38 ! [V_v,V_u,T_b] : % 183.72/184.38 ( ( class_Int_Onumber(T_b) % 183.72/184.38 & class_Orderings_Oord(T_b) ) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__number__of__left,axiom, % 183.72/184.38 ! [V_z,V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__number__of__eq,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__add,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__mult,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_arith__simps_I32_J,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__number__of__left,axiom, % 183.72/184.38 ! [V_z,V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__diff,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__minus,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_arith__simps_I30_J,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Ints__number__of,axiom, % 183.72/184.38 ! [V_w_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Union__quotient,axiom, % 183.72/184.38 ! [V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__divide__eq__number__of1,axiom, % 183.72/184.38 ! [V_w_2,V_b_2,V_a_2,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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)) % 183.72/184.38 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => 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 ) % 183.72/184.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__divide__eq__number__of,axiom, % 183.72/184.38 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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_ca_2) % 183.72/184.38 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) = V_b_2 ) % 183.72/184.38 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__eq__eq__number__of,axiom, % 183.72/184.38 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 183.72/184.38 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => 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_ca_2) ) % 183.72/184.38 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__eq__eq__number__of1,axiom, % 183.72/184.38 ! [V_a_2,V_w_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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 % 183.72/184.38 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__number__of__diff1,axiom, % 183.72/184.38 ! [V_c,V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__number__of__mult,axiom, % 183.72/184.38 ! [V_z,V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__number__of__eq,axiom, % 183.72/184.38 ! [V_w,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__less__eq__number__of1,axiom, % 183.72/184.38 ! [V_a_2,V_w_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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)) % 183.72/184.38 <=> ( ( 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))) % 183.72/184.38 => 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)))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__less__eq__number__of,axiom, % 183.72/184.38 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 183.72/184.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => 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_ca_2))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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_ca_2)),V_b_2)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__divide__eq__number__of,axiom, % 183.72/184.38 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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_ca_2))) % 183.72/184.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => 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_ca_2)),V_b_2)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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_ca_2))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__divide__eq__number__of1,axiom, % 183.72/184.38 ! [V_w_2,V_b_2,V_a_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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)))) % 183.72/184.38 <=> ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_abs__number__of,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__number__of__diff2,axiom, % 183.72/184.38 ! [V_w,V_c,V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__divide__eq__number__of1,axiom, % 183.72/184.38 ! [V_w_2,V_b_2,V_a_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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)))) % 183.72/184.38 <=> ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__divide__eq__number__of,axiom, % 183.72/184.38 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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_ca_2))) % 183.72/184.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => 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_ca_2)),V_b_2)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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_ca_2))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__le__eq__number__of,axiom, % 183.72/184.38 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 183.72/184.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => 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_ca_2))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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_ca_2)),V_b_2)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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))) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__le__eq__number__of1,axiom, % 183.72/184.38 ! [V_a_2,V_w_2,V_b_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber(T_a) ) % 183.72/184.38 => ( 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)) % 183.72/184.38 <=> ( ( 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))) % 183.72/184.38 => 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)))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_equiv__class__self,axiom, % 183.72/184.38 ! [V_a_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.38 => 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)))))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_UN__equiv__class,axiom, % 183.72/184.38 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_UN__equiv__class2,axiom, % 183.72/184.38 ! [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] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 183.72/184.38 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 183.72/184.38 => 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) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__mod__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__div__nat__number__of,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__eq__number__of__int__code,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__number__of__int__code,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_plus__numeral__code_I9_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__is__id,axiom, % 183.72/184.38 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 183.72/184.38 % 183.72/184.38 fof(fact_times__numeral__code_I5_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__numeral__code_I5_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__number__of__def,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__def,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_congruent2__implies__congruent,axiom, % 183.72/184.38 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.38 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__numeral__code_I6_J,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__imp__number__of__eq__0,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__eq__iff__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_m_2] : % 183.72/184.38 ( 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) % 183.72/184.38 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 183.72/184.38 & 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H_2,V_v_2] : % 183.72/184.38 ( 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) % 183.72/184.38 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 183.72/184.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 183.72/184.38 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__add__left,axiom, % 183.72/184.38 ! [V_k,V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__nat__number__of,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mod__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 183.72/184.38 => 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))) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_congruent2__implies__congruent__UN,axiom, % 183.72/184.38 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 183.72/184.38 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 183.72/184.38 => 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__nat__number__of,axiom, % 183.72/184.38 ! [V_n,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__nat__number__of__number__of,axiom, % 183.72/184.38 ! [V_w,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__nat__number__of__add,axiom, % 183.72/184.38 ! [V_n,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__nat__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_v_H_2] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_min__number__of__Suc,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I19_J,axiom, % 183.72/184.38 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I1_J,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Pls,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Pls__right,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__pred,axiom, % 183.72/184.38 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I2_J,axiom, % 183.72/184.38 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Pls__def,axiom, % 183.72/184.38 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__Pls,axiom, % 183.72/184.38 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__Pls,axiom, % 183.72/184.38 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_semiring__norm_I112_J,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__Pls,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__numeral__0__right,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__numeral__0,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_bin__less__0__simps_I1_J,axiom, % 183.72/184.38 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_semiring__norm_I113_J,axiom, % 183.72/184.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__Pls,axiom, % 183.72/184.38 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__is__num__zero,axiom, % 183.72/184.38 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__diff__number__of,axiom, % 183.72/184.38 ! [V_m,V_v] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_not__neg__number__of__Pls,axiom, % 183.72/184.38 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__1__add__number__of,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__add__1,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__iff__pred__less,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__def,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__diff__1,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__Numeral0,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__number__of__0,axiom, % 183.72/184.38 ! [V_v_2] : % 183.72/184.38 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__0__number__of,axiom, % 183.72/184.38 ! [V_v_2] : % 183.72/184.38 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of2,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H_2,V_v_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 183.72/184.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H_2,V_v_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__def,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__special_I3_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__special_I1_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__special_I1_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__special_I3_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__0__number__of,axiom, % 183.72/184.38 ! [V_v_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__succ,axiom, % 183.72/184.38 ! [V_k,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__pred,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__mult__left,axiom, % 183.72/184.38 ! [V_k,V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__nat__number__of,axiom, % 183.72/184.38 ! [V_v_H,V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__number__of__pred__iff__0,axiom, % 183.72/184.38 ! [V_v_2] : % 183.72/184.38 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 183.72/184.38 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__number__of__Suc,axiom, % 183.72/184.38 ! [V_n_2,V_v_2] : % 183.72/184.38 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 183.72/184.38 <=> 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__eq__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_n_2] : % 183.72/184.38 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 183.72/184.38 <=> 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__case__number__of,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__Suc__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_n_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__number__of__Suc,axiom, % 183.72/184.38 ! [V_n_2,V_v_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__number__of__Suc,axiom, % 183.72/184.38 ! [V_n_2,V_v_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__Suc__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_n_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__nat__number__of,axiom, % 183.72/184.38 ! [V_v] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_max__Suc__number__of,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_max__number__of__Suc,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__case__add__eq__if,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_min__Suc__number__of,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__rec__add__eq__if,axiom, % 183.72/184.38 ! [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))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__rec__number__of,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_UN__equiv__class__type2,axiom, % 183.72/184.38 ! [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] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 183.72/184.38 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( ! [B_x1] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 183.72/184.38 => ! [B_x2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 183.72/184.38 => 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)) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__rec__0,axiom, % 183.72/184.38 ! [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 ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__rec__Suc,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_UN__equiv__class__type,axiom, % 183.72/184.38 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( ! [B_x] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 183.72/184.38 => 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__special_I1_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 183.72/184.38 <=> 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__special_I3_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 <=> 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_iszero__0,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_iszero__def,axiom, % 183.72/184.38 ! [V_z_2,T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => ( c_Int_Oiszero(T_a,V_z_2) % 183.72/184.38 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_not__iszero__1,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_iszero__Numeral0,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__number__of__eq,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 183.72/184.38 <=> 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__number__of__odd__number__of,axiom, % 183.72/184.38 ! [V_v_2,V_w_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zpower__number__of__odd,axiom, % 183.72/184.38 ! [V_z_2,V_w_2] : % 183.72/184.38 ( ( 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))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__number__of__odd,axiom, % 183.72/184.38 ! [V_z_2,V_w_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I46_J,axiom, % 183.72/184.38 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I39_J,axiom, % 183.72/184.38 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I17_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__int__code_I16_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I51_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 183.72/184.38 <=> V_k_2 = V_l_2 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__eq__int__code_I16_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I34_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_bin__less__0__simps_I4_J,axiom, % 183.72/184.38 ! [V_w_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I22_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I12_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Bit1__def,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__number__of__Bit1,axiom, % 183.72/184.38 ! [V_w_2] : % 183.72/184.38 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 183.72/184.38 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__Bit1,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_iszero__number__of__Bit1,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Int_Oring__char__0(T_a) ) % 183.72/184.38 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__Pls,axiom, % 183.72/184.38 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__Bit1,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__numeral__1,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__numeral__1__right,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_semiring__norm_I110_J,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_numeral__1__eq__1,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I29_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I5_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__Numeral1,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__numeral__1,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => 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 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__is__num__one,axiom, % 183.72/184.38 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__numeral__1__eq__1,axiom, % 183.72/184.38 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Numeral1__eq1__nat,axiom, % 183.72/184.38 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 183.72/184.38 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_not__iszero__Numeral1,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_numeral__1__eq__Suc__0,axiom, % 183.72/184.38 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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_numeral__3__eq__3,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power3__eq__cube,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Groups_Omonoid__mult(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 183.72/184.38 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))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc3__eq__add__3,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__special_I2_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_le__special_I4_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__special_I4_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__special_I2_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__special_I3_J,axiom, % 183.72/184.38 ! [V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__special_I2_J,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__diff__eq__diff__pred,axiom, % 183.72/184.38 ! [V_m,V_n] : % 183.72/184.38 ( 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)) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__mod__eq__add3__mod,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mod__Suc__eq__mod__add3,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__div__eq__add3__div,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__Suc__eq__div__add3,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__special_I1_J,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__special_I2_J,axiom, % 183.72/184.38 ! [V_v,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__special_I4_J,axiom, % 183.72/184.38 ! [V_x_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 183.72/184.38 <=> 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))))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__special_I2_J,axiom, % 183.72/184.38 ! [V_y_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 183.72/184.38 <=> 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__Bit1,axiom, % 183.72/184.38 ! [V_w_2] : % 183.72/184.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 183.72/184.38 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 183.72/184.38 => 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__zmod__mult__2,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmod__number__of__Bit1,axiom, % 183.72/184.38 ! [V_v,V_w] : % 183.72/184.38 ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_arith__series__int,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I49_J,axiom, % 183.72/184.38 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I50_J,axiom, % 183.72/184.38 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I31_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__eq__int__code_I13_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I7_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__int__code_I13_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I14_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I48_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 183.72/184.38 <=> V_k_2 = V_l_2 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__Bit0,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Bit0__def,axiom, % 183.72/184.38 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Bit0__Bit0,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__Bit0,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Bit0__Pls,axiom, % 183.72/184.38 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I38_J,axiom, % 183.72/184.38 ! [V_l_2] : % 183.72/184.38 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 183.72/184.38 <=> c_Int_OPls = V_l_2 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I44_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 183.72/184.38 <=> V_k_2 = c_Int_OPls ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_bin__less__0__simps_I3_J,axiom, % 183.72/184.38 ! [V_w_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I27_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I21_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__eq__int__code_I14_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I32_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I4_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I10_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I16_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__int__code_I15_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Bit0__Bit1,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Bit1__Bit0,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I3_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I10_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I9_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zdiv__number__of__Bit0,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__number__of__Bit0,axiom, % 183.72/184.38 ! [V_w_2] : % 183.72/184.38 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 183.72/184.38 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__Bit1,axiom, % 183.72/184.38 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__Bit0,axiom, % 183.72/184.38 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_iszero__number__of__Bit0,axiom, % 183.72/184.38 ! [V_w_2,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Int_Oring__char__0(T_a) ) % 183.72/184.38 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 183.72/184.38 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__Bit0,axiom, % 183.72/184.38 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__Bit1,axiom, % 183.72/184.38 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__number__of__Bit0,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__Bit0,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__eq__int__code_I15_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I33_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__int__code_I14_J,axiom, % 183.72/184.38 ! [V_k2_2,V_k1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I15_J,axiom, % 183.72/184.38 ! [V_l_2,V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_card__UNIV__bool,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__Bit1,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I8_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Bit1__Bit1,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__number__of__even,axiom, % 183.72/184.38 ! [V_w_2,V_z_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zpower__number__of__even,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_double__number__of__Bit0,axiom, % 183.72/184.38 ! [V_w,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of1,axiom, % 183.72/184.38 ! [V_n] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( 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)))) % 183.72/184.38 & 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 183.72/184.38 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__number__of__even__number__of,axiom, % 183.72/184.38 ! [V_w_2,V_v_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__2__right,axiom, % 183.72/184.38 ! [V_z,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__2,axiom, % 183.72/184.38 ! [V_z,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__add__one__is__two,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__power2,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__eq__power2,axiom, % 183.72/184.38 ! [V_a_2,T_a] : % 183.72/184.38 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 183.72/184.38 => ( 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) % 183.72/184.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_numeral__2__eq__2,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_semiring__norm_I115_J,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__eq__square,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Groups_Omonoid__mult(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 183.72/184.38 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))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__2__eq__Suc,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__2__eq__Suc_H,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__power2,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__minus,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Rings_Oring__1(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__mult__2__right,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__mult__2,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__even__eq,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Groups_Omonoid__mult(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_abs__power2,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__abs,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__1__add__1,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mod2__Suc__Suc,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div2__Suc__Suc,axiom, % 183.72/184.38 ! [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))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmod__number__of__Bit0,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__self__div__2,axiom, % 183.72/184.38 ! [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 ). % 183.72/184.38 % 183.72/184.38 fof(fact_half__gt__zero__iff,axiom, % 183.72/184.38 ! [V_r_2,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => ( 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)))))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_half__gt__zero,axiom, % 183.72/184.38 ! [V_r,T_a] : % 183.72/184.38 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 183.72/184.38 => 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)))))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__eq__imp__eq,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.38 => ( 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)))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.38 => V_x = V_y ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__le__imp__le,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.38 => ( 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)))))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__le__power2,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => 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)))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__less__0,axiom, % 183.72/184.38 ! [V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ~ 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__less__power2,axiom, % 183.72/184.38 ! [V_a_2,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( 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)))))) % 183.72/184.38 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sum__power2__eq__zero__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( 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) % 183.72/184.38 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__eq__square__number__of,axiom, % 183.72/184.38 ! [V_w,T_b] : % 183.72/184.38 ( ( class_Groups_Omonoid__mult(T_b) % 183.72/184.38 & class_Int_Onumber(T_b) ) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_less__2__cases,axiom, % 183.72/184.38 ! [V_n] : % 183.72/184.38 ( 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))))) % 183.72/184.38 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.38 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__2,axiom, % 183.72/184.38 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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__eq__1__iff,axiom, % 183.72/184.38 ! [V_a_2,T_a] : % 183.72/184.38 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 183.72/184.38 => ( 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) % 183.72/184.38 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 183.72/184.38 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 183.72/184.38 ! [V_n,V_x,T_a] : % 183.72/184.38 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__minus__even,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Rings_Oring__1(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__less__imp__less,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__semidom(T_a) % 183.72/184.38 => ( 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)))))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sum__power2__ge__zero,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => 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))))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sum__power2__le__zero__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( 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))) % 183.72/184.38 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sum__power2__gt__zero__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( 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))))))) % 183.72/184.38 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 183.72/184.38 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_not__sum__power2__lt__zero,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ~ 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__sum,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__le__even__power_H,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__odd__eq,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Groups_Omonoid__mult(T_a) % 183.72/184.38 => 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 183.72/184.38 ! [V_n,V_x,T_a] : % 183.72/184.38 ( class_Rings_Ocomm__semiring__1(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__minus1__even,axiom, % 183.72/184.38 ! [V_n,T_a] : % 183.72/184.38 ( class_Rings_Oring__1(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zdiv__number__of__Bit1,axiom, % 183.72/184.38 ! [V_v,V_w] : % 183.72/184.38 ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mod2__gr__0,axiom, % 183.72/184.38 ! [V_m_2] : % 183.72/184.38 ( 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)))))) % 183.72/184.38 <=> 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__2__gt__zero,axiom, % 183.72/184.38 ! [V_n] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 183.72/184.38 => 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)))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power2__diff,axiom, % 183.72/184.38 ! [V_y,V_x,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_odd__0__le__power__imp__0__le,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( 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))))) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_odd__power__less__zero,axiom, % 183.72/184.38 ! [V_n,V_a,T_a] : % 183.72/184.38 ( class_Rings_Olinordered__idom(T_a) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__minus1__odd,axiom, % 183.72/184.38 ! [V_n,T_a] : % 183.72/184.38 ( class_Rings_Oring__1(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Suc__n__div__2__gt__zero,axiom, % 183.72/184.38 ! [V_n] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.38 => 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)))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__nat__double,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pos__zmod__mult__2,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__zdiv__mult__2,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pos__zdiv__mult__2,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__of__code,axiom, % 183.72/184.38 ! [V_k] : % 183.72/184.38 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.38 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.38 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.38 => ( ( 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) % 183.72/184.38 => 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)))))) ) % 183.72/184.38 & ( 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) % 183.72/184.38 => 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__int__num,axiom, % 183.72/184.38 ! [V_k_2,T_a] : % 183.72/184.38 ( class_Rings_Oring__1(T_a) % 183.72/184.38 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 183.72/184.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => 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))))) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__m1__odd,axiom, % 183.72/184.38 ! [V_n,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I45_J,axiom, % 183.72/184.38 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I42_J,axiom, % 183.72/184.38 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I37_J,axiom, % 183.72/184.38 c_Int_OPls != c_Int_OMin ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I40_J,axiom, % 183.72/184.38 c_Int_OMin != c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I7_J,axiom, % 183.72/184.38 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_code__numeral__zero__minus__one,axiom, % 183.72/184.38 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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I24_J,axiom, % 183.72/184.38 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I47_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 183.72/184.38 <=> V_k_2 = c_Int_OMin ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I43_J,axiom, % 183.72/184.38 ! [V_l_2] : % 183.72/184.38 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 183.72/184.38 <=> c_Int_OMin = V_l_2 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Bit1__Min,axiom, % 183.72/184.38 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 183.72/184.38 % 183.72/184.38 fof(fact_bin__less__0__simps_I2_J,axiom, % 183.72/184.38 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I23_J,axiom, % 183.72/184.38 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I20_J,axiom, % 183.72/184.38 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I26_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I30_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I3_J,axiom, % 183.72/184.38 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I6_J,axiom, % 183.72/184.38 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I13_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I9_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I28_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I8_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__number__of__Pls__Min,axiom, % 183.72/184.38 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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Int_OMin__def,axiom, % 183.72/184.38 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__Min,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_neg__number__of__Min,axiom, % 183.72/184.38 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__Pls,axiom, % 183.72/184.38 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Min__right,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_add__Min,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__Min,axiom, % 183.72/184.38 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nonzero__number__of__Min,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_succ__Min,axiom, % 183.72/184.38 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I2_J,axiom, % 183.72/184.38 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__minus1,axiom, % 183.72/184.38 ! [V_z,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mult__minus1__right,axiom, % 183.72/184.38 ! [V_z,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_number__of__Min,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_arith__simps_I31_J,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_abs__minus__one,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divide__minus1,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I25_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rel__simps_I11_J,axiom, % 183.72/184.38 ! [V_k_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 183.72/184.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmod__minus1__right,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I4_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus__Min,axiom, % 183.72/184.38 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmult__eq__1__iff,axiom, % 183.72/184.38 ! [V_n_2,V_m_2] : % 183.72/184.38 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.38 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.38 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 183.72/184.38 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 183.72/184.38 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 183.72/184.38 ! [V_n,V_m] : % 183.72/184.38 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.38 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 183.72/184.38 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I6_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_diff__bin__simps_I5_J,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__int__m1,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zdiv__minus1__right,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zero__code__numeral__code,axiom, % 183.72/184.38 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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_minus1__divide,axiom, % 183.72/184.38 ! [V_x,T_a] : % 183.72/184.38 ( ( class_Fields_Ofield__inverse__zero(T_a) % 183.72/184.38 & class_Int_Onumber__ring(T_a) ) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_abs__power__minus__one,axiom, % 183.72/184.38 ! [V_n,T_a] : % 183.72/184.38 ( ( class_Int_Onumber__ring(T_a) % 183.72/184.38 & class_Rings_Olinordered__idom(T_a) ) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__eq__minus1,axiom, % 183.72/184.38 ! [V_b] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__pos__neg__trivial,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.38 => ( 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))) % 183.72/184.38 => 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) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmod__minus1,axiom, % 183.72/184.38 ! [V_b] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_one__code__numeral__code,axiom, % 183.72/184.38 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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_power__m1__even,axiom, % 183.72/184.38 ! [V_n,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => 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) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nitpick_OFrac__def,axiom, % 183.72/184.38 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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__ge__less__than__def,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_int__ge__less__than2__def,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inj__graph,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nitpick_Oprod__def,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_nat__of__aux__code,axiom, % 183.72/184.38 ! [V_n,V_i] : % 183.72/184.38 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.38 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 183.72/184.38 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__rel__def,axiom, % 183.72/184.38 ! [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))))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__correct,axiom, % 183.72/184.38 ! [V_a,V_b] : % 183.72/184.38 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmult2__lemma,axiom, % 183.72/184.38 ! [V_c,V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 183.72/184.38 => 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)))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_code__numeral_Osize_I1_J,axiom, % 183.72/184.38 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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nats__number__of,axiom, % 183.72/184.38 ! [V_w_2,T_a] : % 183.72/184.38 ( class_Int_Onumber__ring(T_a) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sup__Un__eq2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 <=> 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__subset__eq2,axiom, % 183.72/184.38 ! [V_S_2,V_R_2,T_b,T_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 <=> 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pred__equals__eq2,axiom, % 183.72/184.38 ! [V_S_2,V_R_2,T_b,T_a] : % 183.72/184.38 ( 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) % 183.72/184.38 <=> V_R_2 = V_S_2 ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inf__Int__eq2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 <=> 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_bot__empty__eq2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 <=> 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_congruent2D,axiom, % 183.72/184.38 ! [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] : % 183.72/184.38 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 183.72/184.38 => ( 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)) % 183.72/184.38 => ( 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)) % 183.72/184.38 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_congruentD,axiom, % 183.72/184.38 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 183.72/184.38 => ( 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)) % 183.72/184.38 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rev__ImageI,axiom, % 183.72/184.38 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.38 => ( 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)) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Image__iff,axiom, % 183.72/184.38 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 183.72/184.38 <=> ? [B_x] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.72/184.38 & 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_unique__remainder,axiom, % 183.72/184.38 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => V_r = V_r_H ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_unique__quotient,axiom, % 183.72/184.38 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => V_q = V_q_H ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_self__remainder,axiom, % 183.72/184.38 ! [V_r,V_q,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__rel__0,axiom, % 183.72/184.38 ! [V_b] : % 183.72/184.38 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_SUP__UN__eq2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 <=> 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_INF__INT__eq2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 <=> 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_self__quotient,axiom, % 183.72/184.38 ! [V_r,V_q,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__rel__mod,axiom, % 183.72/184.38 ! [V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__rel__div,axiom, % 183.72/184.38 ! [V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nats__0,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__mod__div,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nats__add,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 183.72/184.38 => 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))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nats__mult,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 183.72/184.38 => 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))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nats__1,axiom, % 183.72/184.38 ! [T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_of__nat__in__Nats,axiom, % 183.72/184.38 ! [V_n_2,T_a] : % 183.72/184.38 ( class_Rings_Osemiring__1(T_a) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Image__singleton__iff,axiom, % 183.72/184.38 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 183.72/184.38 ( 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)))))) % 183.72/184.38 <=> 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_equiv__class__eq,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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)) % 183.72/184.38 => 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_quotient__eq__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 183.72/184.38 => ( V_X_2 = V_Y_2 % 183.72/184.38 <=> 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)) ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_quotient__eqI,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 183.72/184.38 => ( 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)) % 183.72/184.38 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__rel__div__mod,axiom, % 183.72/184.38 ! [V_a,V_b] : % 183.72/184.38 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => 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)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Image__singleton,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__equiv__class,axiom, % 183.72/184.38 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 183.72/184.38 ( 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)))) % 183.72/184.38 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 183.72/184.38 => 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)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__equiv__class__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.72/184.38 => ( 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)))) % 183.72/184.38 <=> 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_equiv__class__eq__iff,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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)) % 183.72/184.38 <=> ( 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)))) % 183.72/184.38 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.38 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_equiv__class__subset,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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)) % 183.72/184.38 => 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)))))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_eq__equiv__class__iff2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 183.72/184.38 => ( 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) % 183.72/184.38 <=> 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)) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zadd1__lemma,axiom, % 183.72/184.38 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( 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))) % 183.72/184.38 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => 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)))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zminus1__lemma,axiom, % 183.72/184.38 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 183.72/184.38 ( 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))) % 183.72/184.38 => 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))))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_subset__equiv__class,axiom, % 183.72/184.38 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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)))))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 183.72/184.38 => 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)) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_equiv__class__nondisjoint,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.38 => ( 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))))))) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_divmod__int__relI,axiom, % 183.72/184.38 ! [V_r,V_q,V_b,V_a] : % 183.72/184.38 ( 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) % 183.72/184.38 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 183.72/184.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 183.72/184.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_zmult1__lemma,axiom, % 183.72/184.38 ! [V_a,V_r,V_q,V_c,V_b] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 => 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)))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_pair__imageI,axiom, % 183.72/184.38 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_norm__frac_Osimps,axiom, % 183.72/184.38 ! [V_a_2,V_b_2] : % 183.72/184.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.38 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.38 => 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))) ) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_adjust__eq,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sup2E,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sup2CI,axiom, % 183.72/184.38 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 183.72/184.38 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inf2E,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 183.72/184.38 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inf2I,axiom, % 183.72/184.38 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_mem__splitI,axiom, % 183.72/184.38 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 183.72/184.38 => 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_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_splitI,axiom, % 183.72/184.38 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_prod__caseI,axiom, % 183.72/184.38 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 183.72/184.38 => 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))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_bot2E,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_swap__inj__on,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_splitD_H,axiom, % 183.72/184.38 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 183.72/184.38 ( 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_ca_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inf2D2,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_inf2D1,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_predicate2D,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 183.72/184.38 ( 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)) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_rev__predicate2D,axiom, % 183.72/184.38 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 183.72/184.38 => ( 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)) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sup2I1,axiom, % 183.72/184.38 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_sup2I2,axiom, % 183.72/184.38 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 183.72/184.38 => 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Pair__inject,axiom, % 183.72/184.38 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 183.72/184.38 ( 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) % 183.72/184.38 => ~ ( V_a = V_a_H % 183.72/184.38 => V_b != V_b_H ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Pair__eq,axiom, % 183.72/184.38 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.38 ( 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) % 183.72/184.38 <=> ( V_a_2 = V_a_H_2 % 183.72/184.38 & V_b_2 = V_b_H_2 ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__paired__All,axiom, % 183.72/184.38 ! [T_b,T_a,V_P_2] : % 183.72/184.38 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.38 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__weak__cong,axiom, % 183.72/184.38 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 183.72/184.38 ( V_p_2 = V_q_2 % 183.72/184.38 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__twice,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__conv,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_prod_Osimps_I2_J,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_splitD,axiom, % 183.72/184.38 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 183.72/184.38 ( 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))) % 183.72/184.38 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__eta,axiom, % 183.72/184.38 ! [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 ). % 183.72/184.38 % 183.72/184.38 fof(fact_split__paired__The,axiom, % 183.72/184.38 ! [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)))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_The__split__eq,axiom, % 183.72/184.38 ! [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) ). % 183.72/184.38 % 183.72/184.38 fof(fact_adjust__def,axiom, % 183.72/184.38 ! [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))))))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_in__rel__def,axiom, % 183.72/184.38 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 183.72/184.38 <=> 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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_div__mod__code__numeral__def,axiom, % 183.72/184.38 ! [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)) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 183.72/184.38 ! [V_w] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( ( 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)))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ 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)))) % 183.72/184.38 => 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)))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__correct,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__div__mod,axiom, % 183.72/184.38 ! [V_l,V_k] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.38 => 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)) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__minus1,axiom, % 183.72/184.38 ! [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))) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg_Osimps,axiom, % 183.72/184.38 ! [V_b,V_a] : % 183.72/184.38 ( ( ( 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))) % 183.72/184.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ ( 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))) % 183.72/184.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.38 => 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))) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__eqn,axiom, % 183.72/184.38 ! [V_a,V_b] : % 183.72/184.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.38 => ( ( 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))) % 183.72/184.38 => 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)) ) % 183.72/184.38 & ( ~ 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))) % 183.72/184.38 => 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))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_negDivAlg__eqn__number__of,axiom, % 183.72/184.38 ! [V_w,V_v] : % 183.72/184.38 ( 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))) % 183.72/184.38 => ( ( 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)))) % 183.72/184.38 => 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))) ) % 183.72/184.38 & ( ~ 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)))) % 183.72/184.38 => 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)))) ) ) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_Nitpick_Orefl_H__def,axiom, % 183.72/184.38 ! [V_r_2,T_a] : % 183.72/184.38 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 183.72/184.38 <=> ! [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)) ) ). % 183.72/184.38 % 183.72/184.38 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 183.72/184.38 ! [V_w] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( 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))) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( ~ 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))) % 183.72/184.39 => 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)))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg_Osimps,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg__0,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg__correct,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg__div__mod,axiom, % 183.72/184.39 ! [V_l,V_k] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg__eqn__number__of,axiom, % 183.72/184.39 ! [V_w,V_v] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( 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))) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( ~ 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))) % 183.72/184.39 => 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)))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg__eqn,axiom, % 183.72/184.39 ! [V_a,V_b] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 183.72/184.39 => 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))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__int__def,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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))) ) ) ) ) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => 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))) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__step,axiom, % 183.72/184.39 ! [V_m,V_n] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__int__pdivmod,axiom, % 183.72/184.39 ! [V_l_2,V_k_2] : % 183.72/184.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)))) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__compose,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_negateSnd__def,axiom, % 183.72/184.39 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__conv,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__zero,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__base,axiom, % 183.72/184.39 ! [V_n,V_m] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 183.72/184.39 => 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) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_negateSnd__eq,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__div__mod,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__int__rel__neg,axiom, % 183.72/184.39 ! [V_qr,V_b,V_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__if,axiom, % 183.72/184.39 ! [V_m_2,V_n_2] : % 183.72/184.39 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pdivmod__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pdivmod__posDivAlg,axiom, % 183.72/184.39 ! [V_k,V_l] : % 183.72/184.39 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__int__code,axiom, % 183.72/184.39 ! [V_l_2,V_k_2] : % 183.72/184.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 => 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)))) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_UN__equiv__class__inject,axiom, % 183.72/184.39 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 183.72/184.39 => ( 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) % 183.72/184.39 => ( 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))) % 183.72/184.39 => ( 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))) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => ! [B_y] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 183.72/184.39 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 183.72/184.39 => 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)) ) ) ) % 183.72/184.39 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 183.72/184.39 ! [V_a,V_r,V_q,V_c,V_b] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 183.72/184.39 ! [V_c,V_r,V_q,V_b,V_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 183.72/184.39 => 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)))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__unique,axiom, % 183.72/184.39 ! [V_qr_H,V_qr,V_n,V_m] : % 183.72/184.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 183.72/184.39 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 183.72/184.39 => V_qr = V_qr_H ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 183.72/184.39 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__eq,axiom, % 183.72/184.39 ! [V_qr,V_n,V_m] : % 183.72/184.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 183.72/184.39 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__eq,axiom, % 183.72/184.39 ! [V_r,V_q,V_n,V_m] : % 183.72/184.39 ( 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))) % 183.72/184.39 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__eq,axiom, % 183.72/184.39 ! [V_r,V_q,V_n,V_m] : % 183.72/184.39 ( 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))) % 183.72/184.39 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__add1__eq,axiom, % 183.72/184.39 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( 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))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 183.72/184.39 => 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)))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_negDivAlg_Opsimps,axiom, % 183.72/184.39 ! [V_b_2,V_a_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( ( 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))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( ~ ( 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))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg_Opsimps,axiom, % 183.72/184.39 ! [V_b_2,V_a_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__pos__neg__1__number__of,axiom, % 183.72/184.39 ! [V_w] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__eq__conv,axiom, % 183.72/184.39 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 183.72/184.39 ( 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) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__apsnd,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__def,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__conv,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__eqD,axiom, % 183.72/184.39 ! [V_a,V_y,V_x,T_a,T_b] : % 183.72/184.39 ( 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 % 183.72/184.39 => V_y = V_a ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__int__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__neg__pos,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__pos__pos,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__pos__pos__1__number__of,axiom, % 183.72/184.39 ! [V_w] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__pos__neg,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__neg__neg,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_norm__frac_Opsimps,axiom, % 183.72/184.39 ! [V_b_2,V_a_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 183.72/184.39 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 183.72/184.39 => 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))) ) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_negDivAlg_Opinduct,axiom, % 183.72/184.39 ! [V_P_2,V_a1_2,V_a0_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ! [B_a,B_b] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( ~ ( 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))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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))) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_posDivAlg_Opinduct,axiom, % 183.72/184.39 ! [V_P_2,V_a1_2,V_a0_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ! [B_a,B_b] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 183.72/184.39 => 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))) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mod__nat__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp__subset,axiom, % 183.72/184.39 ! [V_R2_2,V_R1_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_irrefl__def,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Relation_Oirrefl(T_a,V_r_2) % 183.72/184.39 <=> ! [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_norm__frac_Opinduct,axiom, % 183.72/184.39 ! [V_P_2,V_a1_2,V_a0_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ! [B_a,B_b] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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))) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp_Osimps,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 183.72/184.39 <=> ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 183.72/184.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp_Oequations,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 183.72/184.39 <=> ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 183.72/184.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp__downward,axiom, % 183.72/184.39 ! [V_a_2,V_b_2,V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 183.72/184.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat__gcd_Opsimps,axiom, % 183.72/184.39 ! [V_y_2,V_x_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 183.72/184.39 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat_Osize_I2_J,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_in__measure,axiom, % 183.72/184.39 ! [V_f_2,V_y_2,V_x_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat_Osize_I1_J,axiom, % 183.72/184.39 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__pos__neg__1__number__of,axiom, % 183.72/184.39 ! [V_w] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat__def,axiom, % 183.72/184.39 ! [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)))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat__gcd_Opinduct,axiom, % 183.72/184.39 ! [V_P_2,V_a1_2,V_a0_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ! [B_x,B_y] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__apsnd,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__def,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Rep__Integ__inject,axiom, % 183.72/184.39 ! [V_y_2,V_x_2] : % 183.72/184.39 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 183.72/184.39 <=> V_x_2 = V_y_2 ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__conv,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__eqD,axiom, % 183.72/184.39 ! [V_a,V_y,V_x,T_b,T_a] : % 183.72/184.39 ( 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 % 183.72/184.39 => V_x = V_a ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Pair__fst__snd__eq,axiom, % 183.72/184.39 ! [T_b,T_a,V_t_2,V_s_2] : % 183.72/184.39 ( V_s_2 = V_t_2 % 183.72/184.39 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 183.72/184.39 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_prod__eqI,axiom, % 183.72/184.39 ! [V_q,V_p,T_b,T_a] : % 183.72/184.39 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 183.72/184.39 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 183.72/184.39 => V_p = V_q ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_surjective__pairing,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__collapse,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_prod__case__beta,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__int__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__beta,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__comp__eq,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__def,axiom, % 183.72/184.39 ! [V_p_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__comp,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_The__split,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__neg__pos,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__pos__pos,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__pos__pos__1__number__of,axiom, % 183.72/184.39 ! [V_w] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__pos__neg,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__neg__neg,axiom, % 183.72/184.39 ! [V_b,V_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_prod__size__simp,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_exI__realizer,axiom, % 183.72/184.39 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 183.72/184.39 => 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_conjI__realizer,axiom, % 183.72/184.39 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_p_2)) % 183.72/184.39 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 183.72/184.39 => ( 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)))) % 183.72/184.39 & 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)))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_div__nat__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_divmod__nat__rel__def,axiom, % 183.72/184.39 ! [V_qr_2,V_n_2,V_m_2] : % 183.72/184.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 183.72/184.39 <=> ( 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)) % 183.72/184.39 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.72/184.39 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 183.72/184.39 => ( 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))) % 183.72/184.39 & 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)) ) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 183.72/184.39 => ( 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))) % 183.72/184.39 & 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))) ) ) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_inv__image__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mlex__leq,axiom, % 183.72/184.39 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osize_I2_J,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Oinject,axiom, % 183.72/184.39 ! [V_code__numeral_H_2,V_code__numeral_2] : % 183.72/184.39 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 183.72/184.39 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osimps_I3_J,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osimps_I2_J,axiom, % 183.72/184.39 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 183.72/184.39 % 183.72/184.39 fof(fact_in__inv__image,axiom, % 183.72/184.39 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Suc__code__numeral__minus__one,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_mlex__less,axiom, % 183.72/184.39 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osize_I4_J,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rp__inv__image__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__psubset__def,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osize_I3_J,axiom, % 183.72/184.39 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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_in__finite__psubset,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat_Osize_I4_J,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_prod_Orecs,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_in__lex__prod,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> ( 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)) % 183.72/184.39 | ( V_a_2 = V_a_H_2 % 183.72/184.39 & 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat__size,axiom, % 183.72/184.39 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat_Osize_I3_J,axiom, % 183.72/184.39 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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_same__fstI,axiom, % 183.72/184.39 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.72/184.39 => ( 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))) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equivp__equiv,axiom, % 183.72/184.39 ! [V_A_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__apsnd,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__conv,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__eq__conv,axiom, % 183.72/184.39 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 183.72/184.39 ( 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) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__apfst,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__apfst,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_identity__equivp,axiom, % 183.72/184.39 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equivp__def,axiom, % 183.72/184.39 ! [V_R_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 183.72/184.39 <=> ! [B_x,B_y] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 183.72/184.39 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equivp__reflp,axiom, % 183.72/184.39 ! [V_x_2,V_R_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equivp__symp,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_R_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equivp__transp,axiom, % 183.72/184.39 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__compose,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__apfst__commute,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__apfst,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__lessI2,axiom, % 183.72/184.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_ImageE,axiom, % 183.72/184.39 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 183.72/184.39 => ~ ! [B_x] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mlex__prod__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__less__def,axiom, % 183.72/184.39 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 183.72/184.39 % 183.72/184.39 fof(fact_measure__def,axiom, % 183.72/184.39 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 183.72/184.39 % 183.72/184.39 fof(fact_less__than__iff,axiom, % 183.72/184.39 ! [V_y_2,V_x_2] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__lessI1,axiom, % 183.72/184.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__leqI2,axiom, % 183.72/184.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_smin__insertI,axiom, % 183.72/184.39 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_smax__insertI,axiom, % 183.72/184.39 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_smin__emptyI,axiom, % 183.72/184.39 ! [V_X_2] : % 183.72/184.39 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_smax__emptyI,axiom, % 183.72/184.39 ! [V_Y_2] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 183.72/184.39 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pair__leqI1,axiom, % 183.72/184.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wmax__insertI,axiom, % 183.72/184.39 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wmin__insertI,axiom, % 183.72/184.39 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Field__insert,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Field__Union,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Field__empty,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mono__Field,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Field__Un,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__Field,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wmax__emptyI,axiom, % 183.72/184.39 ! [V_X_2] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wmin__emptyI,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_min__weak__def,axiom, % 183.72/184.39 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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__weak__def,axiom, % 183.72/184.39 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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__def,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__def_H,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__empty,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Image__Id__on,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__iff,axiom, % 183.72/184.39 ! [V_A_2,V_y_2,V_x_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> ( V_x_2 = V_y_2 % 183.72/184.39 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__eqI,axiom, % 183.72/184.39 ! [V_A_2,T_a,V_b_2,V_a_2] : % 183.72/184.39 ( V_a_2 = V_b_2 % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__strict__def,axiom, % 183.72/184.39 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__ext__additive,axiom, % 183.72/184.39 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( 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))) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_min__strict__def,axiom, % 183.72/184.39 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__extp__max__ext__eq,axiom, % 183.72/184.39 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 183.72/184.39 ( 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) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__rpair__set,axiom, % 183.72/184.39 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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_min__rpair__set,axiom, % 183.72/184.39 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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rp__inv__image__rp,axiom, % 183.72/184.39 ! [V_f_2,T_b,V_P_2,T_a] : % 183.72/184.39 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 183.72/184.39 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equiv__intrel__iff,axiom, % 183.72/184.39 ! [V_y_2,V_x_2] : % 183.72/184.39 ( 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)))) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_intrel__iff,axiom, % 183.72/184.39 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> 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) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__onE,axiom, % 183.72/184.39 ! [V_A_2,V_ca_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 183.72/184.39 => ~ ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equiv__intrel,axiom, % 183.72/184.39 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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_of__int,axiom, % 183.72/184.39 ! [V_j_2,V_i_2,T_a] : % 183.72/184.39 ( class_Rings_Oring__1(T_a) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_One__int__def,axiom, % 183.72/184.39 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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mult,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Rep__Integ__inverse,axiom, % 183.72/184.39 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 183.72/184.39 % 183.72/184.39 fof(fact_minus,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Zero__int__def,axiom, % 183.72/184.39 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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_int__def,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_add,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_nat,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_minus__int__def,axiom, % 183.72/184.39 ! [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))))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_less,axiom, % 183.72/184.39 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 183.72/184.39 ( 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))))))) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_le,axiom, % 183.72/184.39 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 183.72/184.39 ( 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))))))) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_eq__Abs__Integ,axiom, % 183.72/184.39 ! [V_z_2] : % 183.72/184.39 ~ ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Integ__def,axiom, % 183.72/184.39 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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osimps_I5_J,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Rep__Integ,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_code__numeral_Osimps_I4_J,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition__Integ,axiom, % 183.72/184.39 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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp__acc__eq,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__def,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__compI,axiom, % 183.72/184.39 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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_ca_2)),V_s_2)) % 183.72/184.39 => 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_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__UNION__distrib,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__UNION__distrib2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__empty1,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__empty2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__distrib,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__distrib2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__mono,axiom, % 183.72/184.39 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_O__assoc,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_union__comp__emptyR,axiom, % 183.72/184.39 ! [V_C_2,V_B_2,V_A_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_union__comp__emptyL,axiom, % 183.72/184.39 ! [V_B_2,V_C_2,V_A_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acc__subset,axiom, % 183.72/184.39 ! [V_R2_2,V_R1_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acc__downward,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,V_b_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 183.72/184.39 => ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acc_Osimps,axiom, % 183.72/184.39 ! [V_r_2,V_a_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 183.72/184.39 <=> ! [B_x] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__ext__compat,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_min__ext__compat,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_OAbs__image,axiom, % 183.72/184.39 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_ORep__range,axiom, % 183.72/184.39 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => 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 ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_ORep,axiom, % 183.72/184.39 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_ORep__inject,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 183.72/184.39 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_ORep__inverse,axiom, % 183.72/184.39 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_OAbs__inject,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 183.72/184.39 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 183.72/184.39 <=> V_x_2 = V_y_2 ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_type__definition_OAbs__inverse,axiom, % 183.72/184.39 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 183.72/184.39 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 183.72/184.39 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pred__comp__rel__comp__eq,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reduction__pairI,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__extp_Oequations,axiom, % 183.72/184.39 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 183.72/184.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 183.72/184.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 183.72/184.39 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 & ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 183.72/184.39 => ? [B_xa] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 183.72/184.39 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__less__than,axiom, % 183.72/184.39 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pred__comp_Ointros,axiom, % 183.72/184.39 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__empty,axiom, % 183.72/184.39 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__inv__image,axiom, % 183.72/184.39 ! [V_f_2,T_b,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__lex__prod,axiom, % 183.72/184.39 ! [V_rb_2,T_b,V_ra_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_ra_2) % 183.72/184.39 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__measure,axiom, % 183.72/184.39 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__comp__self,axiom, % 183.72/184.39 ! [V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__subset,axiom, % 183.72/184.39 ! [V_p_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_min__ext__wf,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__less,axiom, % 183.72/184.39 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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__finite__psubset,axiom, % 183.72/184.39 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pred__comp_Oequations,axiom, % 183.72/184.39 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> ? [B_b] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 183.72/184.39 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__Int2,axiom, % 183.72/184.39 ! [V_r_H_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__Int1,axiom, % 183.72/184.39 ! [V_r_H_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__mlex,axiom, % 183.72/184.39 ! [V_f_2,V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__pair__less,axiom, % 183.72/184.39 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__ext__wf,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__not__refl,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ~ 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__not__sym,axiom, % 183.72/184.39 ! [V_x_2,V_a_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ~ 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__asym,axiom, % 183.72/184.39 ! [V_x_2,V_a_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => ~ 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__irrefl,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ~ 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__int__ge__less__than2,axiom, % 183.72/184.39 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__int__ge__less__than,axiom, % 183.72/184.39 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acc__wfD,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__acc__iff,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__no__loop,axiom, % 183.72/184.39 ! [V_R_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__union__merge,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 <=> ~ ? [B_f] : % 183.72/184.39 ! [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfE__pf,axiom, % 183.72/184.39 ! [V_A_2,V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 => ( 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))) % 183.72/184.39 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__union__compatible,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 => ( c_Wellfounded_Owf(T_a,V_S_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf,axiom, % 183.72/184.39 ! [T_a] : % 183.72/184.39 ( class_Orderings_Owellorder(T_a) % 183.72/184.39 => 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reduction__pair__def,axiom, % 183.72/184.39 ! [V_P_2,T_a] : % 183.72/184.39 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 183.72/184.39 <=> ( 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)) % 183.72/184.39 & 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reduction__pair__lemma,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,V_P_2,T_a] : % 183.72/184.39 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 183.72/184.39 => ( 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))) % 183.72/184.39 => ( 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))) % 183.72/184.39 => ( c_Wellfounded_Owf(T_a,V_S_2) % 183.72/184.39 => 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)) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__lenlex,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__if__measure,axiom, % 183.72/184.39 ! [T_a,V_g_2,V_f_2,V_P_2] : % 183.72/184.39 ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.39 => 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))) ) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__ext_Ointros,axiom, % 183.72/184.39 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 183.72/184.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 183.72/184.39 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 183.72/184.39 => ? [B_xa] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 183.72/184.39 & 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)) ) ) % 183.72/184.39 => 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))) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_pred__nat__def,axiom, % 183.72/184.39 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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__lex,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__lexn,axiom, % 183.72/184.39 ! [V_n_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_lex__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_lexn_Osimps_I1_J,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__pred__nat,axiom, % 183.72/184.39 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__same__fst,axiom, % 183.72/184.39 ! [T_a,V_R_2,T_b,V_P_2] : % 183.72/184.39 ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.39 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 183.72/184.39 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Nitpick_Ozero__frac__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Collect__split,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_RangeI,axiom, % 183.72/184.39 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Id__on,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Diff__subset,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Union,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__empty,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__empty__iff,axiom, % 183.72/184.39 ! [V_r_2,T_a,T_b] : % 183.72/184.39 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Un__eq,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__Range,axiom, % 183.72/184.39 ! [V_r_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__eq__Range,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__iff,axiom, % 183.72/184.39 ! [V_r_2,T_b,V_a_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 183.72/184.39 <=> ? [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__insert,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__Int__subset,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Nitpick_Oone__frac__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_RangeP__Range__eq,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_RangeP_Ointros,axiom, % 183.72/184.39 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 183.72/184.39 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_RangeP_Oequations,axiom, % 183.72/184.39 ! [V_a2_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 183.72/184.39 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Nitpick_Ofrac__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_RangeE,axiom, % 183.72/184.39 ! [V_r_2,T_b,V_b_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 183.72/184.39 => ~ ! [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__Un,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ( c_Wellfounded_Owf(T_a,V_s_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_DomainI,axiom, % 183.72/184.39 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Id__on,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__empty,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__empty__iff,axiom, % 183.72/184.39 ! [V_r_2,T_b,T_a] : % 183.72/184.39 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__mono,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Un__eq,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__Domain,axiom, % 183.72/184.39 ! [V_r_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__eq__Domain,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__iff,axiom, % 183.72/184.39 ! [V_r_2,T_b,V_a_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 183.72/184.39 <=> ? [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__insert,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Int__subset,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Diff__subset,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Field__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Union,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__Collect__split,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_DomainP__Domain__eq,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_DomainE,axiom, % 183.72/184.39 ! [V_r_2,T_b,V_a_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 183.72/184.39 => ~ ! [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_image__split__eq__Sigma,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_DomainP_Ointros,axiom, % 183.72/184.39 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 183.72/184.39 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SigmaI,axiom, % 183.72/184.39 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__empty1,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__eq__cancel2,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 183.72/184.39 => ( 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)) % 183.72/184.39 <=> V_A_2 = V_B_2 ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Union,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_card__cartesian__product,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setsum__cartesian__product,axiom, % 183.72/184.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__empty2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__empty,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Compl__Times__UNIV1,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Compl__Times__UNIV2,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setprod__cartesian__product,axiom, % 183.72/184.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__mult(T_a) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Un__distrib2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__Un__distrib1,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Un__distrib1,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rel__comp__subset__Sigma,axiom, % 183.72/184.39 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => ( 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)))) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_swap__product,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__cartesian__product,axiom, % 183.72/184.39 ! [V_B_2,T_b,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 183.72/184.39 => 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)))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_equiv__type,axiom, % 183.72/184.39 ! [V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.39 => 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Int__distrib2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__Int__distrib1,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Int__distrib1,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Id__on__subset__Times,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Diff__distrib1,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__Diff__distrib1,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__Diff__distrib2,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_DomainP_Oequations,axiom, % 183.72/184.39 ! [V_a1_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 183.72/184.39 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_UNIV__Times__UNIV,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SigmaE2,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.39 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SigmaD2,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SigmaD1,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mem__Sigma__iff,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.39 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_card__cartesian__product__singleton,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Times__subset__cancel2,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 183.72/184.39 => ( 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)))) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Image__subset,axiom, % 183.72/184.39 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__cartesian__productD1,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_b,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__cartesian__productD2,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_b,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Collect__split,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SetCompr__Sigma__eq,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__image__times,axiom, % 183.72/184.39 ! [V_A_2,T_b,T_a,V_B_2] : % 183.72/184.39 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => 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 ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__image__times,axiom, % 183.72/184.39 ! [V_B_2,T_b,T_a,V_A_2] : % 183.72/184.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 => 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 ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_insert__times__insert,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__equiv__class,axiom, % 183.72/184.39 ! [V_X_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( 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)))) % 183.72/184.39 => ( 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))) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_vimage__Times,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_UN__Times__distrib,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__def,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__quotient,axiom, % 183.72/184.39 ! [V_r_2,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( 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)))) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setsum__mult__setsum__if__inj,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 183.72/184.39 ( class_Rings_Osemiring__0(T_c) % 183.72/184.39 => ( 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))) % 183.72/184.39 => 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))))))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 183.72/184.39 ! [V_A_2,V_I_2,T_b,T_a] : % 183.72/184.39 ? [B_f] : % 183.72/184.39 ( 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)) % 183.72/184.39 & 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fold__image__Sigma,axiom, % 183.72/184.39 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__mult(T_c) % 183.72/184.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_image__id,axiom, % 183.72/184.39 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 183.72/184.39 % 183.72/184.39 fof(fact_of__int__eq__id,axiom, % 183.72/184.39 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 183.72/184.39 % 183.72/184.39 fof(fact_inj__on__id,axiom, % 183.72/184.39 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 183.72/184.39 % 183.72/184.39 fof(fact_id__def,axiom, % 183.72/184.39 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 183.72/184.39 % 183.72/184.39 fof(fact_id__apply,axiom, % 183.72/184.39 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 183.72/184.39 % 183.72/184.39 fof(fact_vimage__id,axiom, % 183.72/184.39 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__id,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_o__id,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_id__o,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_o__eq__id__dest,axiom, % 183.72/184.39 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 183.72/184.39 ( 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_ca_2) % 183.72/184.39 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__id,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_surj__id,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_folding_Oempty,axiom, % 183.72/184.39 ! [V_F_2,V_f_2,T_b,T_a] : % 183.72/184.39 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 183.72/184.39 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__Pair,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setsum__reindex__id,axiom, % 183.72/184.39 ! [V_B_2,V_f_2,T_a,T_b] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.39 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setprod__reindex__id,axiom, % 183.72/184.39 ! [V_B_2,V_f_2,T_a,T_b] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 183.72/184.39 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setprod__Sigma,axiom, % 183.72/184.39 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__mult(T_c) % 183.72/184.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setsum__Sigma,axiom, % 183.72/184.39 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 183.72/184.39 ( class_Groups_Ocomm__monoid__add(T_c) % 183.72/184.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_card__SigmaI,axiom, % 183.72/184.39 ! [V_B_2,T_b,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 183.72/184.39 => 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) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__SigmaI,axiom, % 183.72/184.39 ! [V_B_2,T_b,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.39 => ( ! [B_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 183.72/184.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_SigmaE,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 183.72/184.39 => ~ ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => ! [B_y] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 183.72/184.39 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__surj,axiom, % 183.72/184.39 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__imageI,axiom, % 183.72/184.39 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__simp,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__ident,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__prod__fun,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__map__pair,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_fst__comp__map__pair,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_snd__comp__map__pair,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair_Ocompositionality,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__compose,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair_Ocomp,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair_Oidentity,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apsnd__def,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_apfst__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair_Oid,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__surj__on,axiom, % 183.72/184.39 ! [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] : % 183.72/184.39 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 183.72/184.39 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__map__pair__image,axiom, % 183.72/184.39 ! [V_f_2,T_b,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_map__pair__inj__on,axiom, % 183.72/184.39 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 183.72/184.39 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 183.72/184.39 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_prod__fun__imageE,axiom, % 183.72/184.39 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_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))) % 183.72/184.39 => ~ ! [B_x,B_y] : % 183.72/184.39 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 183.72/184.39 => ~ 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__def,axiom, % 183.72/184.39 ! [V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 <=> ( 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)))) % 183.72/184.39 & ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__def,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_OwfP(T_a,V_r_2) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__empty,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__Id__on,axiom, % 183.72/184.39 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_accp__wfPD,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_OwfP(T_a,V_r_2) % 183.72/184.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__accp__iff,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_OwfP(T_a,V_r_2) % 183.72/184.39 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__subset,axiom, % 183.72/184.39 ! [V_p_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_OwfP(T_a,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__empty,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__Un,axiom, % 183.72/184.39 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__Int,axiom, % 183.72/184.39 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__onD2,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__onD1,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__onD,axiom, % 183.72/184.39 ! [V_a_2,V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__in__rel,axiom, % 183.72/184.39 ! [V_R_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_R_2) % 183.72/184.39 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__wf__eq,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reflp__def,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Predicate_Oreflp(T_a,V_r_2) % 183.72/184.39 <=> 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__onI,axiom, % 183.72/184.39 ! [V_A_2,V_r_2,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => 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)) ) % 183.72/184.39 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reflpE,axiom, % 183.72/184.39 ! [V_x_2,V_r_2,T_a] : % 183.72/184.39 ( c_Predicate_Oreflp(T_a,V_r_2) % 183.72/184.39 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__acyclicP,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_OwfP(T_a,V_r_2) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Rep__Integ__cases,axiom, % 183.72/184.39 ! [V_y_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 183.72/184.39 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__acyclic,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acyclic__subset,axiom, % 183.72/184.39 ! [V_r_2,V_s_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 183.72/184.39 => ( 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)) % 183.72/184.39 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__acyclic__wf,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 183.72/184.39 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__iff__acyclic__if__finite,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 183.72/184.39 => ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Nitpick_Owf_H__def,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Nitpick_Owf_H(T_a,V_r_2) % 183.72/184.39 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 183.72/184.39 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 183.72/184.39 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Rep__Integ__induct,axiom, % 183.72/184.39 ! [V_P_2,V_y_2] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 183.72/184.39 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 183.72/184.39 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_refl__on__def_H,axiom, % 183.72/184.39 ! [V_r_2,V_A_2,T_a] : % 183.72/184.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.39 <=> ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 183.72/184.39 => 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)) ) % 183.72/184.39 & ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => 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)) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Abs__Integ__induct,axiom, % 183.72/184.39 ! [V_x_2,V_P_2] : % 183.72/184.39 ( ! [B_y] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 183.72/184.39 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 183.72/184.39 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_ball__empty,axiom, % 183.72/184.39 ! [V_P_2,T_a,B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 183.72/184.39 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Powp__def,axiom, % 183.72/184.39 ! [V_B_2,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 183.72/184.39 <=> ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 183.72/184.39 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_INFI__bool__eq,axiom, % 183.72/184.39 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 183.72/184.39 % 183.72/184.39 fof(fact_ball__UNIV,axiom, % 183.72/184.39 ! [V_P_2,T_a] : % 183.72/184.39 ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.72/184.39 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.72/184.39 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Collect__ball__eq,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_congruent__def,axiom, % 183.72/184.39 ! [V_f_2,V_r_2,T_b,T_a] : % 183.72/184.39 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 183.72/184.39 <=> ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_INTER__def,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Inf__Sup,axiom, % 183.72/184.39 ! [V_A_2,T_a] : % 183.72/184.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sup__Inf,axiom, % 183.72/184.39 ! [V_A_2,T_a] : % 183.72/184.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.39 => 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)))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Abs__Integ__cases,axiom, % 183.72/184.39 ! [V_x_2] : % 183.72/184.39 ~ ! [B_y] : % 183.72/184.39 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 183.72/184.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfP__SUP,axiom, % 183.72/184.39 ! [T_a,V_r_2,T_b] : % 183.72/184.39 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 183.72/184.39 => ( ! [B_i,B_j] : % 183.72/184.39 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 183.72/184.39 => 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)) ) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_triples__valid__Suc,axiom, % 183.72/184.39 ! [V_n_2,V_ts_2,T_a] : % 183.72/184.39 ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 183.72/184.39 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 183.72/184.39 => ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 183.72/184.39 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_hoare__valids__def,axiom, % 183.72/184.39 ! [V_ts_2,V_Ga_2,T_a] : % 183.72/184.39 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 183.72/184.39 <=> ! [B_n] : % 183.72/184.39 ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 183.72/184.39 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 183.72/184.39 => ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 183.72/184.39 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Inter__eq,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mem__splitE,axiom, % 183.72/184.39 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 183.72/184.39 ( 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_ca_2),V_p_2))) % 183.72/184.39 => ~ ! [B_x,B_y] : % 183.72/184.39 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 183.72/184.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_mem__splitI2,axiom, % 183.72/184.39 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 183.72/184.39 ( ! [B_a,B_b] : % 183.72/184.39 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 183.72/184.39 => 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_ca_2),V_p_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Eps__split,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wfI__pf,axiom, % 183.72/184.39 ! [V_R_2,T_a] : % 183.72/184.39 ( ! [B_A] : % 183.72/184.39 ( 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))) % 183.72/184.39 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 183.72/184.39 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_someI__ex,axiom, % 183.72/184.39 ! [T_a,V_P_2] : % 183.72/184.39 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.39 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_some__eq__ex,axiom, % 183.72/184.39 ! [T_a,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 183.72/184.39 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_some__eq__trivial,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_some__sym__eq__trivial,axiom, % 183.72/184.39 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 183.72/184.39 % 183.72/184.39 fof(fact_tfl__some,axiom, % 183.72/184.39 ! [T_a,B_P] : % 183.72/184.39 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 183.72/184.39 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_someI,axiom, % 183.72/184.39 ! [T_a,V_x_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.72/184.39 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_exE__some,axiom, % 183.72/184.39 ! [T_a,V_ca_2,V_P_2] : % 183.72/184.39 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.39 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 183.72/184.39 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_split__paired__Eps,axiom, % 183.72/184.39 ! [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)))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Eps__split__eq,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_LeastM__def,axiom, % 183.72/184.39 ! [V_P_2,V_m_2,T_a,T_b] : % 183.72/184.39 ( class_Orderings_Oord(T_b) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_GreatestM__def,axiom, % 183.72/184.39 ! [V_P_2,V_m_2,T_a,T_b] : % 183.72/184.39 ( class_Orderings_Oord(T_b) % 183.72/184.39 => 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))))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_LeastM__nat__lemma,axiom, % 183.72/184.39 ! [V_m_2,T_a,V_k_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_k_2)) % 183.72/184.39 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 183.72/184.39 & ! [B_y] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,B_y)) % 183.72/184.39 => 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))) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_LeastM__nat__le,axiom, % 183.72/184.39 ! [T_a,V_m_2,V_x_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Greatest__def,axiom, % 183.72/184.39 ! [T_a] : % 183.72/184.39 ( class_Orderings_Oord(T_a) % 183.72/184.39 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Sigma__mono,axiom, % 183.72/184.39 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.39 => 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))) ) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_LeastM__natI,axiom, % 183.72/184.39 ! [V_m_2,T_a,V_k_2,V_P_2] : % 183.72/184.39 ( hBOOL(hAPP(V_P_2,V_k_2)) % 183.72/184.39 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_not__acc__down,axiom, % 183.72/184.39 ! [V_R_2,V_x_2,T_a] : % 183.72/184.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 183.72/184.39 => ~ ! [B_z] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acc_OaccI,axiom, % 183.72/184.39 ! [V_r_2,V_x_2,T_a] : % 183.72/184.39 ( ! [B_y] : % 183.72/184.39 ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_max__ext_Osimps,axiom, % 183.72/184.39 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 183.72/184.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 183.72/184.39 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.39 & ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 183.72/184.39 => ? [B_xa] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 183.72/184.39 & 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)) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__no__infinite__down__chainE,axiom, % 183.72/184.39 ! [V_f_2,V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => ~ ! [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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_scomp__unfold,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_setsum__ivl__cong,axiom, % 183.72/184.39 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 183.72/184.39 ( ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.39 & class_Orderings_Oord(T_a) ) % 183.72/184.39 => ( V_a_2 = V_ca_2 % 183.72/184.39 => ( V_b_2 = V_d_2 % 183.72/184.39 => ( ! [B_x] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 183.72/184.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 183.72/184.39 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 183.72/184.39 => 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_ca_2),V_d_2)) ) ) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_scomp__apply,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_scomp__scomp,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Pair__scomp,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_scomp__Pair,axiom, % 183.72/184.39 ! [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 ). % 183.72/184.39 % 183.72/184.39 fof(fact_scomp__def,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_iterate_Osimps,axiom, % 183.72/184.39 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 183.72/184.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_less__eq,axiom, % 183.72/184.39 ! [V_n_2,V_m_2] : % 183.72/184.39 ( 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))) % 183.72/184.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_wf__trancl,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.39 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_less__than__def,axiom, % 183.72/184.39 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 183.72/184.39 % 183.72/184.39 fof(fact_acyclic__def,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 183.72/184.39 <=> ! [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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl_Or__into__trancl,axiom, % 183.72/184.39 ! [V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__subset__Field2,axiom, % 183.72/184.39 ! [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))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_r__into__trancl_H,axiom, % 183.72/184.39 ! [V_r_2,V_p_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__empty,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__domain,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__range,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_finite__trancl,axiom, % 183.72/184.39 ! [V_r_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 183.72/184.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_r__r__into__trancl,axiom, % 183.72/184.39 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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_ca_2)),V_R_2)) % 183.72/184.39 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__into__trancl2,axiom, % 183.72/184.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 183.72/184.39 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 183.72/184.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( 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_ca_2)),V_r_2)) % 183.72/184.39 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__trans,axiom, % 183.72/184.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 183.72/184.39 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__mono,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,V_p_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 183.72/184.39 => ( 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)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__unfold,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__subset__Sigma,axiom, % 183.72/184.39 ! [V_A_2,V_r_2,T_a] : % 183.72/184.39 ( 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)))) % 183.72/184.39 => 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__Int__subset,axiom, % 183.72/184.39 ! [V_s_2,V_r_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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)) % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_log_Osimps,axiom, % 183.72/184.39 ! [V_i,V_b] : % 183.72/184.39 ( ( ( 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))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 183.72/184.39 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 183.72/184.39 & ( ~ ( 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))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 183.72/184.39 => 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))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_minus__shift__def,axiom, % 183.72/184.39 ! [V_r,V_l,V_k] : % 183.72/184.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 183.72/184.39 => 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) ) % 183.72/184.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 183.72/184.39 => 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) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_inc__shift__def,axiom, % 183.72/184.39 ! [V_k,V_v] : % 183.72/184.39 ( ( V_v = V_k % 183.72/184.39 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 183.72/184.39 & ( V_v != V_k % 183.72/184.39 => 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)) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_range,axiom, % 183.72/184.39 ! [V_s,V_k] : % 183.72/184.39 ( 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)) % 183.72/184.39 => 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)) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__insert,axiom, % 183.72/184.39 ! [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)))))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reflcl__set__eq,axiom, % 183.72/184.39 ! [V_y_2,V_x_2,V_r_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 <=> 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_r__into__rtrancl,axiom, % 183.72/184.39 ! [V_r_2,V_p_2,T_a] : % 183.72/184.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 183.72/184.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl_Ortrancl__refl,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_IdI,axiom, % 183.72/184.39 ! [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))) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__into__rtrancl,axiom, % 183.72/184.39 ! [V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.39 => 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))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__rtrancl__absorb,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__trancl__absorb,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_reflcl__trancl,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__reflcl,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__unfold__right,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_trancl__unfold__left,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Domain__rtrancl,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_Range__rtrancl,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__empty,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__unfold,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_in__rtrancl__UnI,axiom, % 183.72/184.39 ! [V_S_2,V_R_2,V_x_2,T_a] : % 183.72/184.39 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 183.72/184.39 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 183.72/184.39 => 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)))) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_r__comp__rtrancl__eq,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__idemp__self__comp,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__reflcl,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__Un__rtrancl,axiom, % 183.72/184.39 ! [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)) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__reflcl__absorb,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl__idemp,axiom, % 183.72/184.39 ! [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) ). % 183.72/184.39 % 183.72/184.39 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 183.72/184.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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)) % 183.72/184.39 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 183.72/184.39 => 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 183.72/184.39 % 183.72/184.39 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 183.72/184.39 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.39 ( 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))) % 183.72/184.40 => ( 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_ca_2)),V_r_2)) % 183.72/184.40 => 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__trans,axiom, % 183.72/184.40 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 183.72/184.40 => 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__r__diff__Id,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_refl__rtrancl,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Image__Id,axiom, % 183.72/184.40 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 183.72/184.40 % 183.72/184.40 fof(fact_Id__O__R,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_R__O__Id,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_Image__closed__trancl,axiom, % 183.72/184.40 ! [V_X_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__Un__subset,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__subset__rtrancl,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__subset,axiom, % 183.72/184.40 ! [V_S_2,V_R_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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))) % 183.72/184.40 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__mono,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__Int__subset,axiom, % 183.72/184.40 ! [V_r_2,V_s_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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)) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_pair__in__Id__conv,axiom, % 183.72/184.40 ! [V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> V_a_2 = V_b_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__eq__or__trancl,axiom, % 183.72/184.40 ! [V_R_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( V_x_2 = V_y_2 % 183.72/184.40 | ( V_x_2 != V_y_2 % 183.72/184.40 & 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__into__trancl2,axiom, % 183.72/184.40 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 183.72/184.40 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtranclD,axiom, % 183.72/184.40 ! [V_R_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( V_a_2 = V_b_2 % 183.72/184.40 | ( V_a_2 != V_b_2 % 183.72/184.40 & 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__into__trancl1,axiom, % 183.72/184.40 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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_ca_2)),V_r_2)) % 183.72/184.40 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__rtrancl__trancl,axiom, % 183.72/184.40 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 183.72/184.40 => 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_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__trancl__trancl,axiom, % 183.72/184.40 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Domain__Id,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Range__Id,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_refl__Id,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_pair__leq__def,axiom, % 183.72/184.40 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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Not__Domain__rtrancl,axiom, % 183.72/184.40 ! [V_y_2,V_R_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 183.72/184.40 => ( 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))) % 183.72/184.40 <=> V_x_2 = V_y_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_acc__downwards__aux,axiom, % 183.72/184.40 ! [V_r_2,V_a_2,V_b_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_acc__downwards,axiom, % 183.72/184.40 ! [V_b_2,V_r_2,V_a_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_wf__insert,axiom, % 183.72/184.40 ! [V_r_2,V_x_2,V_y_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.40 & ~ 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_acyclic__insert,axiom, % 183.72/184.40 ! [V_r_2,V_x_2,V_y_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 183.72/184.40 & ~ 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_refl__reflcl,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Id__def,axiom, % 183.72/184.40 ! [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))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_irrefl__diff__Id,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_pred__nat__trancl__eq__le,axiom, % 183.72/184.40 ! [V_n_2,V_m_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__subset__Sigma__aux,axiom, % 183.72/184.40 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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)))) % 183.72/184.40 => ( V_a_2 = V_b_2 % 183.72/184.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_irrefl__tranclI,axiom, % 183.72/184.40 ! [V_x_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ~ 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sequence__trans,axiom, % 183.72/184.40 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 183.72/184.40 ( ! [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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__converse,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__Id,axiom, % 183.72/184.40 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__INTER,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__UNION,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converseD,axiom, % 183.72/184.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converseI,axiom, % 183.72/184.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__iff,axiom, % 183.72/184.40 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__rel__comp,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__Un,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__Id__on,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__inv__image,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__Int,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__converse,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__converse,axiom, % 183.72/184.40 ! [V_r_2,T_b,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 183.72/184.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Field__converse,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_refl__on__converse,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 183.72/184.40 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_acyclic__converse,axiom, % 183.72/184.40 ! [V_r_2,T_a] : % 183.72/184.40 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 183.72/184.40 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__converse,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_wf__converse__trancl,axiom, % 183.72/184.40 ! [V_r_2,T_a] : % 183.72/184.40 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 183.72/184.40 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_equiv__comp__eq,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.40 => 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 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Range__converse,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Domain__converse,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Range__def,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__converseD,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__converseI,axiom, % 183.72/184.40 ! [V_r_2,V_x_2,V_y_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__converseD,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__converseI,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Image__subset__eq,axiom, % 183.72/184.40 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 <=> 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_refl__on__comp__subset,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_comp__equivI,axiom, % 183.72/184.40 ! [V_A_2,V_r_2,T_a] : % 183.72/184.40 ( 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 % 183.72/184.40 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 183.72/184.40 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__acyclic__wf__converse,axiom, % 183.72/184.40 ! [V_r_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 183.72/184.40 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 183.72/184.40 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converse__def,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Image__INT__eq,axiom, % 183.72/184.40 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 183.72/184.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_total__on__diff__Id,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__Id,axiom, % 183.72/184.40 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__rel__comp,axiom, % 183.72/184.40 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 183.72/184.40 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__subset,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_b,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 183.72/184.40 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__Id__on,axiom, % 183.72/184.40 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_total__on__empty,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_total__on__converse,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 183.72/184.40 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__def,axiom, % 183.72/184.40 ! [V_r_2,T_b,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 183.72/184.40 <=> ! [B_x,B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ! [B_z] : % 183.72/184.40 ( 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)) % 183.72/184.40 => B_y = B_z ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valuedD,axiom, % 183.72/184.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ( 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)) % 183.72/184.40 => V_y_2 = V_z_2 ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_total__on__def,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 183.72/184.40 <=> ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.40 => ! [B_xa] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 183.72/184.40 => ( B_x != B_xa % 183.72/184.40 => ( 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)) % 183.72/184.40 | 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)) ) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__confluent,axiom, % 183.72/184.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 | 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))) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Image__Int__eq,axiom, % 183.72/184.40 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 183.72/184.40 ! [V_R_2,V_p_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_acyclicI,axiom, % 183.72/184.40 ! [V_r_2,T_a] : % 183.72/184.40 ( ! [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))) % 183.72/184.40 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_single__valued__rel__pow,axiom, % 183.72/184.40 ! [V_n_2,V_R_2,T_a] : % 183.72/184.40 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_wf__exp,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow__mult,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow__swap1,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_comp__funpow,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__1,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__commute,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__imp__rtrancl,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_p_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__power,axiom, % 183.72/184.40 ! [V_R_2,V_p_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 183.72/184.40 <=> ? [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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_relpow_Osimps_I2_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__add,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_relpow_Osimps_I1_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__0__I,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__0__E,axiom, % 183.72/184.40 ! [V_R_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => V_x_2 = V_y_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__Suc__I,axiom, % 183.72/184.40 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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)) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__Suc__I2,axiom, % 183.72/184.40 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow_Osimps_I2_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow__add,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow_Osimps_I1_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_trancl__power,axiom, % 183.72/184.40 ! [V_R_2,V_p_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 183.72/184.40 <=> ? [B_n] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 183.72/184.40 & 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_funpow__code__def,axiom, % 183.72/184.40 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__E2,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => V_x_2 != V_z_2 ) % 183.72/184.40 => ~ ! [B_y,B_m] : % 183.72/184.40 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ~ 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))) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__E,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => V_x_2 != V_z_2 ) % 183.72/184.40 => ~ ! [B_y,B_m] : % 183.72/184.40 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ~ 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)) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__Un__separatorE,axiom, % 183.72/184.40 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => ( ! [B_x] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ! [B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => B_x = B_y ) ) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__Un__separator__converseE,axiom, % 183.72/184.40 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => ( ! [B_x] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ! [B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => B_y = B_x ) ) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__Suc__D2,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ? [B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 & 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__Suc__E,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_y] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__pow__Suc__E2,axiom, % 183.72/184.40 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ~ 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tranclD,axiom, % 183.72/184.40 ! [V_R_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ? [B_z] : % 183.72/184.40 ( 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)) % 183.72/184.40 & 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tranclD2,axiom, % 183.72/184.40 ! [V_R_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ? [B_z] : % 183.72/184.40 ( 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))) % 183.72/184.40 & 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_IdE,axiom, % 183.72/184.40 ! [V_p_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 183.72/184.40 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nat__intermed__int__val,axiom, % 183.72/184.40 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 183.72/184.40 ( ! [B_i] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 183.72/184.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 183.72/184.40 => 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))) ) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 183.72/184.40 => ? [B_i] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 183.72/184.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 183.72/184.40 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_mod__div__decomp,axiom, % 183.72/184.40 ! [V_b,V_a,T_a] : % 183.72/184.40 ( class_Divides_Osemiring__div(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_wf__eq__minimal,axiom, % 183.72/184.40 ! [V_r_2,T_a] : % 183.72/184.40 ( c_Wellfounded_Owf(T_a,V_r_2) % 183.72/184.40 <=> ! [B_Q] : % 183.72/184.40 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 183.72/184.40 => ? [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 183.72/184.40 & ! [B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_transfer__nat__int__set__cong,axiom, % 183.72/184.40 ! [V_P_H_2,V_P_2] : % 183.72/184.40 ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 183.72/184.40 => ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.40 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Int__Collect__mono,axiom, % 183.72/184.40 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.40 => ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.40 => ( hBOOL(hAPP(V_P_2,B_x)) % 183.72/184.40 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 183.72/184.40 => 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)))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_UnionE,axiom, % 183.72/184.40 ! [V_C_2,V_A_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_X] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 183.72/184.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_converseE,axiom, % 183.72/184.40 ! [V_r_2,V_yx_2,T_b,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_x,B_y] : % 183.72/184.40 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 183.72/184.40 => ~ 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rel__compE,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_x,B_y,B_z] : % 183.72/184.40 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ~ 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Oplus__frac__def,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Otimes__frac__def,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Oof__frac__def,axiom, % 183.72/184.40 ! [V_q,T_a,T_b] : % 183.72/184.40 ( ( class_Rings_Oinverse(T_b) % 183.72/184.40 & class_Rings_Oring__1(T_b) ) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Oless__frac__def,axiom, % 183.72/184.40 ! [V_r_2,V_q_2,T_a] : % 183.72/184.40 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 183.72/184.40 <=> 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 183.72/184.40 ! [V_r_2,V_q_2,T_a] : % 183.72/184.40 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 183.72/184.40 <=> 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Onum__def,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Odenom__def,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_setprod__pos,axiom, % 183.72/184.40 ! [V_f_2,V_A_2,T_a,T_b] : % 183.72/184.40 ( class_Rings_Olinordered__semidom(T_b) % 183.72/184.40 => ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_internal__split__def,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_internal__split__conv,axiom, % 183.72/184.40 ! [V_b_2,V_a_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ). % 183.72/184.40 % 183.72/184.40 fof(fact_setprod__nonneg,axiom, % 183.72/184.40 ! [V_f_2,V_A_2,T_a,T_b] : % 183.72/184.40 ( class_Rings_Olinordered__semidom(T_b) % 183.72/184.40 => ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_bool_Osize_I2_J,axiom, % 183.72/184.40 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.40 % 183.72/184.40 fof(fact_bool_Osize_I1_J,axiom, % 183.72/184.40 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__less__ub,axiom, % 183.72/184.40 ! [V_u_2,V_f_2] : % 183.72/184.40 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lenlex__def,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexn__length,axiom, % 183.72/184.40 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 183.72/184.40 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_neq__if__length__neq,axiom, % 183.72/184.40 ! [V_ys,V_xs,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => V_xs != V_ys ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lenlex__conv,axiom, % 183.72/184.40 ! [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)))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__sublist,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexn_Osimps_I2_J,axiom, % 183.72/184.40 ! [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)))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_impossible__Cons,axiom, % 183.72/184.40 ! [V_x,V_ys,V_xs,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Oinject,axiom, % 183.72/184.40 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( V_a_2 = V_a_H_2 % 183.72/184.40 & V_list_2 = V_list_H_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_not__Cons__self2,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 183.72/184.40 % 183.72/184.40 fof(fact_not__Cons__self,axiom, % 183.72/184.40 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osize_I4_J,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__in__lex,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( ( 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)) % 183.72/184.40 & 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) ) % 183.72/184.40 | ( V_x_2 = V_y_2 % 183.72/184.40 & 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__Cons__def,axiom, % 183.72/184.40 ! [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)))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_pick_Osimps,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_i] : % 183.72/184.40 ( ( 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))) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_select__weight__cons__zero,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__cons__cons,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( 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)) % 183.72/184.40 | ( V_a_2 = V_b_2 % 183.72/184.40 & 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__lex,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( 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))) % 183.72/184.40 & 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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)))) % 183.72/184.40 => 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)))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osize_I2_J,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__acc__listrel1I,axiom, % 183.72/184.40 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 183.72/184.40 => ( 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)))) % 183.72/184.40 => 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)))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__converse,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__mono,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1I2,axiom, % 183.72/184.40 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 183.72/184.40 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__eq__len,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__listrel1__eq__len,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__listrel1__converse,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 <=> 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1I1,axiom, % 183.72/184.40 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__listrel1__Cons,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( ( 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)) % 183.72/184.40 & V_xs_2 = V_ys_2 ) % 183.72/184.40 | ( V_x_2 = V_y_2 % 183.72/184.40 & 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Cons,axiom, % 183.72/184.40 ! [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))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__irreflexive,axiom, % 183.72/184.40 ! [V_y_2,V_r_2,T_a] : % 183.72/184.40 ( ! [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)) % 183.72/184.40 => ~ 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__rtrancl__refl,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__mono,axiom, % 183.72/184.40 ! [V_s_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__eq__len,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__rtrancl__trans,axiom, % 183.72/184.40 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => ( 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)))) % 183.72/184.40 => 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)))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__reflcl__if__listrel1,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__subset__listrel,axiom, % 183.72/184.40 ! [V_r_H_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel_OCons,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrelp__listrel__eq,axiom, % 183.72/184.40 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Cons2,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_x,B_xs] : % 183.72/184.40 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ~ 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrelp_Oequations_I2_J,axiom, % 183.72/184.40 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 183.72/184.40 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrelp_OCons,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 183.72/184.40 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Cons1,axiom, % 183.72/184.40 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_y,B_ys] : % 183.72/184.40 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ~ 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__subset,axiom, % 183.72/184.40 ! [V_A_2,V_r_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__UNIV,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__mono,axiom, % 183.72/184.40 ! [V_B_2,V_A_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_equiv__listrel,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__refl__on,axiom, % 183.72/184.40 ! [V_r_2,V_A_2,T_a] : % 183.72/184.40 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__in__lists__iff,axiom, % 183.72/184.40 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.40 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__accD,axiom, % 183.72/184.40 ! [V_r_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__accI,axiom, % 183.72/184.40 ! [V_r_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__iff__nth,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( 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) % 183.72/184.40 & ! [B_n] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__linear,axiom, % 183.72/184.40 ! [V_y_2,V_x_2,V_r_2,T_a] : % 183.72/184.40 ( ! [B_a,B_b] : % 183.72/184.40 ( 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)) % 183.72/184.40 | B_a = B_b % 183.72/184.40 | 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)) ) % 183.72/184.40 => ( 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))) % 183.72/184.40 | V_x_2 = V_y_2 % 183.72/184.40 | 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_infinite__UNIV__listI,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__eq__iff__nth__eq,axiom, % 183.72/184.40 ! [T_a,V_ys_2,V_xs_2] : % 183.72/184.40 ( V_xs_2 = V_ys_2 % 183.72/184.40 <=> ( 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) % 183.72/184.40 & ! [B_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__Cons__Suc,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__Cons__0,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth_Osimps,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__Cons_H,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_n] : % 183.72/184.40 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 183.72/184.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__Cons__number__of,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_v] : % 183.72/184.40 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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 ) % 183.72/184.40 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__take__index__conv,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( ( 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))) % 183.72/184.40 & 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 ) % 183.72/184.40 | ? [B_i] : % 183.72/184.40 ( 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)))) % 183.72/184.40 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 183.72/184.40 & 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__sublist,axiom, % 183.72/184.40 ! [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))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__set,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__subset__Cons,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__all,axiom, % 183.72/184.40 ! [V_n,V_xs,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__take__subset,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__take__subset__set__take,axiom, % 183.72/184.40 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__sublist__subset,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__take,axiom, % 183.72/184.40 ! [V_xs,T_a,V_n,V_i] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__upt__eq__take,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Suc__Cons,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_notin__set__sublistI,axiom, % 183.72/184.40 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => ~ 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__takeD,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__sublistD,axiom, % 183.72/184.40 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__ConsD,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => ( V_y_2 = V_x_2 % 183.72/184.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__take,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__take,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_List_Oset_Osimps_I2_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_card__length,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_all__set__conv__all__nth,axiom, % 183.72/184.40 ! [V_P_2,V_xs_2,T_a] : % 183.72/184.40 ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.72/184.40 <=> ! [B_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__size__estimation,axiom, % 183.72/184.40 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__size__estimation_H,axiom, % 183.72/184.40 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__lists__conv__set,axiom, % 183.72/184.40 ! [V_A_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 183.72/184.40 <=> ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__pos__if__in__set,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__mem,axiom, % 183.72/184.40 ! [V_xs_2,T_a,V_n_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__conv__nth,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 <=> ? [B_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__eq__set,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__conv__nth,axiom, % 183.72/184.40 ! [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))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__lists__length__eq,axiom, % 183.72/184.40 ! [V_n_2,V_A_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__lists__length__le,axiom, % 183.72/184.40 ! [V_n_2,V_A_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__iff__zip,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( 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) % 183.72/184.40 & ! [B_x] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__zip,axiom, % 183.72/184.40 ! [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)))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__zip,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__zip,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__Cons__Cons,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__eq__iff__zip__eq,axiom, % 183.72/184.40 ! [T_a,V_ys_2,V_xs_2] : % 183.72/184.40 ( V_xs_2 = V_ys_2 % 183.72/184.40 <=> ( 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) % 183.72/184.40 & ! [B_x] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__same,axiom, % 183.72/184.40 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 & V_a_2 = V_b_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__zip__leftD,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__zip__rightD,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__zipE,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__zip,axiom, % 183.72/184.40 ! [V_ys,T_b,V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_greaterThanLessThan__upto,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__setsum__nth,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 183.72/184.40 ! [V_ns_2] : % 183.72/184.40 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 <=> ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 183.72/184.40 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__upto,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_atLeastAtMost__upto,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_elem__le__listsum__nat,axiom, % 183.72/184.40 ! [V_ns,V_k] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__simps_I2_J,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a] : % 183.72/184.40 ( class_Groups_Omonoid__add(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_atLeastLessThan__upto,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_greaterThanAtMost__upto,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nat__list__def,axiom, % 183.72/184.40 ! [V_l_2] : % 183.72/184.40 ( c_List_Onat__list(V_l_2) % 183.72/184.40 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__size__pointwise,axiom, % 183.72/184.40 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 183.72/184.40 ( ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__update__nat,axiom, % 183.72/184.40 ! [V_n,V_ns,V_k] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__take,axiom, % 183.72/184.40 ! [V_xs,T_a,V_n] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__beyond,axiom, % 183.72/184.40 ! [V_x,V_i,V_xs,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__id,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__list__update__neq,axiom, % 183.72/184.40 ! [V_x,V_xs,T_a,V_j,V_i] : % 183.72/184.40 ( V_i != V_j % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__list__update,axiom, % 183.72/184.40 ! [V_x,V_xs,T_a,V_k] : % 183.72/184.40 ( ( 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)) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( 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)) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__list__update,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__update,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_update__zip,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__swap,axiom, % 183.72/184.40 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 183.72/184.40 ( V_i != V_i_H % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__overwrite,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update_Osimps_I2_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__code_I3_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__code_I2_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__butlastD,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__update__subsetI,axiom, % 183.72/184.40 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__update__subset__insert,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__list__update__eq,axiom, % 183.72/184.40 ! [V_x,V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__same__conv,axiom, % 183.72/184.40 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 183.72/184.40 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__list__update,axiom, % 183.72/184.40 ! [V_x,V_j,V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ( V_i = V_j % 183.72/184.40 => 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 ) % 183.72/184.40 & ( V_i != V_j % 183.72/184.40 => 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) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__butlast,axiom, % 183.72/184.40 ! [V_xs,T_a,V_n] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__butlast,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__update__memI,axiom, % 183.72/184.40 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__conv__take,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1__iff__update,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ? [B_y,B_n] : % 183.72/184.40 ( 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)) % 183.72/184.40 & 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))) % 183.72/184.40 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__list__update,axiom, % 183.72/184.40 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => ( ~ 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)))))) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__upto,axiom, % 183.72/184.40 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__take,axiom, % 183.72/184.40 ! [V_i,V_xs,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__sublistI,axiom, % 183.72/184.40 ! [V_I_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__zipI2,axiom, % 183.72/184.40 ! [V_xs,T_b,V_ys,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__zipI1,axiom, % 183.72/184.40 ! [V_ys,T_b,V_xs,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct_Osimps_I2_J,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 183.72/184.40 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_card__distinct,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__card,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__eq__iff__index__eq,axiom, % 183.72/184.40 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ( 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) % 183.72/184.40 <=> V_i_2 = V_j_2 ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__conv__nth,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 <=> ! [B_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ! [B_j] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( B_i != B_j % 183.72/184.40 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__listsum__conv__Setsum,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.40 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nitpick_Ocard_H__def,axiom, % 183.72/184.40 ! [V_A_2,T_a] : % 183.72/184.40 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => 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)))) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_dom__map__upds,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__apply__nontin,axiom, % 183.72/184.40 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__list__update2__drop,axiom, % 183.72/184.40 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__take__lemma,axiom, % 183.72/184.40 ! [V_ys,V_xs,T_a,V_k] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( 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))) % 183.72/184.40 => ( ! [B_i] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 183.72/184.40 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 183.72/184.40 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__map__upds,axiom, % 183.72/184.40 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => ( 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)) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__map__insert,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__restrict,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__in,axiom, % 183.72/184.40 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_dom__restrict,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__upd__restrict,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__upd__restrict__conv,axiom, % 183.72/184.40 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__fun__upd,axiom, % 183.72/184.40 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__remove1__eq,axiom, % 183.72/184.40 ! [V_x_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Cons__number__of,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_v] : % 183.72/184.40 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists_ONil,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Nil2,axiom, % 183.72/184.40 ! [V_r_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Nil1,axiom, % 183.72/184.40 ! [V_r_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__code_I1_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update_Osimps_I1_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__nonempty,axiom, % 183.72/184.40 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__empty,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__empty2,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_List_Oset_Osimps_I1_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__0__conv,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osize_I3_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__simps_I1_J,axiom, % 183.72/184.40 ! [T_a] : % 183.72/184.40 ( class_Groups_Omonoid__add(T_a) % 183.72/184.40 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__Nil,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip_Osimps_I1_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrelp_Oequations_I1_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrelp_ONil,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osize_I1_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1__commute,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1_Osimps_I1_J,axiom, % 183.72/184.40 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__nil,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__eq__Nil,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__0,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Nil,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upto__empty,axiom, % 183.72/184.40 ! [V_i,V_j] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 183.72/184.40 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osimps_I2_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osimps_I3_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1_Osimps_I2_J,axiom, % 183.72/184.40 ! [V_xs,T_a,V_y,V_x] : % 183.72/184.40 ( ( V_x = V_y % 183.72/184.40 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 183.72/184.40 & ( V_x != V_y % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast_Osimps_I2_J,axiom, % 183.72/184.40 ! [V_x,T_a,V_xs] : % 183.72/184.40 ( ( V_xs = c_List_Olist_ONil(T_a) % 183.72/184.40 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 183.72/184.40 & ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast_Osimps_I1_J,axiom, % 183.72/184.40 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__Nil1,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__Nil2,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__remove1,axiom, % 183.72/184.40 ! [V_x,V_xs,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct_Osimps_I1_J,axiom, % 183.72/184.40 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__butlast,axiom, % 183.72/184.40 ! [T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__remove1,axiom, % 183.72/184.40 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 183.72/184.40 ( V_a_2 != V_b_2 % 183.72/184.40 => ( 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)))) % 183.72/184.40 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_notin__set__remove1,axiom, % 183.72/184.40 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => ~ 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1__idem,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__empty,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__remove1__subset,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__greater__0__conv,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__1__Cons,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_not__listrel1__Nil,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_not__Nil__listrel1,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel_ONil,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__Nil__right,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nil2__notin__lex,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nil__notin__lex,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upto_Osimps,axiom, % 183.72/184.40 ! [V_j,V_i] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 183.72/184.40 => 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)) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 183.72/184.40 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__singleton,axiom, % 183.72/184.40 ! [V_x_2,T_a,V_A_2] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 183.72/184.40 => 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)) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lists__empty,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Cons_H,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_n] : % 183.72/184.40 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upto__rec__number__of,axiom, % 183.72/184.40 ! [V_n,V_m] : % 183.72/184.40 ( ( 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))) % 183.72/184.40 => 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))) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel__Nil,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__Cons__sing__Nil,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__remove1,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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)) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upto_Opsimps,axiom, % 183.72/184.40 ! [V_j_2,V_i_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 183.72/184.40 => 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)) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 183.72/184.40 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_select,axiom, % 183.72/184.40 ! [V_s_2,T_a,V_xs_2] : % 183.72/184.40 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listset_Osimps_I1_J,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osimps_I5_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list_Osimps_I4_J,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_listset_Osimps_I2_J,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__Cons1,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sorted__list__of__set__remove,axiom, % 183.72/184.40 ! [V_x_2,V_A_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upto_Opinduct,axiom, % 183.72/184.40 ! [V_P_2,V_a1_2,V_a0_2] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ! [B_i,B_j] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 183.72/184.40 => 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)) ) % 183.72/184.40 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 183.72/184.40 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sorted__list__of__set__empty,axiom, % 183.72/184.40 ! [T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_anamorph_Osimps,axiom, % 183.72/184.40 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 183.72/184.40 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__Cons,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__eq__Cons__conv,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 183.72/184.40 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 183.72/184.40 | ? [B_ys_H] : % 183.72/184.40 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 183.72/184.40 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__eq__append__conv,axiom, % 183.72/184.40 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 183.72/184.40 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 183.72/184.40 | ? [B_ys_H] : % 183.72/184.40 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 183.72/184.40 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append1__eq__conv,axiom, % 183.72/184.40 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( V_xs_2 = V_ys_2 % 183.72/184.40 & V_x_2 = V_y_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__Cons,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Cons__eq__appendI,axiom, % 183.72/184.40 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 183.72/184.40 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 183.72/184.40 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__append,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__append,axiom, % 183.72/184.40 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => ( 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) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__append,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__append,axiom, % 183.72/184.40 ! [V_ys,V_xs,T_a] : % 183.72/184.40 ( class_Groups_Omonoid__add(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__eq__appendI,axiom, % 183.72/184.40 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 183.72/184.40 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 183.72/184.40 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__same__eq,axiom, % 183.72/184.40 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> V_ys_2 = V_zs_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_same__append__eq,axiom, % 183.72/184.40 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> V_ys_2 = V_zs_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__eq__append__conv2,axiom, % 183.72/184.40 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ? [B_us] : % 183.72/184.40 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 183.72/184.40 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 183.72/184.40 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 183.72/184.40 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__assoc,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__in__lists__conv,axiom, % 183.72/184.40 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 183.72/184.40 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__upds__append__drop,axiom, % 183.72/184.40 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__upds__append2__drop,axiom, % 183.72/184.40 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.40 ( 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) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__append,axiom, % 183.72/184.40 ! [V_xs,T_a,V_ys] : % 183.72/184.40 ( ( V_ys = c_List_Olist_ONil(T_a) % 183.72/184.40 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 183.72/184.40 & ( V_ys != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__Nil,axiom, % 183.72/184.40 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 183.72/184.40 % 183.72/184.40 fof(fact_Nil__is__append__conv,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 183.72/184.40 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 183.72/184.40 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__Nil2,axiom, % 183.72/184.40 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 183.72/184.40 % 183.72/184.40 fof(fact_self__append__conv,axiom, % 183.72/184.40 ! [V_ys_2,T_a,V_xs_2] : % 183.72/184.40 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 183.72/184.40 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_self__append__conv2,axiom, % 183.72/184.40 ! [V_xs_2,T_a,V_ys_2] : % 183.72/184.40 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__is__Nil__conv,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 183.72/184.40 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__self__conv,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 183.72/184.40 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__self__conv2,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_eq__Nil__appendI,axiom, % 183.72/184.40 ! [T_a,V_ys,V_xs] : % 183.72/184.40 ( V_xs = V_ys % 183.72/184.40 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__append__length,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__append__length__plus,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__append,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__append1,axiom, % 183.72/184.40 ! [V_x,V_ys,V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__length,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1__append,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__butlast__appendI,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 183.72/184.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 183.72/184.40 => 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__snoc,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__listrel1I,axiom, % 183.72/184.40 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( ( ( 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))) % 183.72/184.40 & V_us_2 = V_vs_2 ) % 183.72/184.40 | ( V_xs_2 = V_ys_2 % 183.72/184.40 & 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))) ) ) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__append__leftI,axiom, % 183.72/184.40 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__append,axiom, % 183.72/184.40 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 183.72/184.40 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 183.72/184.40 & 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__append,axiom, % 183.72/184.40 ! [V_ys,V_xs,T_a,V_n] : % 183.72/184.40 ( ( 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))) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_list__update__append,axiom, % 183.72/184.40 ! [V_x,V_ys,V_xs,T_a,V_n] : % 183.72/184.40 ( ( 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))) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sublist__append,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1I,axiom, % 183.72/184.40 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ( 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)) % 183.72/184.40 => ( 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)) % 183.72/184.40 => 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))) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__append__left__rightI,axiom, % 183.72/184.40 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Suc__conv__app__nth,axiom, % 183.72/184.40 ! [V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_snoc__listrel1__snoc__iff,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ( ( 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))) % 183.72/184.40 & V_x_2 = V_y_2 ) % 183.72/184.40 | ( V_xs_2 = V_ys_2 % 183.72/184.40 & 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listrel1E,axiom, % 183.72/184.40 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ~ ! [B_x,B_y] : % 183.72/184.40 ( 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)) % 183.72/184.40 => ! [B_us,B_vs] : % 183.72/184.40 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 183.72/184.40 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__append__leftD,axiom, % 183.72/184.40 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => ( ! [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)) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate1__def,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__append1,axiom, % 183.72/184.40 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_image__map__upd,axiom, % 183.72/184.40 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__rotate1,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__rotate1,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_dom__const,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_domI,axiom, % 183.72/184.40 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 183.72/184.40 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insert__dom,axiom, % 183.72/184.40 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 183.72/184.40 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct1__rotate,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 183.72/184.40 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upd__eqD1,axiom, % 183.72/184.40 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => V_x_2 = V_y_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upd__triv,axiom, % 183.72/184.40 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 183.72/184.40 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 183.72/184.40 => 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 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upd__Some__unfold,axiom, % 183.72/184.40 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( ( V_x_2 = V_a_2 % 183.72/184.40 & V_b_2 = V_y_2 ) % 183.72/184.40 | ( V_x_2 != V_a_2 % 183.72/184.40 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate1__is__Nil__conv,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_finite__range__updI,axiom, % 183.72/184.40 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 183.72/184.40 ( 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))))) % 183.72/184.40 => 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))))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__twist,axiom, % 183.72/184.40 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 183.72/184.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_restrict__upd__same,axiom, % 183.72/184.40 ! [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))))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__simps,axiom, % 183.72/184.40 ! [V_xs,V_x,T_b,T_a] : % 183.72/184.40 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 183.72/184.40 & 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate1__length01,axiom, % 183.72/184.40 ! [V_xs,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upd__upds__conv__if,axiom, % 183.72/184.40 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 183.72/184.40 ( ( 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)))) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( ~ 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)))) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_option_Osize_I2_J,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_option_Osimps_I5_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_option_Oinject,axiom, % 183.72/184.40 ! [V_a_H_2,V_a_2,T_a] : % 183.72/184.40 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 183.72/184.40 <=> V_a_2 = V_a_H_2 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_inj__Some,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_the_Osimps,axiom, % 183.72/184.40 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 183.72/184.40 % 183.72/184.40 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_upd__conv__take__nth__drop,axiom, % 183.72/184.40 ! [V_a,V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__take__drop__id,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__via__drop,axiom, % 183.72/184.40 ! [V_ys,V_y,V_xs,V_n,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 183.72/184.40 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__1__Cons,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Suc__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__drop__subset,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_in__set__dropD,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 183.72/184.40 ( 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)))) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__drop,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__zip,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__drop,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__0,axiom, % 183.72/184.40 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__drop,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__take,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_butlast__drop,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__butlast,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__drop,axiom, % 183.72/184.40 ! [V_i,V_xs,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Nil,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__drop__subset__set__drop,axiom, % 183.72/184.40 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 183.72/184.40 => 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)))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__all,axiom, % 183.72/184.40 ! [V_n,V_xs,T_a] : % 183.72/184.40 ( 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)) % 183.72/184.40 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__eq__Nil,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__append,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__eq__conv__conj,axiom, % 183.72/184.40 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 183.72/184.40 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 183.72/184.40 <=> ( 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) % 183.72/184.40 & 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Cons_H,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_n] : % 183.72/184.40 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__drop,axiom, % 183.72/184.40 ! [V_xs,T_a,V_i,V_n] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_append__eq__append__conv__if,axiom, % 183.72/184.40 ! [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] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( ( 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))) % 183.72/184.40 => ( 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) % 183.72/184.40 & 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) ) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => ( 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 % 183.72/184.40 & 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 ) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_nth__drop_H,axiom, % 183.72/184.40 ! [V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Cons__number__of,axiom, % 183.72/184.40 ! [V_xs,V_x,T_a,V_v] : % 183.72/184.40 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__add,axiom, % 183.72/184.40 ! [V_xs,T_a,V_j,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_elem__set,axiom, % 183.72/184.40 ! [V_xo_2,V_x_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 183.72/184.40 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__append2,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_zip__append1,axiom, % 183.72/184.40 ! [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))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_id__take__nth__drop,axiom, % 183.72/184.40 ! [V_xs,T_a,V_i] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__hd__drop,axiom, % 183.72/184.40 ! [V_xs,T_a,V_n] : % 183.72/184.40 ( 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))) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__drop__conv__nth,axiom, % 183.72/184.40 ! [V_n,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => ( 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))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd_Osimps,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__append2,axiom, % 183.72/184.40 ! [V_ys,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__append,axiom, % 183.72/184.40 ! [V_ys,T_a,V_xs] : % 183.72/184.40 ( ( V_xs = c_List_Olist_ONil(T_a) % 183.72/184.40 => 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) ) % 183.72/184.40 & ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__in__set,axiom, % 183.72/184.40 ! [T_a,V_xs_2] : % 183.72/184.40 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__conv__nth,axiom, % 183.72/184.40 ! [T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate1__hd__tl,axiom, % 183.72/184.40 ! [T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_option_Osize_I4_J,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__tl,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl__drop,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl_Osimps_I2_J,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__tl,axiom, % 183.72/184.40 ! [V_xs,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.40 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl_Osimps_I1_J,axiom, % 183.72/184.40 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl__append2,axiom, % 183.72/184.40 ! [V_ys,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__tl,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_drop__Suc,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl__append,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__tl,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_tl__take,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_take__Suc,axiom, % 183.72/184.40 ! [V_n,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fold1__set,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 183.72/184.40 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_hd__rotate__conv__nth,axiom, % 183.72/184.40 ! [V_n,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__rotate,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__def,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate1__rotate__swap,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_foldl__Nil,axiom, % 183.72/184.40 ! [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 ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__is__Nil__conv,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,T_a] : % 183.72/184.40 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 183.72/184.40 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__rotate,axiom, % 183.72/184.40 ! [V_xs_2,V_n_2,T_a] : % 183.72/184.40 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 183.72/184.40 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__add,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate0,axiom, % 183.72/184.40 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_foldl__assoc,axiom, % 183.72/184.40 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( class_Groups_Osemigroup__add(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__rotate,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_foldl__absorb0,axiom, % 183.72/184.40 ! [V_zs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Groups_Omonoid__add(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_start__le__sum,axiom, % 183.72/184.40 ! [V_ns_2,V_n_2,V_m_2] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__rotate,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_foldl__Cons,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_foldl__append,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__conv__mod,axiom, % 183.72/184.40 ! [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) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__Suc,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_listsum__foldl,axiom, % 183.72/184.40 ! [T_a] : % 183.72/184.40 ( class_Groups_Omonoid__add(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sum__eq__0__conv,axiom, % 183.72/184.40 ! [V_ns_2,V_m_2] : % 183.72/184.40 ( 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) % 183.72/184.40 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.40 & ! [B_x] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 183.72/184.40 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__id,axiom, % 183.72/184.40 ! [V_xs,T_a,V_n] : % 183.72/184.40 ( 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) % 183.72/184.40 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__length01,axiom, % 183.72/184.40 ! [V_n,V_xs,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 183.72/184.40 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 183.72/184.40 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Sup__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Inf__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,T_a] : % 183.72/184.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Sup__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Lattices_Olattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Inf__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Lattices_Olattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Min__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_Max__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_min__max_OInf__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_min__max_OSup__fin__set__fold,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_SUPR__set__fold,axiom, % 183.72/184.40 ! [V_f_2,V_xs_2,T_b,T_a] : % 183.72/184.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_INFI__set__fold,axiom, % 183.72/184.40 ! [V_f_2,V_xs_2,T_b,T_a] : % 183.72/184.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_map__upds__fold__map__upd,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_elem__le__sum,axiom, % 183.72/184.40 ! [V_ns_2,V_n_2] : % 183.72/184.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_rotate__drop__take,axiom, % 183.72/184.40 ! [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)) ). % 183.72/184.40 % 183.72/184.40 fof(fact_ran__def,axiom, % 183.72/184.40 ! [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)))) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__append__rightI,axiom, % 183.72/184.40 ! [V_r_2,V_x_2,T_a,V_y_2] : % 183.72/184.40 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_ranI,axiom, % 183.72/184.40 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 183.72/184.40 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 183.72/184.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_sorted__list__of__set__insert,axiom, % 183.72/184.40 ! [V_x_2,V_A_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.40 => 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)))))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_lexord__Nil__left,axiom, % 183.72/184.40 ! [V_r_2,V_y_2,T_a] : % 183.72/184.40 ( 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))) % 183.72/184.40 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_length__insort,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__not__Nil,axiom, % 183.72/184.40 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => 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) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_remove1__insort,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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 ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_fun__left__comm__insort,axiom, % 183.72/184.40 ! [T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__left__comm,axiom, % 183.72/184.40 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__key__left__comm,axiom, % 183.72/184.40 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 183.72/184.40 => 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)) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__insort,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__key_Osimps_I2_J,axiom, % 183.72/184.40 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( ( 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))) % 183.72/184.40 => 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)) ) % 183.72/184.40 & ( ~ 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))) % 183.72/184.40 => 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)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__key_Osimps_I1_J,axiom, % 183.72/184.40 ! [V_x_2,V_f_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__insort,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => ( 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))) % 183.72/184.40 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__insert__insort__key,axiom, % 183.72/184.40 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( ~ 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)))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__insert__insort,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => 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) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_distinct__insort__insert,axiom, % 183.72/184.40 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 183.72/184.40 ( class_Orderings_Olinorder(T_b) % 183.72/184.40 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.40 => 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))) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__insert__triv,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.40 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_set__insort__insert,axiom, % 183.72/184.40 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => 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)) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_insort__insert__key__triv,axiom, % 183.72/184.40 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 183.72/184.40 ( class_Orderings_Olinorder(T_a) % 183.72/184.40 => ( 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)))) % 183.72/184.40 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_last__list__update,axiom, % 183.72/184.40 ! [V_x,V_k,T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => ( ( 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)) % 183.72/184.40 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 183.72/184.40 & ( 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)) % 183.72/184.40 => 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) ) ) ) ). % 183.72/184.40 % 183.72/184.40 fof(fact_last__conv__nth,axiom, % 183.72/184.40 ! [T_a,V_xs] : % 183.72/184.40 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.40 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__append,axiom, % 183.72/184.41 ! [V_xs,T_a,V_ys] : % 183.72/184.41 ( ( V_ys = c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 183.72/184.41 & ( V_ys != c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__appendR,axiom, % 183.72/184.41 ! [V_xs,T_a,V_ys] : % 183.72/184.41 ( V_ys != c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__appendL,axiom, % 183.72/184.41 ! [V_xs,T_a,V_ys] : % 183.72/184.41 ( V_ys = c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last_Osimps,axiom, % 183.72/184.41 ! [V_x,T_a,V_xs] : % 183.72/184.41 ( ( V_xs = c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 183.72/184.41 & ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__ConsR,axiom, % 183.72/184.41 ! [V_x,T_a,V_xs] : % 183.72/184.41 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__ConsL,axiom, % 183.72/184.41 ! [V_x,T_a,V_xs] : % 183.72/184.41 ( V_xs = c_List_Olist_ONil(T_a) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__in__set,axiom, % 183.72/184.41 ! [T_a,V_as_2] : % 183.72/184.41 ( V_as_2 != c_List_Olist_ONil(T_a) % 183.72/184.41 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__snoc,axiom, % 183.72/184.41 ! [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 ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__drop,axiom, % 183.72/184.41 ! [V_xs,T_a,V_n] : % 183.72/184.41 ( 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))) % 183.72/184.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_snoc__eq__iff__butlast,axiom, % 183.72/184.41 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 183.72/184.41 ( 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 % 183.72/184.41 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 183.72/184.41 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 183.72/184.41 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_append__butlast__last__id,axiom, % 183.72/184.41 ! [T_a,V_xs] : % 183.72/184.41 ( V_xs != c_List_Olist_ONil(T_a) % 183.72/184.41 => 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 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_lists_Osimps,axiom, % 183.72/184.41 ! [V_A_2,V_a_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 183.72/184.41 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 183.72/184.41 | ? [B_a,B_l] : % 183.72/184.41 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 183.72/184.41 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 183.72/184.41 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__upd,axiom, % 183.72/184.41 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( 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) % 183.72/184.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 183.72/184.41 => ( 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)) % 183.72/184.41 => 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)) ) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_finite__dom__map__of,axiom, % 183.72/184.41 ! [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)))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__inject,axiom, % 183.72/184.41 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( 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) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 183.72/184.41 => ( 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)) % 183.72/184.41 => V_ys_2 = V_zs_2 ) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__Cons__code_I2_J,axiom, % 183.72/184.41 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 183.72/184.41 ( ( V_l = V_k % 183.72/184.41 => 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) ) % 183.72/184.41 & ( V_l != V_k % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__eq__dom,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,T_b,T_a] : % 183.72/184.41 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_finite__range__map__of,axiom, % 183.72/184.41 ! [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))))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__SomeD,axiom, % 183.72/184.41 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__is__SomeD,axiom, % 183.72/184.41 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__map__of__conv__image__fst,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__is__Some,axiom, % 183.72/184.41 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 <=> ? [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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__map__of__zip,axiom, % 183.72/184.41 ! [V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of_Osimps_I2_J,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_ran__distinct,axiom, % 183.72/184.41 ! [V_al_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__map__of__compr,axiom, % 183.72/184.41 ! [V_xs_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__mapI,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a] : % 183.72/184.41 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_foldl__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__size__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_List_Omap_Oid,axiom, % 183.72/184.41 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_List_Omap_Oidentity,axiom, % 183.72/184.41 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_List_Omap_Ocompositionality,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__comp__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_List_Omap_Ocomp,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__map2,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__zip__map2,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__zip__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__map1,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__map__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__on__map__eq__map,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( 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) % 183.72/184.41 <=> V_xs_2 = V_ys_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__inj__on,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( 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))) % 183.72/184.41 => V_xs_2 = V_ys_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nth__map,axiom, % 183.72/184.41 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__fun__upd,axiom, % 183.72/184.41 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 183.72/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__eq__imp__length__eq,axiom, % 183.72/184.41 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__tl,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__injective,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 183.72/184.41 => V_xs_2 = V_ys_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__map__eq__map,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.41 => ( 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) % 183.72/184.41 <=> V_xs_2 = V_ys_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__is__Nil__conv,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 183.72/184.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map_Osimps_I1_J,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Nil__is__map__conv,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 183.72/184.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__butlast,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_take__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__ident,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__subtractf,axiom, % 183.72/184.41 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( class_Groups_Oab__group__add(T_a) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__const__mult,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 183.72/184.41 ( class_Rings_Osemiring__0(T_a) % 183.72/184.41 => 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_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__mult__const,axiom, % 183.72/184.41 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( class_Rings_Osemiring__0(T_a) % 183.72/184.41 => 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_ca_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_ca_2) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__0,axiom, % 183.72/184.41 ! [V_xs_2,T_b,T_a] : % 183.72/184.41 ( class_Groups_Omonoid__add(T_a) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__addf,axiom, % 183.72/184.41 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__eq__conv,axiom, % 183.72/184.41 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 <=> ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 183.72/184.41 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__update,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map_Osimps_I2_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__append,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_hd__map,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a,V_xs_2] : % 183.72/184.41 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_drop__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_rotate__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_last__map,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a,V_xs_2] : % 183.72/184.41 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__map,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 183.72/184.41 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 183.72/184.41 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__abs,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 183.72/184.41 => 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_uminus__listsum__map,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( class_Groups_Oab__group__add(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__on__mapI,axiom, % 183.72/184.41 ! [V_A_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__fst__zip,axiom, % 183.72/184.41 ! [V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__snd__zip,axiom, % 183.72/184.41 ! [V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__map__fst__snd,axiom, % 183.72/184.41 ! [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 ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__mapD,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_inj__map,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_pick__member,axiom, % 183.72/184.41 ! [V_xs_2,T_a,V_i_2] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 183.72/184.41 ! [V_f_2,V_xs_2,T_a,T_b] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__eq__conv,axiom, % 183.72/184.41 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 183.72/184.41 <=> ( 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 % 183.72/184.41 & 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 ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__triv,axiom, % 183.72/184.41 ! [V_xs_2,V_r_2,T_b,T_a] : % 183.72/184.41 ( class_Rings_Osemiring__1(T_a) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__inject__set,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( 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))) % 183.72/184.41 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 183.72/184.41 <=> 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) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__map__remove1,axiom, % 183.72/184.41 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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)))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_select__weight__member,axiom, % 183.72/184.41 ! [V_s_2,V_xs_2,T_a] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_select__weight__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__mapk__SomeI,axiom, % 183.72/184.41 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 183.72/184.41 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.72/184.41 => ( 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) % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__is__SomeI,axiom, % 183.72/184.41 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( 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))) % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__eq__Some__iff,axiom, % 183.72/184.41 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( 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) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Some__eq__map__of__iff,axiom, % 183.72/184.41 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( 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) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Nitpick_Osetsum_H__def,axiom, % 183.72/184.41 ! [V_f_2,V_A_2,T_a,T_b] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_b) % 183.72/184.41 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.41 => 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))))) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.72/184.41 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsum__mono,axiom, % 183.72/184.41 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 183.72/184.41 ( ( class_Groups_Omonoid__add(T_b) % 183.72/184.41 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 183.72/184.41 => ( ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 183.72/184.41 => 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)))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zip__same__conv__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__size__conv__listsum,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 183.72/184.41 ! [V_j_2,V_i_2,V_f_2,T_a] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 183.72/184.41 ! [V_l_2,V_k_2,V_f_2,T_a] : % 183.72/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__map__restrict,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__map__keys,axiom, % 183.72/184.41 ! [V_m_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 183.72/184.41 => 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 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_select__weigth__select,axiom, % 183.72/184.41 ! [T_a,V_xs_2] : % 183.72/184.41 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_pick__same,axiom, % 183.72/184.41 ! [V_xs_2,T_a,V_l_2] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__map,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Omap_Ocomp,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Omap_Ocompositionality,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__comp,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__o__map__upd,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Omap_Oidentity,axiom, % 183.72/184.41 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Omap_Oid,axiom, % 183.72/184.41 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_less__code__numeral__code,axiom, % 183.72/184.41 ! [V_m_2,V_n_2] : % 183.72/184.41 ( 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))) % 183.72/184.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_code__numeral_Oof__nat__inject,axiom, % 183.72/184.41 ! [V_y_2,V_x_2] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 183.72/184.41 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 183.72/184.41 <=> V_x_2 = V_y_2 ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__option__map,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_times__code__numeral__code,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 183.72/184.41 ! [V_m_2,V_n_2] : % 183.72/184.41 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 183.72/184.41 <=> V_n_2 = V_m_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 183.72/184.41 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 183.72/184.41 % 183.72/184.41 fof(fact_zero__code__numeral__def,axiom, % 183.72/184.41 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__eq__Some,axiom, % 183.72/184.41 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( 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) % 183.72/184.41 <=> ? [B_z] : % 183.72/184.41 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 183.72/184.41 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__Some,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_one__code__numeral__def,axiom, % 183.72/184.41 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_number__of__code__numeral__def,axiom, % 183.72/184.41 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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_plus__code__numeral__code,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_less__eq__code__numeral__code,axiom, % 183.72/184.41 ! [V_m_2,V_n_2] : % 183.72/184.41 ( 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))) % 183.72/184.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_code__numeral__not__eq__zero,axiom, % 183.72/184.41 ! [V_i_2] : % 183.72/184.41 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.41 <=> 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_select__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_subtract__code__numeral__code,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_times__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of__of__nat,axiom, % 183.72/184.41 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 183.72/184.41 % 183.72/184.41 fof(fact_of__nat__nat__of,axiom, % 183.72/184.41 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of__inverse,axiom, % 183.72/184.41 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 183.72/184.41 % 183.72/184.41 fof(fact_code__numeral_Onat__of__inject,axiom, % 183.72/184.41 ! [V_y_2,V_x_2] : % 183.72/184.41 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 183.72/184.41 <=> V_x_2 = V_y_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 183.72/184.41 ! [V_l_2,V_k_2] : % 183.72/184.41 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 183.72/184.41 <=> V_k_2 = V_l_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_type__definition__code__numeral,axiom, % 183.72/184.41 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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_less__code__numeral__def,axiom, % 183.72/184.41 ! [V_m_2,V_n_2] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 183.72/184.41 <=> 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of,axiom, % 183.72/184.41 ! [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)))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of__number,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_int__of__def,axiom, % 183.72/184.41 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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_less__eq__code__numeral__def,axiom, % 183.72/184.41 ! [V_m_2,V_n_2] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 183.72/184.41 <=> 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of__code,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_nat__of__aux__def,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Suc__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_minus__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_of__nat__inverse,axiom, % 183.72/184.41 ! [V_y_2] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 183.72/184.41 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_plus__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_div__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_minus__code__numeral__code,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_subtract__code__numeral__def,axiom, % 183.72/184.41 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 183.72/184.41 % 183.72/184.41 fof(fact_mod__code__numeral__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_code__numeral__decr,axiom, % 183.72/184.41 ! [V_k] : % 183.72/184.41 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_weak__map__of__SomeI,axiom, % 183.72/184.41 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ? [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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__map,axiom, % 183.72/184.41 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 183.72/184.41 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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)) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_partition__set,axiom, % 183.72/184.41 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__None,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__is__None,axiom, % 183.72/184.41 ! [V_opt_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 183.72/184.41 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_ran__empty,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option_Osimps_I2_J,axiom, % 183.72/184.41 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option_Osimps_I3_J,axiom, % 183.72/184.41 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 183.72/184.41 % 183.72/184.41 fof(fact_not__Some__eq,axiom, % 183.72/184.41 ! [T_a,V_x_2] : % 183.72/184.41 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 183.72/184.41 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_not__None__eq,axiom, % 183.72/184.41 ! [T_a,V_x_2] : % 183.72/184.41 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 183.72/184.41 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option_Osimps_I4_J,axiom, % 183.72/184.41 ! [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 ). % 183.72/184.41 % 183.72/184.41 fof(fact_restrict__map__to__empty,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_restrict__map__empty,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_restrict__map__def,axiom, % 183.72/184.41 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 183.72/184.41 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.41 => 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) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.41 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_restrict__out,axiom, % 183.72/184.41 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 183.72/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 183.72/184.41 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__def,axiom, % 183.72/184.41 ! [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)))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_domIff,axiom, % 183.72/184.41 ! [V_m_2,T_b,V_a_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 183.72/184.41 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__empty,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__eq__empty__conv,axiom, % 183.72/184.41 ! [V_f_2,T_b,T_a] : % 183.72/184.41 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.41 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_empty__upd__none,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__upd__nonempty,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__empty__eq,axiom, % 183.72/184.41 ! [V_xo_2,T_a] : % 183.72/184.41 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 183.72/184.41 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__Cons__code_I1_J,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of_Osimps_I1_J,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option__map__o__empty,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Option_Omap__def,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option_Osize_I3_J,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_option_Osize_I1_J,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__minus,axiom, % 183.72/184.41 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 183.72/184.41 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_partition__P,axiom, % 183.72/184.41 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 183.72/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.72/184.41 & ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 183.72/184.41 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_partition_Osimps_I1_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_ran__map__upd,axiom, % 183.72/184.41 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 183.72/184.41 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__is__None,axiom, % 183.72/184.41 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( 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) % 183.72/184.41 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_partition_Osimps_I2_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__fun__upd,axiom, % 183.72/184.41 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 183.72/184.41 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 183.72/184.41 => 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)))) ) % 183.72/184.41 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_restrict__complement__singleton__eq,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__eq__None__iff,axiom, % 183.72/184.41 ! [V_x_2,V_xys_2,T_a,T_b] : % 183.72/184.41 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 183.72/184.41 <=> ~ 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_UNIV__option__conv,axiom, % 183.72/184.41 ! [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)))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_dom__eq__singleton__conv,axiom, % 183.72/184.41 ! [V_x_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( 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))) % 183.72/184.41 <=> ? [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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_fun__upd__None__restrict,axiom, % 183.72/184.41 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 183.72/184.41 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 183.72/184.41 => 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))))) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 183.72/184.41 => 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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_lists__Int__eq,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_lists__IntI,axiom, % 183.72/184.41 ! [V_B_2,V_A_2,V_l_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp_ONil,axiom, % 183.72/184.41 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp_Oequations_I1_J,axiom, % 183.72/184.41 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp__infI,axiom, % 183.72/184.41 ! [V_B_2,V_l_2,V_A_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp__inf__eq,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp__conj__eq,axiom, % 183.72/184.41 ! [V_x_2,V_B_2,V_A_2,T_a] : % 183.72/184.41 ( 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)) % 183.72/184.41 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 183.72/184.41 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_in__listsp__conv__set,axiom, % 183.72/184.41 ! [V_xs_2,V_A_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 183.72/184.41 <=> ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp_Oequations_I2_J,axiom, % 183.72/184.41 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 183.72/184.41 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 183.72/184.41 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_append__in__listsp__conv,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 183.72/184.41 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 183.72/184.41 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp__mono,axiom, % 183.72/184.41 ! [V_B_2,V_A_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_listsp__lists__eq,axiom, % 183.72/184.41 ! [V_x_2,V_A_2,T_a] : % 183.72/184.41 ( 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)) % 183.72/184.41 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_product_Osimps_I2_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_product_Osimps_I1_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__product,axiom, % 183.72/184.41 ! [V_ys,T_b,V_xs,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 183.72/184.41 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_product__list__set,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sublists__powset,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__sublists,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sublists_Osimps_I1_J,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sublists_Osimps_I2_J,axiom, % 183.72/184.41 ! [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))))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__set__sublists,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.72/184.41 => 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)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__n__lists,axiom, % 183.72/184.41 ! [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)))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__the__def,axiom, % 183.72/184.41 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__n__lists,axiom, % 183.72/184.41 ! [V_n,V_xs,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.41 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_n__lists__Nil,axiom, % 183.72/184.41 ! [T_a,V_n] : % 183.72/184.41 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.41 => 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))) ) % 183.72/184.41 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.72/184.41 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_n__lists_Osimps_I1_J,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__n__lists,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__n__lists__elem,axiom, % 183.72/184.41 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_full__small__int__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__enum__inject,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( 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)) % 183.72/184.41 => ( 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)) % 183.72/184.41 => ( 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))) % 183.72/184.41 => V_xs_2 = V_ys_2 ) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__option__def,axiom, % 183.72/184.41 ! [T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__distinct,axiom, % 183.72/184.41 ! [T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__prod__def,axiom, % 183.72/184.41 ! [T_b,T_a] : % 183.72/184.41 ( ( class_Enum_Oenum(T_a) % 183.72/184.41 & class_Enum_Oenum(T_b) ) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_in__enum,axiom, % 183.72/184.41 ! [V_x_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__UNIV,axiom, % 183.72/184.41 ! [T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_UNIV__enum,axiom, % 183.72/184.41 ! [T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__fun__def,axiom, % 183.72/184.41 ! [T_b,T_a] : % 183.72/184.41 ( ( class_Enum_Oenum(T_a) % 183.72/184.41 & class_Enum_Oenum(T_b) ) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__fun__code,axiom, % 183.72/184.41 ! [T_b,T_a] : % 183.72/184.41 ( ( class_Enum_Oenum(T_a) % 183.72/184.41 & class_HOL_Oequal(T_a) % 183.72/184.41 & class_Enum_Oenum(T_b) ) % 183.72/184.41 => 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))) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_ex__n__lists__def,axiom, % 183.72/184.41 ! [V_n_2,V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 183.72/184.41 <=> ? [B_x] : % 183.72/184.41 ( 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))))) % 183.72/184.41 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_all__n__lists__def,axiom, % 183.72/184.41 ! [V_n_2,V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 183.72/184.41 <=> ! [B_x] : % 183.72/184.41 ( 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))))) % 183.72/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__all__fun__def,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__ex__fun__def,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__ex,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 183.72/184.41 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__all,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 183.72/184.41 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_exists__code,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.41 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_all__code,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 183.72/184.41 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__all__prod__def,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__ex__prod__def,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__all__option__def,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 183.72/184.41 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 183.72/184.41 & 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)))) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__ex__option__def,axiom, % 183.72/184.41 ! [V_P_2,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 183.72/184.41 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 183.72/184.41 | 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)))) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_order__fun_I1_J,axiom, % 183.72/184.41 ! [V_g_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( ( class_Orderings_Oorder(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_order__fun_I2_J,axiom, % 183.72/184.41 ! [V_g_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( ( class_Orderings_Oorder(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.72/184.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.72/184.41 & 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)))) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__ex__fun__code,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) % 183.72/184.41 & class_HOL_Oequal(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_enum__all__fun__code,axiom, % 183.72/184.41 ! [V_P_2,T_a,T_b] : % 183.72/184.41 ( ( class_Enum_Oenum(T_b) % 183.72/184.41 & class_Enum_Oenum(T_a) % 183.72/184.41 & class_HOL_Oequal(T_a) ) % 183.72/184.41 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 183.72/184.41 <=> 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_small_H_Osimps,axiom, % 183.72/184.41 ! [V_f_2,V_i_2,V_d_2] : % 183.72/184.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.72/184.41 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__of__zip__enum__is__Some,axiom, % 183.72/184.41 ! [V_x,V_ys,T_b,T_a] : % 183.72/184.41 ( class_Enum_Oenum(T_a) % 183.72/184.41 => ( 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)) % 183.72/184.41 => ? [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) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_small_H_Opsimps,axiom, % 183.72/184.41 ! [V_i_2,V_d_2,V_f_2] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.72/184.41 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.72/184.41 => 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)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_small__int__def,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_small__prod__def,axiom, % 183.72/184.41 ! [V_d_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( ( class_Smallcheck_Osmall(T_b) % 183.72/184.41 & class_Smallcheck_Osmall(T_a) ) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_small_H_Opinduct,axiom, % 183.72/184.41 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => ( ! [B_f,B_d,B_i] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 183.72/184.41 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 183.72/184.41 => 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)))) ) ) % 183.72/184.41 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 183.72/184.41 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__def,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 <=> ( 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) % 183.72/184.41 & ! [B_x] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__lengthD,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__dropI,axiom, % 183.72/184.41 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__eq,axiom, % 183.72/184.41 ! [T_a,V_ys_2,V_xs_2] : % 183.72/184.41 ( V_xs_2 = V_ys_2 % 183.72/184.41 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__takeI,axiom, % 183.72/184.41 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__Nil2,axiom, % 183.72/184.41 ! [V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 183.72/184.41 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__Nil,axiom, % 183.72/184.41 ! [V_ys_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 183.72/184.41 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__appendI,axiom, % 183.72/184.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 183.72/184.41 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 183.72/184.41 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__append,axiom, % 183.72/184.41 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 => ( 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)) % 183.72/184.41 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__map1,axiom, % 183.72/184.41 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 <=> 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__map2,axiom, % 183.72/184.41 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( 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)) % 183.72/184.41 <=> 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__Cons,axiom, % 183.72/184.41 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( 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)) % 183.72/184.41 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 183.72/184.41 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__conv__all__nth,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 <=> ( 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) % 183.72/184.41 & ! [B_i] : % 183.72/184.41 ( 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))) % 183.72/184.41 => 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))) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__nthD,axiom, % 183.72/184.41 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => ( 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))) % 183.72/184.41 => 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__nthD2,axiom, % 183.72/184.41 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => ( 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))) % 183.72/184.41 => 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))) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__update__cong,axiom, % 183.72/184.41 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 183.72/184.41 ( 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))) % 183.72/184.41 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 183.72/184.41 => 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)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2__update__cong2,axiom, % 183.72/184.41 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.72/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 183.72/184.41 => ( 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))) % 183.72/184.41 => 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)) ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_list__all2I,axiom, % 183.72/184.41 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 183.72/184.41 ( ! [B_x] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 183.72/184.41 => ( 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) % 183.72/184.41 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_all__nth__imp__all__set,axiom, % 183.72/184.41 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 183.72/184.41 ( ! [B_i] : % 183.72/184.41 ( 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))) % 183.72/184.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 183.72/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_body__def,axiom, % 183.72/184.41 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 183.72/184.41 % 183.72/184.41 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 183.72/184.41 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 183.72/184.41 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__remdups,axiom, % 183.72/184.41 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__remdups__leq,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remove1__remdups,axiom, % 183.72/184.41 ! [V_x,V_xs,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__remdups__id,axiom, % 183.72/184.41 ! [V_xs,T_a] : % 183.72/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.72/184.41 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups__id__iff__distinct,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 183.72/184.41 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__remdups__eq,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( 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) % 183.72/184.41 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__remdups,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups__remdups,axiom, % 183.72/184.41 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups__eq__nil__iff,axiom, % 183.72/184.41 ! [V_x_2,T_a] : % 183.72/184.41 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 183.72/184.41 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups__eq__nil__right__iff,axiom, % 183.72/184.41 ! [V_x_2,T_a] : % 183.72/184.41 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 183.72/184.41 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups_Osimps_I1_J,axiom, % 183.72/184.41 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups__map__remdups,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_remdups_Osimps_I2_J,axiom, % 183.72/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.72/184.41 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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) ) % 183.72/184.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.72/184.41 => 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)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__remdups__card__conv,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__remdups__concat,axiom, % 183.72/184.41 ! [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))) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( class_Orderings_Olinorder(T_a) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat_Osimps_I2_J,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_map__concat,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat__eq__Nil__conv,axiom, % 183.72/184.41 ! [V_xss_2,T_a] : % 183.72/184.41 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 183.72/184.41 <=> ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 183.72/184.41 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_Nil__eq__concat__conv,axiom, % 183.72/184.41 ! [V_xss_2,T_a] : % 183.72/184.41 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 183.72/184.41 <=> ! [B_x] : % 183.72/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 183.72/184.41 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat_Osimps_I1_J,axiom, % 183.72/184.41 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sort__key__simps_I1_J,axiom, % 183.72/184.41 ! [V_f_2,T_a,T_b] : % 183.72/184.41 ( class_Orderings_Olinorder(T_b) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_foldl__conv__concat,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat__conv__foldl,axiom, % 183.72/184.41 ! [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) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__sort,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( class_Orderings_Olinorder(T_b) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__sort,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( class_Orderings_Olinorder(T_b) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_distinct__sort,axiom, % 183.72/184.41 ! [V_xs_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( class_Orderings_Olinorder(T_b) % 183.72/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 183.72/184.41 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_length__concat,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_set__concat,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sort__key__simps_I2_J,axiom, % 183.72/184.41 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 183.72/184.41 ( class_Orderings_Olinorder(T_b) % 183.72/184.41 => 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)) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat__append,axiom, % 183.72/184.41 ! [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)) ). % 183.72/184.41 % 183.72/184.41 fof(fact_sort__foldl__insort,axiom, % 183.72/184.41 ! [V_xs_2,T_a] : % 183.72/184.41 ( class_Orderings_Olinorder(T_a) % 183.72/184.41 => 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) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat__eq__concat__iff,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.41 ( ! [B_x] : % 183.72/184.41 ( 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)))) % 183.72/184.41 => 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)) ) % 183.72/184.41 => ( 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) % 183.72/184.41 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 183.72/184.41 <=> V_xs_2 = V_ys_2 ) ) ) ). % 183.72/184.41 % 183.72/184.41 fof(fact_concat__injective,axiom, % 183.72/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.72/184.41 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 183.90/184.41 => ( 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) % 183.90/184.41 => ( ! [B_x] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => 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)) ) % 183.90/184.41 => V_xs_2 = V_ys_2 ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_concat__map__singleton,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_n__lists_Osimps_I2_J,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Osimps_I3_J,axiom, % 183.90/184.41 ! [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))))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__aux__filter__head,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__concat,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__sort,axiom, % 183.90/184.41 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 183.90/184.41 ( class_Orderings_Olinorder(T_b) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Osimps_I2_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__filter,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_partition__filter2,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__filter__le,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sum__length__filter__compl,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__id__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 183.90/184.41 <=> ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__is__subset,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__insort__triv,axiom, % 183.90/184.41 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 183.90/184.41 ( class_Orderings_Olinorder(T_b) % 183.90/184.41 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__filter,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__remove1,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_remove1__filter__not,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_partition__filter1,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter_Osimps_I1_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Osimps_I1_J,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__append,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__empty__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 183.90/184.41 <=> ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter_Osimps_I2_J,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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)) ) % 183.90/184.41 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_remdups__filter,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_nth__transpose,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_i_2] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__map__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__filter,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__filter__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__filter__less,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_partition__filter__conv,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__minus__filter__out,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__in__sublist,axiom, % 183.90/184.41 ! [V_s_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__empty,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 183.90/184.41 <=> ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 183.90/184.41 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__filter__conv__card,axiom, % 183.90/184.41 ! [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))))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__aux__filter__tail,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Opsimps_I3_J,axiom, % 183.90/184.41 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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))))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__filter__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__filter__simps_I2_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__of__filter__in,axiom, % 183.90/184.41 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 183.90/184.41 ( 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) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__filter__simps_I1_J,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sublist__shift__lemma__Suc,axiom, % 183.90/184.41 ! [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)))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_pick__drop__zero,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_select__weigth__drop__zero,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Opsimps_I1_J,axiom, % 183.90/184.41 ! [T_a] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__filter__map__filter,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose_Opsimps_I2_J,axiom, % 183.90/184.41 ! [V_xss_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__max__length,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__aux__max,axiom, % 183.90/184.41 ! [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)))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr__conv__foldl,axiom, % 183.90/184.41 ! [V_a_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Groups_Oab__semigroup__add(T_a) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr_Osimps_I1_J,axiom, % 183.90/184.41 ! [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 ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr__append,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr_Osimps_I2_J,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr__map,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldl__foldr1,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( class_Groups_Omonoid__add(T_a) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldl__foldr1__lemma,axiom, % 183.90/184.41 ! [V_xs_2,V_a_2,T_a] : % 183.90/184.41 ( class_Groups_Omonoid__add(T_a) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__transpose,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sublist__def,axiom, % 183.90/184.41 ! [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))))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sublist__shift__lemma,axiom, % 183.90/184.41 ! [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))))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__upt,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_atLeastLessThan__upt,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__conv__Cons,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__rec,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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)) ) % 183.90/184.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__Suc,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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))) ) % 183.90/184.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__Suc__append,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__add__eq__append,axiom, % 183.90/184.41 ! [V_k,V_j,V_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__0,axiom, % 183.90/184.41 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__eq__Nil__conv,axiom, % 183.90/184.41 ! [V_j_2,V_i_2] : % 183.90/184.41 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 183.90/184.41 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__conv__Nil,axiom, % 183.90/184.41 ! [V_i,V_j] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 183.90/184.41 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_take__upt,axiom, % 183.90/184.41 ! [V_n,V_m,V_i] : % 183.90/184.41 ( 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)) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__list__of__set__range,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_hd__upt,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_drop__upt,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__upt,axiom, % 183.90/184.41 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__upt,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__rec__number__of,axiom, % 183.90/184.41 ! [V_n,V_m] : % 183.90/184.41 ( ( 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))) % 183.90/184.41 => 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))) ) % 183.90/184.41 & ( ~ 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))) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_upt__eq__Cons__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 183.90/184.41 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 183.90/184.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 183.90/184.41 & V_i_2 = V_x_2 % 183.90/184.41 & 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 ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_last__upt,axiom, % 183.90/184.41 ! [V_j,V_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__Suc__upt,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_atLeastAtMost__upt,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_atLeast__upt,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_nth__upt,axiom, % 183.90/184.41 ! [V_j,V_k,V_i] : % 183.90/184.41 ( 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)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_greaterThanAtMost__upt,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_greaterThanLessThan__upt,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_atMost__upto,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__nth,axiom, % 183.90/184.41 ! [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 ). % 183.90/184.41 % 183.90/184.41 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 183.90/184.41 ! [V_n_2,V_m_2,V_f_2,T_a] : % 183.90/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 183.90/184.41 ! [V_n_2,V_m_2,V_f_2,T_a] : % 183.90/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_nth__map__upt,axiom, % 183.90/184.41 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__rectangle,axiom, % 183.90/184.41 ! [V_n_2,T_a,V_xs_2] : % 183.90/184.41 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 183.90/184.41 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 183.90/184.41 => ( ! [B_i] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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 ) % 183.90/184.41 => 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)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_insort__key__remove1,axiom, % 183.90/184.41 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 183.90/184.41 ( class_Orderings_Olinorder(T_b) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 183.90/184.41 => ( 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 % 183.90/184.41 => 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 ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted_ONil,axiom, % 183.90/184.41 ! [T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__single,axiom, % 183.90/184.41 ! [V_x,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__upt,axiom, % 183.90/184.41 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__sort,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__insort,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( 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)) % 183.90/184.41 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__drop,axiom, % 183.90/184.41 ! [V_n,V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__take,axiom, % 183.90/184.41 ! [V_n,V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__upto,axiom, % 183.90/184.41 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__remove1,axiom, % 183.90/184.41 ! [V_a,V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__tl,axiom, % 183.90/184.41 ! [V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__insort__insert,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 => 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)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted_Oequations_I1_J,axiom, % 183.90/184.41 ! [T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__butlast,axiom, % 183.90/184.41 ! [V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( V_xs != c_List_Olist_ONil(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__many,axiom, % 183.90/184.41 ! [V_zs,V_y,V_x,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 183.90/184.41 => 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))) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__many__eq,axiom, % 183.90/184.41 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( 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))) % 183.90/184.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 183.90/184.41 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__remdups,axiom, % 183.90/184.41 ! [V_l,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__distinct__set__unique,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 183.90/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 183.90/184.41 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 183.90/184.41 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__sort__key,axiom, % 183.90/184.41 ! [V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__insort__insert__key,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__map__remove1,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__insort__key,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( 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))) % 183.90/184.41 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__filter,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__map__same,axiom, % 183.90/184.41 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__same,axiom, % 183.90/184.41 ! [V_xs_2,V_g_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__Cons,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 183.90/184.41 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 & ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__append,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 183.90/184.41 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 183.90/184.41 & ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ! [B_xa] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 183.90/184.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__insort,axiom, % 183.90/184.41 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 183.90/184.41 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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)) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted_Oequations_I2_J,axiom, % 183.90/184.41 ! [V_a1_2,V_a2_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 183.90/184.41 <=> ( ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 183.90/184.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 183.90/184.41 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__list__of__set,axiom, % 183.90/184.41 ! [V_A_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.90/184.41 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 183.90/184.41 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 183.90/184.41 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_insort__remove1,axiom, % 183.90/184.41 ! [V_xs_2,V_a_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 => 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 ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__nth__mono,axiom, % 183.90/184.41 ! [V_j,V_i,V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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))) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__equals__nth__mono,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 <=> ! [B_j] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ! [B_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 183.90/184.41 => 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))) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__sorted__distinct__set__unique,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 183.90/184.41 ( class_Orderings_Olinorder(T_b) % 183.90/184.41 => ( 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))) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 183.90/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 183.90/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 183.90/184.41 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 183.90/184.41 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__column,axiom, % 183.90/184.41 ! [V_i_2,V_xs_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_nth__nth__transpose__sorted,axiom, % 183.90/184.41 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ( 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)))) % 183.90/184.41 => ( 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)))) % 183.90/184.41 => 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) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_inj__on__rev,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__rev,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 183.90/184.41 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__is__Nil__conv,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 183.90/184.41 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_Nil__is__rev__conv,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 183.90/184.41 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev_Osimps_I1_J,axiom, % 183.90/184.41 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__append,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__singleton__conv,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,T_a] : % 183.90/184.41 ( 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)) % 183.90/184.41 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_singleton__rev__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( 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) % 183.90/184.41 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__concat,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev_Osimps_I2_J,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__eq__Cons__iff,axiom, % 183.90/184.41 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 183.90/184.41 <=> 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__filter,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_zip__rev,axiom, % 183.90/184.41 ! [V_ys,T_b,V_xs,T_a] : % 183.90/184.41 ( 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) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__rev,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_list__all2__rev,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.90/184.41 ( 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)) % 183.90/184.41 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_list__all2__rev1,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 183.90/184.41 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 183.90/184.41 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_listsum__rev,axiom, % 183.90/184.41 ! [V_xs,T_a] : % 183.90/184.41 ( class_Groups_Ocomm__monoid__add(T_a) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__rev__ident,axiom, % 183.90/184.41 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__swap,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 183.90/184.41 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__is__rev__conv,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,T_a] : % 183.90/184.41 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 183.90/184.41 <=> V_xs_2 = V_ys_2 ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__rev,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr__foldl,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldl__foldr,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_hd__rev,axiom, % 183.90/184.41 ! [T_a,V_xs] : % 183.90/184.41 ( V_xs != c_List_Olist_ONil(T_a) % 183.90/184.41 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_last__rev,axiom, % 183.90/184.41 ! [T_a,V_xs] : % 183.90/184.41 ( V_xs != c_List_Olist_ONil(T_a) % 183.90/184.41 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__transpose,axiom, % 183.90/184.41 ! [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)))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__foldl__cons,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__drop,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__take,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rotate__rev,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__nth,axiom, % 183.90/184.41 ! [V_xs,T_a,V_n] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_rev__update,axiom, % 183.90/184.41 ! [V_y,V_xs,T_a,V_k] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__rev__nth__mono,axiom, % 183.90/184.41 ! [V_j,V_i,V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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))) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldr__max__sorted,axiom, % 183.90/184.41 ! [V_y_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 183.90/184.41 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 183.90/184.41 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 183.90/184.41 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.90/184.41 => 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) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__transpose__sorted,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 183.90/184.41 => 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) ) % 183.90/184.41 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 183.90/184.41 => 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))) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__column__length,axiom, % 183.90/184.41 ! [V_i_2,V_xs_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transpose__transpose,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 183.90/184.41 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__takeWhile,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__takeWhile__le,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__takeWhileD,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__eq__all__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 183.90/184.41 <=> ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_zip__takeWhile__snd,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_zip__takeWhile__fst,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile_Osimps_I2_J,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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)) ) % 183.90/184.41 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__tail,axiom, % 183.90/184.41 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile_Osimps_I1_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__eq__take,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__takeWhile,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_return__list__def,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__append1,axiom, % 183.90/184.41 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__nth,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_nth__length__takeWhile,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ~ 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))))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__not__last,axiom, % 183.90/184.41 ! [T_a,V_xs_2] : % 183.90/184.41 ( V_xs_2 != c_List_Olist_ONil(T_a) % 183.90/184.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 183.90/184.41 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transfer__nat__int__list__return__embed,axiom, % 183.90/184.41 ! [V_l] : % 183.90/184.41 ( c_List_Onat__list(V_l) % 183.90/184.41 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_embed__list__def,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__neq__rev,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__neq__rev,axiom, % 183.90/184.41 ! [V_x_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => 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))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__dropWhile__id,axiom, % 183.90/184.41 ! [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 ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__map,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__dropWhile,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__dropWhile__le,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__eq__Nil__conv,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 183.90/184.41 <=> ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile_Osimps_I2_J,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) % 183.90/184.41 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile_Osimps_I1_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__dropWhile,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_hd__dropWhile,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 183.90/184.41 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__append1,axiom, % 183.90/184.41 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__eq__Cons__conv,axiom, % 183.90/184.41 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( 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) % 183.90/184.41 <=> ( 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)) % 183.90/184.41 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__eq__drop,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__nth,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => 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)))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_listsum__map__filter,axiom, % 183.90/184.41 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 183.90/184.41 ( class_Groups_Omonoid__add(T_b) % 183.90/184.41 => ( ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 183.90/184.41 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 183.90/184.41 => 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)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted__nth__monoI,axiom, % 183.90/184.41 ! [V_xs,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( ! [B_i,B_j] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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))) ) ) % 183.90/184.41 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__eq__filter,axiom, % 183.90/184.41 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.41 ( ! [B_x] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.41 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_takeWhile__eq__take__P__nth,axiom, % 183.90/184.41 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 183.90/184.41 ( ! [B_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 183.90/184.41 => ( 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))) % 183.90/184.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 183.90/184.41 => ( ( 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))) % 183.90/184.41 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 183.90/184.41 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_length__takeWhile__less__P__nth,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 183.90/184.41 ( ! [B_i] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 183.90/184.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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)))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_sorted_Osimps,axiom, % 183.90/184.41 ! [V_a_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 183.90/184.41 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 183.90/184.41 | ? [B_xs,B_x] : % 183.90/184.41 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 183.90/184.41 & ! [B_xa] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 183.90/184.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 183.90/184.41 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__upds__def,axiom, % 183.90/184.41 ! [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)))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__removeAll__inj__on,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__of__append,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll__append,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dom__map__add,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 183.90/184.41 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 183.90/184.41 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 183.90/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 183.90/184.41 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 183.90/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__assoc,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__upds,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__empty,axiom, % 183.90/184.41 ! [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 ). % 183.90/184.41 % 183.90/184.41 fof(fact_empty__map__add,axiom, % 183.90/184.41 ! [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 ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__None,axiom, % 183.90/184.41 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 183.90/184.41 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 183.90/184.41 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 183.90/184.41 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__Some__iff,axiom, % 183.90/184.41 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 183.90/184.41 ( 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) % 183.90/184.41 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 183.90/184.41 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 183.90/184.41 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__SomeD,axiom, % 183.90/184.41 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 183.90/184.41 ( 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) % 183.90/184.41 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 183.90/184.41 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 183.90/184.41 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__find__right,axiom, % 183.90/184.41 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 183.90/184.41 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__upd,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll__id,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll__filter__not__eq,axiom, % 183.90/184.41 ! [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))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll__filter__not,axiom, % 183.90/184.41 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 183.90/184.41 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll_Osimps_I2_J,axiom, % 183.90/184.41 ! [V_xs,T_a,V_y,V_x] : % 183.90/184.41 ( ( V_x = V_y % 183.90/184.41 => 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) ) % 183.90/184.41 & ( V_x != V_y % 183.90/184.41 => 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)) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_removeAll_Osimps_I1_J,axiom, % 183.90/184.41 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__removeAll,axiom, % 183.90/184.41 ! [V_x,V_xs,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_inj__on__map__add__dom,axiom, % 183.90/184.41 ! [V_m_H_2,V_m_2,T_b,T_a] : % 183.90/184.41 ( 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)) % 183.90/184.41 <=> 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__remove1__removeAll,axiom, % 183.90/184.41 ! [V_x,V_xs,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.90/184.41 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__comm,axiom, % 183.90/184.41 ! [V_m2_2,V_m1_2,T_b,T_a] : % 183.90/184.41 ( 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)) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__map__of__foldr,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__removeAll__inj,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__add__upd__left,axiom, % 183.90/184.41 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 183.90/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_finite__range__map__of__map__add,axiom, % 183.90/184.41 ! [V_l_2,V_f_2,T_b,T_a] : % 183.90/184.41 ( 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))))) % 183.90/184.41 => 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))))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_set__removeAll,axiom, % 183.90/184.41 ! [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)))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_List_Oinsert__def,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 183.90/184.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => 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) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__insert,axiom, % 183.90/184.41 ! [V_x,V_xs,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__empty_I1_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__empty_I2_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_insert__remdups,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__Some__iff,axiom, % 183.90/184.41 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 183.90/184.41 ( 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) % 183.90/184.41 <=> ? [B_k_H] : % 183.90/184.41 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 183.90/184.41 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__simps_I2_J,axiom, % 183.90/184.41 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 183.90/184.41 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__simps_I1_J,axiom, % 183.90/184.41 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 183.90/184.41 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_in__set__insert,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_List_Oset__insert,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_insert__Nil,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__comp__None__iff,axiom, % 183.90/184.41 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 183.90/184.41 ( 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) % 183.90/184.41 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 183.90/184.41 | ? [B_k_H] : % 183.90/184.41 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 183.90/184.41 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_not__in__set__insert,axiom, % 183.90/184.41 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_maps__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_concat__map__maps,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_maps__simps_I2_J,axiom, % 183.90/184.41 ! [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) ). % 183.90/184.41 % 183.90/184.41 fof(fact_maps__simps_I1_J,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_distinct__concat,axiom, % 183.90/184.41 ! [V_xs_2,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 183.90/184.41 => ( ! [B_ys] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 183.90/184.41 => ( ! [B_ys] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 183.90/184.41 => ! [B_zs] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 183.90/184.41 => ( B_ys != B_zs % 183.90/184.41 => 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)) ) ) ) % 183.90/184.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_ran__restrictD,axiom, % 183.90/184.41 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => ? [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 183.90/184.41 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_measures__lesseq,axiom, % 183.90/184.41 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 183.90/184.41 ( 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))) % 183.90/184.41 => ( 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))) % 183.90/184.41 => 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)))) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_in__measures_I2_J,axiom, % 183.90/184.41 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 183.90/184.41 ( 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)))) % 183.90/184.41 <=> ( 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))) % 183.90/184.41 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 183.90/184.41 & 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))) ) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_wf__measures,axiom, % 183.90/184.41 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_in__measures_I1_J,axiom, % 183.90/184.41 ! [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))))) ). % 183.90/184.41 % 183.90/184.41 fof(fact_measures__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_measures__less,axiom, % 183.90/184.41 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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)))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_foldl__apply,axiom, % 183.90/184.41 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 183.90/184.41 ( ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => 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)) ) % 183.90/184.41 => 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)) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_zip__obtain__same__length,axiom, % 183.90/184.41 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 183.90/184.41 ( ( 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)) % 183.90/184.41 => 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)))) ) % 183.90/184.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_map__of__eqI,axiom, % 183.90/184.41 ! [V_ys_2,V_xs_2,T_b,T_a] : % 183.90/184.41 ( 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)) % 183.90/184.41 => ( ! [B_x] : % 183.90/184.41 ( 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)))) % 183.90/184.41 => 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) ) % 183.90/184.41 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_pos__not__random__dseq__def,axiom, % 183.90/184.41 ! [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)) ). % 183.90/184.41 % 183.90/184.41 fof(fact_dropWhile__append2,axiom, % 183.90/184.41 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 183.90/184.41 ( ! [B_x] : % 183.90/184.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.41 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.41 => 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) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_list__all2__all__nthI,axiom, % 183.90/184.41 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 183.90/184.41 ( 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) % 183.90/184.41 => ( ! [B_n] : % 183.90/184.41 ( 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))) % 183.90/184.41 => 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))) ) % 183.90/184.41 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_finite__map__freshness,axiom, % 183.90/184.41 ! [V_f_2,T_b,T_a] : % 183.90/184.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 183.90/184.41 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 183.90/184.41 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 183.90/184.41 % 183.90/184.41 fof(fact_finite__sorted__distinct__unique,axiom, % 183.90/184.41 ! [V_A_2,T_a] : % 183.90/184.41 ( class_Orderings_Olinorder(T_a) % 183.90/184.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 183.90/184.41 => ? [B_x] : % 183.90/184.42 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 183.90/184.42 & c_List_Olinorder__class_Osorted(T_a,B_x) % 183.90/184.42 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 183.90/184.42 & ! [B_y] : % 183.90/184.42 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 183.90/184.42 & c_List_Olinorder__class_Osorted(T_a,B_y) % 183.90/184.42 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 183.90/184.42 => B_y = B_x ) ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_takeWhile__append2,axiom, % 183.90/184.42 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 183.90/184.42 ( ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 => 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)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_insort__is__Cons,axiom, % 183.90/184.42 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 183.90/184.42 ( class_Orderings_Olinorder(T_b) % 183.90/184.42 => ( ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 183.90/184.42 => 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) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_Cons__eq__filter__iff,axiom, % 183.90/184.42 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 183.90/184.42 ( 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) % 183.90/184.42 <=> ? [B_us,B_vs] : % 183.90/184.42 ( 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)) % 183.90/184.42 & ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 183.90/184.42 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 & hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_filter__eq__Cons__iff,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 183.90/184.42 ( 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) % 183.90/184.42 <=> ? [B_us,B_vs] : % 183.90/184.42 ( 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)) % 183.90/184.42 & ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 183.90/184.42 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 & hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ball__nth,axiom, % 183.90/184.42 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 183.90/184.42 ( 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))) % 183.90/184.42 => ( ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_sorted_OCons,axiom, % 183.90/184.42 ! [V_x_2,V_xs_2,T_a] : % 183.90/184.42 ( class_Orderings_Olinorder(T_a) % 183.90/184.42 => ( ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 183.90/184.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 183.90/184.42 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__length,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ? [B_n] : % 183.90/184.42 ( 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))) % 183.90/184.42 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_in__set__conv__decomp__first,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 <=> ? [B_ys] : % 183.90/184.42 ( ? [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)) % 183.90/184.42 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__simps_I2_J,axiom, % 183.90/184.42 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__append,axiom, % 183.90/184.42 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 183.90/184.42 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 183.90/184.42 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__iff,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ? [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__rev,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 183.90/184.42 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex__simps_I1_J,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 183.90/184.42 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_in__set__conv__decomp,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 <=> ? [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)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_in__set__conv__decomp__last,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 <=> ? [B_ys,B_zs] : % 183.90/184.42 ( 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)) % 183.90/184.42 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_option_Orecs_I2_J,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_option_Orecs_I1_J,axiom, % 183.90/184.42 ! [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 ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__length,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ! [B_n] : % 183.90/184.42 ( 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))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_measure__function__int,axiom, % 183.90/184.42 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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__simps_I1_J,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 183.90/184.42 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__rev,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 183.90/184.42 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_measure__snd,axiom, % 183.90/184.42 ! [T_b,V_f_2,T_a] : % 183.90/184.42 ( c_FunDef_Ois__measure(T_a,V_f_2) % 183.90/184.42 => 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))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_measure__fst,axiom, % 183.90/184.42 ! [T_b,V_f_2,T_a] : % 183.90/184.42 ( c_FunDef_Ois__measure(T_a,V_f_2) % 183.90/184.42 => 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))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__iff,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_is__measure_Ointros,axiom, % 183.90/184.42 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_is__measure_Oequations,axiom, % 183.90/184.42 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_is__measure_Osimps,axiom, % 183.90/184.42 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_measure__size,axiom, % 183.90/184.42 ! [T_a] : % 183.90/184.42 ( class_Nat_Osize(T_a) % 183.90/184.42 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__append,axiom, % 183.90/184.42 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 183.90/184.42 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 183.90/184.42 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_Ball__set__list__all,axiom, % 183.90/184.42 ! [V_P_2,V_xs_2,T_a] : % 183.90/184.42 ( ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__simps_I2_J,axiom, % 183.90/184.42 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__all__iff__raw,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex1__simps_I2_J,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 183.90/184.42 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 => 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) ) % 183.90/184.42 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_equal__fun__def,axiom, % 183.90/184.42 ! [V_g_2,V_f_2,T_a,T_b] : % 183.90/184.42 ( ( class_HOL_Oequal(T_b) % 183.90/184.42 & class_Enum_Oenum(T_a) ) % 183.90/184.42 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 183.90/184.42 <=> ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 183.90/184.42 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex1__simps_I1_J,axiom, % 183.90/184.42 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__equal,axiom, % 183.90/184.42 ! [T_a] : % 183.90/184.42 ( class_HOL_Oequal(T_a) % 183.90/184.42 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_equal__eq,axiom, % 183.90/184.42 ! [V_y_2,V_x_2,T_a] : % 183.90/184.42 ( class_HOL_Oequal(T_a) % 183.90/184.42 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 183.90/184.42 <=> V_x_2 = V_y_2 ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_equal__refl,axiom, % 183.90/184.42 ! [V_x,T_a] : % 183.90/184.42 ( class_HOL_Oequal(T_a) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_equal,axiom, % 183.90/184.42 ! [T_a] : % 183.90/184.42 ( class_HOL_Oequal(T_a) % 183.90/184.42 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_exists1__code,axiom, % 183.90/184.42 ! [V_P_2,T_a] : % 183.90/184.42 ( class_Enum_Oenum(T_a) % 183.90/184.42 => ( ? [B_x] : % 183.90/184.42 ( hBOOL(hAPP(V_P_2,B_x)) % 183.90/184.42 & ! [B_y] : % 183.90/184.42 ( hBOOL(hAPP(V_P_2,B_y)) % 183.90/184.42 => B_y = B_x ) ) % 183.90/184.42 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_bool_Osize_I3_J,axiom, % 183.90/184.42 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(fact_bool_Osize_I4_J,axiom, % 183.90/184.42 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(fact_list__ex1__iff,axiom, % 183.90/184.42 ! [V_xs_2,V_P_2,T_a] : % 183.90/184.42 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 183.90/184.42 <=> ? [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 & hBOOL(hAPP(V_P_2,B_x)) % 183.90/184.42 & ! [B_y] : % 183.90/184.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 183.90/184.42 & hBOOL(hAPP(V_P_2,B_y)) ) % 183.90/184.42 => B_y = B_x ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_size__code,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_transfer__morphism__int__nat,axiom, % 183.90/184.42 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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I2_J,axiom, % 183.90/184.42 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I5_J,axiom, % 183.90/184.42 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I12_J,axiom, % 183.90/184.42 ! [V_k1_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I8_J,axiom, % 183.90/184.42 ! [V_k2_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I11_J,axiom, % 183.90/184.42 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I7_J,axiom, % 183.90/184.42 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I10_J,axiom, % 183.90/184.42 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I4_J,axiom, % 183.90/184.42 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I9_J,axiom, % 183.90/184.42 ! [V_k1_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I3_J,axiom, % 183.90/184.42 ! [V_k2_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I15_J,axiom, % 183.90/184.42 ! [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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I14_J,axiom, % 183.90/184.42 ! [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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_equal__int__def,axiom, % 183.90/184.42 ! [V_l_2,V_k_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 183.90/184.42 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I6_J,axiom, % 183.90/184.42 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__number__of__int__code,axiom, % 183.90/184.42 ! [V_l_2,V_k_2] : % 183.90/184.42 ( 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))) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I16_J,axiom, % 183.90/184.42 ! [V_k2_2,V_k1_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I1_J,axiom, % 183.90/184.42 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__code_I13_J,axiom, % 183.90/184.42 ! [V_k2_2,V_k1_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_lazy__sequence__size__code,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_seq__case,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__int__refl,axiom, % 183.90/184.42 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_yieldn__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 183.90/184.42 ! [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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_lazy__sequence_Oinject,axiom, % 183.90/184.42 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 183.90/184.42 ( 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) % 183.90/184.42 <=> ( V_a_2 = V_a_H_2 % 183.90/184.42 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact__01,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 183.90/184.42 ! [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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 183.90/184.42 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 183.90/184.42 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.90/184.42 => 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) ) % 183.90/184.42 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.90/184.42 => 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)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 183.90/184.42 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 183.90/184.42 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.90/184.42 => 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) ) % 183.90/184.42 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 183.90/184.42 => 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)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Opos__empty__def,axiom, % 183.90/184.42 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 183.90/184.42 % 183.90/184.42 fof(fact_pos__empty__def,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_neg__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Opos__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_neg__map__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_neg__single__def,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_pos__bind__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Oneg__single__def,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_pos__map__def,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_pos__single__def,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_length__splice,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_splice_Osimps_I3_J,axiom, % 183.90/184.42 ! [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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_splice_Osimps_I1_J,axiom, % 183.90/184.42 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 183.90/184.42 % 183.90/184.42 fof(fact_splice__Nil2,axiom, % 183.90/184.42 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 183.90/184.42 % 183.90/184.42 fof(fact_splice_Osimps_I2_J,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Opos__single__def,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_acyclicP__converse,axiom, % 183.90/184.42 ! [V_r_2,T_a] : % 183.90/184.42 ( 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)))) % 183.90/184.42 <=> 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))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_converse__meet,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversepD,axiom, % 183.90/184.42 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 183.90/184.42 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep_Ointros,axiom, % 183.90/184.42 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep_Oequations,axiom, % 183.90/184.42 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep__iff,axiom, % 183.90/184.42 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 183.90/184.42 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep__conversep,axiom, % 183.90/184.42 ! [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 ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep__eq,axiom, % 183.90/184.42 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep__noteq,axiom, % 183.90/184.42 ! [V_y_2,V_x_2,T_a] : % 183.90/184.42 ( 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)) % 183.90/184.42 <=> V_x_2 != V_y_2 ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_converse__pred__comp,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_converse__join,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_conversep__converse__eq,axiom, % 183.90/184.42 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 183.90/184.42 ( 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)) % 183.90/184.42 <=> 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))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact__02,axiom, % 183.90/184.42 ! [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)))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_tl__replicate,axiom, % 183.90/184.42 ! [V_x,T_a,V_n] : % 183.90/184.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => 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) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_zip__replicate,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__app__Cons__same,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__Suc,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_rev__replicate,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_last__replicate,axiom, % 183.90/184.42 ! [V_x,T_a,V_n] : % 183.90/184.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_drop__replicate,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_hd__replicate,axiom, % 183.90/184.42 ! [V_x,T_a,V_n] : % 183.90/184.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_take__replicate,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(fact_Bex__set__replicate,axiom, % 183.90/184.42 ! [V_P_2,V_a_2,V_n_2,T_a] : % 183.90/184.42 ( ? [B_x] : % 183.90/184.42 ( 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)))) % 183.90/184.42 & hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 183.90/184.42 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_Ball__set__replicate,axiom, % 183.90/184.42 ! [V_P_2,V_a_2,V_n_2,T_a] : % 183.90/184.42 ( ! [B_x] : % 183.90/184.42 ( 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)))) % 183.90/184.42 => hBOOL(hAPP(V_P_2,B_x)) ) % 183.90/184.42 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 183.90/184.42 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__eq__replicate,axiom, % 183.90/184.42 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 183.90/184.42 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 183.90/184.42 <=> ( V_m_2 = V_n_2 % 183.90/184.42 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => V_x_2 = V_y_2 ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_nth__replicate,axiom, % 183.90/184.42 ! [V_x,T_a,V_n,V_i] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 183.90/184.42 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__add,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_append__replicate__commute,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_in__set__replicate,axiom, % 183.90/184.42 ! [V_y_2,V_n_2,V_x_2,T_a] : % 183.90/184.42 ( 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)))) % 183.90/184.42 <=> ( V_x_2 = V_y_2 % 183.90/184.42 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_filter__replicate,axiom, % 183.90/184.42 ! [V_n_2,T_a,V_x_2,V_P_2] : % 183.90/184.42 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,V_x_2) ) % 183.90/184.42 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 183.90/184.42 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Olist_ONil(T_a) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_concat__replicate__trivial,axiom, % 183.90/184.42 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__0,axiom, % 183.90/184.42 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ). % 183.90/184.42 % 183.90/184.42 fof(fact_empty__replicate,axiom, % 183.90/184.42 ! [V_x_2,V_n_2,T_a] : % 183.90/184.42 ( c_List_Olist_ONil(T_a) = c_List_Oreplicate(T_a,V_n_2,V_x_2) % 183.90/184.42 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__empty,axiom, % 183.90/184.42 ! [V_x_2,V_n_2,T_a] : % 183.90/184.42 ( c_List_Oreplicate(T_a,V_n_2,V_x_2) = c_List_Olist_ONil(T_a) % 183.90/184.42 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_map__replicate,axiom, % 183.90/184.42 ! [V_x_2,V_n_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,hAPP(V_f_2,V_x_2)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__append__same,axiom, % 183.90/184.42 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_replicate__length__filter,axiom, % 183.90/184.42 ! [V_xs_2,V_x_2,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_length__replicate,axiom, % 183.90/184.42 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ). % 183.90/184.42 % 183.90/184.42 fof(fact_map__replicate__const,axiom, % 183.90/184.42 ! [V_lst_2,V_k_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_k_2)),V_lst_2) = c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_lst_2),V_k_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_map__replicate__trivial,axiom, % 183.90/184.42 ! [V_i_2,V_x_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_COMBK(T_a,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_a,V_i_2,V_x_2) ). % 183.90/184.42 % 183.90/184.42 fof(fact_set__replicate__conv__if,axiom, % 183.90/184.42 ! [V_x_2,T_a,V_n_2] : % 183.90/184.42 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 183.90/184.42 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,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))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_set__replicate,axiom, % 183.90/184.42 ! [V_x_2,T_a,V_n_2] : % 183.90/184.42 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 183.90/184.42 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,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))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_set__replicate__Suc,axiom, % 183.90/184.42 ! [V_x_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n_2),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))) ). % 183.90/184.42 % 183.90/184.42 fof(fact_small__lazy__list_Osimps,axiom, % 183.90/184.42 ! [V_d_2,T_a] : % 183.90/184.42 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_eq__comp__r,axiom, % 183.90/184.42 ! [V_R_2,T_a] : c_Predicate_Opred__comp(T_a,T_a,T_a,c_fequal,c_Predicate_Opred__comp(T_a,T_a,T_a,V_R_2,c_fequal)) = V_R_2 ). % 183.90/184.42 % 183.90/184.42 fof(fact_small__lazy__prod__def,axiom, % 183.90/184.42 ! [V_d,T_b,T_a] : % 183.90/184.42 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 183.90/184.42 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact__03,axiom, % 183.90/184.42 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_New__DSequence_Opos__union__def,axiom, % 183.90/184.42 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_field__le__epsilon,axiom, % 183.90/184.42 ! [V_y,V_x,T_a] : % 183.90/184.42 ( class_Fields_Olinordered__field(T_a) % 183.90/184.42 => ( ! [B_e] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) ) % 183.90/184.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_pos__union__def,axiom, % 183.90/184.42 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_small__lazy_H_Osimps,axiom, % 183.90/184.42 ! [V_i,V_d] : % 183.90/184.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 183.90/184.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_small__lazy__int__def,axiom, % 183.90/184.42 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ). % 183.90/184.42 % 183.90/184.42 fof(fact_small__lazy_H_Opsimps,axiom, % 183.90/184.42 ! [V_i_2,V_d_2] : % 183.90/184.42 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) % 183.90/184.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 183.90/184.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 183.90/184.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ). % 183.90/184.42 % 183.90/184.42 fof(fact_hb__flat_Osimps_I2_J,axiom, % 183.90/184.42 ! [V_xqq_2,V_xq_2,T_a] : c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_xq_2,V_xqq_2)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_a),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),c_Lazy__Sequence_Ohit__bound(T_a),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),V_xq_2),c_Lazy__Sequence_Ohb__flat(T_a,V_xqq_2)) ). % 183.90/184.42 % 183.90/184.42 %----Arity declarations (235) % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 183.90/184.42 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Obounded__lattice(T_1) % 183.90/184.42 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 183.90/184.42 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Obounded__lattice(T_1) % 183.90/184.42 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Obounded__lattice(T_1) % 183.90/184.42 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Olattice(T_1) % 183.90/184.42 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Olattice(T_1) % 183.90/184.42 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Odistrib__lattice(T_1) % 183.90/184.42 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Oboolean__algebra(T_1) % 183.90/184.42 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Orderings_Opreorder,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Orderings_Opreorder(T_1) % 183.90/184.42 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Finite__Set_Ofinite,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Finite__Set_Ofinite(T_2) % 183.90/184.42 & class_Finite__Set_Ofinite(T_1) ) % 183.90/184.42 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Lattices_Olattice,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Lattices_Olattice(T_1) % 183.90/184.42 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Orderings_Oorder,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Orderings_Oorder(T_1) % 183.90/184.42 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Orderings_Otop,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Orderings_Otop(T_1) % 183.90/184.42 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Orderings_Oord,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Orderings_Oord(T_1) % 183.90/184.42 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Orderings_Obot,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Orderings_Obot(T_1) % 183.90/184.42 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Groups_Ouminus,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Groups_Ouminus(T_1) % 183.90/184.42 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Groups_Ominus,axiom, % 183.90/184.42 ! [T_2,T_1] : % 183.90/184.42 ( class_Groups_Ominus(T_1) % 183.90/184.42 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Enum_Oenum(T_2) % 183.90/184.42 & class_HOL_Oequal(T_1) ) % 183.90/184.42 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_fun__Enum_Oenum,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Enum_Oenum(T_2) % 183.90/184.42 & class_Enum_Oenum(T_1) ) % 183.90/184.42 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Com_Ocom) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Com__Ocom__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Com_Ocom) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 183.90/184.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 183.90/184.42 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 183.90/184.42 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 183.90/184.42 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 183.90/184.42 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 183.90/184.42 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 183.90/184.42 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 183.90/184.42 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 183.90/184.42 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 183.90/184.42 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 183.90/184.42 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 183.90/184.42 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 183.90/184.42 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 183.90/184.42 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 183.90/184.42 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 183.90/184.42 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 183.90/184.42 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 183.90/184.42 class_Divides_Osemiring__div(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 183.90/184.42 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 183.90/184.42 class_Groups_Oab__group__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 183.90/184.42 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 183.90/184.42 class_Rings_Oordered__ring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 183.90/184.42 class_Orderings_Opreorder(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 183.90/184.42 class_Orderings_Olinorder(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 183.90/184.42 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 183.90/184.42 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 183.90/184.42 class_Groups_Omonoid__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 183.90/184.42 class_Smallcheck_Osmall(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 183.90/184.42 class_Rings_Osemiring__1(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 183.90/184.42 class_Rings_Osemiring__0(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 183.90/184.42 class_Lattices_Olattice(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 183.90/184.42 class_Groups_Ogroup__add(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 183.90/184.42 class_Divides_Oring__div(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 183.90/184.42 class_Rings_Omult__zero(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 183.90/184.42 class_Orderings_Oorder(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 183.90/184.42 class_Int_Oring__char__0(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 183.90/184.42 class_Int_Onumber__ring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 183.90/184.42 class_Rings_Osemiring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Orderings_Oord,axiom, % 183.90/184.42 class_Orderings_Oord(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 183.90/184.42 class_Groups_Ouminus(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 183.90/184.42 class_Groups_Osgn__if(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 183.90/184.42 class_Groups_Oabs__if(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 183.90/184.42 class_Rings_Oring__1(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ominus,axiom, % 183.90/184.42 class_Groups_Ominus(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Power_Opower,axiom, % 183.90/184.42 class_Power_Opower(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Ozero,axiom, % 183.90/184.42 class_Groups_Ozero(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oring,axiom, % 183.90/184.42 class_Rings_Oring(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Rings_Oidom,axiom, % 183.90/184.42 class_Rings_Oidom(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Int_Onumber,axiom, % 183.90/184.42 class_Int_Onumber(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__Groups_Oone,axiom, % 183.90/184.42 class_Groups_Oone(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Int__Oint__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Int_Oint) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 183.90/184.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 183.90/184.42 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 183.90/184.42 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 183.90/184.42 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 183.90/184.42 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 183.90/184.42 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 183.90/184.42 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 183.90/184.42 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 183.90/184.42 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 183.90/184.42 class_Orderings_Owellorder(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 183.90/184.42 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 183.90/184.42 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 183.90/184.42 class_Orderings_Opreorder(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 183.90/184.42 class_Orderings_Olinorder(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 183.90/184.42 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 183.90/184.42 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 183.90/184.42 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 183.90/184.42 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 183.90/184.42 class_Lattices_Olattice(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 183.90/184.42 class_Rings_Omult__zero(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 183.90/184.42 class_Orderings_Oorder(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 183.90/184.42 class_Rings_Osemiring(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 183.90/184.42 class_Orderings_Oord(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 183.90/184.42 class_Orderings_Obot(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 183.90/184.42 class_Groups_Ominus(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Power_Opower,axiom, % 183.90/184.42 class_Power_Opower(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 183.90/184.42 class_Groups_Ozero(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Int_Onumber,axiom, % 183.90/184.42 class_Int_Onumber(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Groups_Oone,axiom, % 183.90/184.42 class_Groups_Oone(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Nat__Onat__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Nat_Onat) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 183.90/184.42 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 183.90/184.42 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 183.90/184.42 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 183.90/184.42 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 183.90/184.42 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 183.90/184.42 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 183.90/184.42 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 183.90/184.42 class_Orderings_Opreorder(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 183.90/184.42 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 183.90/184.42 class_Lattices_Olattice(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 183.90/184.42 class_Orderings_Oorder(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 183.90/184.42 class_Orderings_Otop(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 183.90/184.42 class_Orderings_Oord(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 183.90/184.42 class_Orderings_Obot(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 183.90/184.42 class_Groups_Ouminus(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 183.90/184.42 class_Groups_Ominus(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 183.90/184.42 class_Enum_Oenum(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_HOL__Obool__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_HOL_Obool) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Com_Ostate) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Com__Ostate__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Com_Ostate) ). % 183.90/184.42 % 183.90/184.42 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 183.90/184.42 ! [T_1] : % 183.90/184.42 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 183.90/184.42 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_List__Olist__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_List__Olist__Nat_Osize,axiom, % 183.90/184.42 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_sum__Finite__Set_Ofinite,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Finite__Set_Ofinite(T_2) % 183.90/184.42 & class_Finite__Set_Ofinite(T_1) ) % 183.90/184.42 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_sum__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_sum__Enum_Oenum,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Enum_Oenum(T_2) % 183.90/184.42 & class_Enum_Oenum(T_1) ) % 183.90/184.42 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_sum__Nat_Osize,axiom, % 183.90/184.42 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 183.90/184.42 ! [T_1] : % 183.90/184.42 ( class_Finite__Set_Ofinite(T_1) % 183.90/184.42 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 183.90/184.42 ! [T_1] : % 183.90/184.42 ( class_Enum_Oenum(T_1) % 183.90/184.42 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Option__Ooption__Nat_Osize,axiom, % 183.90/184.42 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 183.90/184.42 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 183.90/184.42 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__Finite__Set_Ofinite,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Finite__Set_Ofinite(T_2) % 183.90/184.42 & class_Finite__Set_Ofinite(T_1) ) % 183.90/184.42 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__Smallcheck_Osmall,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Smallcheck_Osmall(T_2) % 183.90/184.42 & class_Smallcheck_Osmall(T_1) ) % 183.90/184.42 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__Enum_Oenum,axiom, % 183.90/184.42 ! [T_1,T_2] : % 183.90/184.42 ( ( class_Enum_Oenum(T_2) % 183.90/184.42 & class_Enum_Oenum(T_1) ) % 183.90/184.42 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 183.90/184.42 % 183.90/184.42 fof(arity_prod__Nat_Osize,axiom, % 183.90/184.42 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 183.90/184.42 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 183.90/184.42 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 183.90/184.42 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 183.90/184.42 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Product__Type_Ounit) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 183.90/184.42 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 183.90/184.42 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 183.90/184.42 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 183.90/184.42 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 183.90/184.42 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 183.90/184.42 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 183.90/184.42 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 183.90/184.42 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 183.90/184.42 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 183.90/184.42 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 183.90/184.42 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 183.90/184.42 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 183.90/184.42 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 183.90/184.42 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 183.90/184.42 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 183.90/184.42 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 183.90/184.42 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 183.90/184.42 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 183.90/184.42 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 183.90/184.42 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 183.90/184.42 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 183.90/184.42 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 183.90/184.42 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 183.90/184.42 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 183.90/184.42 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 183.90/184.42 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 183.90/184.42 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 183.90/184.42 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 183.90/184.42 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 183.90/184.42 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 183.90/184.42 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 183.90/184.42 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 183.90/184.42 % 183.90/184.42 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 183.90/184.42 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 183.90/184.42 % 183.90/184.42 %----Helper facts (20) % 183.90/184.42 fof(help_c__COMBI__1,axiom, % 183.90/184.42 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 183.90/184.42 % 183.90/184.42 fof(help_c__COMBK__1,axiom, % 183.90/184.42 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 183.90/184.42 % 183.90/184.42 fof(help_c__COMBB__1,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__COMBC__1,axiom, % 183.90/184.42 ! [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) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__COMBS__1,axiom, % 183.90/184.42 ! [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)) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fequal__1,axiom, % 183.90/184.42 ! [V_y_2,V_x_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 183.90/184.42 | V_x_2 = V_y_2 ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fequal__2,axiom, % 183.90/184.42 ! [V_y_2,V_x_2] : % 183.90/184.42 ( V_x_2 != V_y_2 % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fFalse__1,axiom, % 183.90/184.42 ~ hBOOL(c_fFalse) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fTrue__1,axiom, % 183.90/184.42 hBOOL(c_fTrue) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fNot__1,axiom, % 183.90/184.42 ! [V_P_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 183.90/184.42 | ~ hBOOL(V_P_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fNot__2,axiom, % 183.90/184.42 ! [V_P_2] : % 183.90/184.42 ( ~ ~ hBOOL(V_P_2) % 183.90/184.42 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fconj__1,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(V_P_2) % 183.90/184.42 | ~ hBOOL(V_Q_2) % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fconj__2,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 183.90/184.42 | hBOOL(V_P_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fconj__3,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 183.90/184.42 | hBOOL(V_Q_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fdisj__1,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(V_P_2) % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fdisj__2,axiom, % 183.90/184.42 ! [V_P_2,V_Q_2] : % 183.90/184.42 ( ~ hBOOL(V_Q_2) % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fdisj__3,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 183.90/184.42 | hBOOL(V_P_2) % 183.90/184.42 | hBOOL(V_Q_2) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fimplies__1,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( hBOOL(V_P_2) % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fimplies__2,axiom, % 183.90/184.42 ! [V_P_2,V_Q_2] : % 183.90/184.42 ( ~ hBOOL(V_Q_2) % 183.90/184.42 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 183.90/184.42 % 183.90/184.42 fof(help_c__fimplies__3,axiom, % 183.90/184.42 ! [V_Q_2,V_P_2] : % 183.90/184.42 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 183.90/184.42 | ~ hBOOL(V_P_2) % 183.90/184.42 | hBOOL(V_Q_2) ) ). % 183.90/184.42 % 183.90/184.42 %----Conjectures (2) % 183.90/184.42 fof(conj_0,hypothesis, % 183.90/184.42 ! [B_x] : % 183.90/184.42 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 183.90/184.42 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,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_Com_Ocom_OBODY,B_x)),c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,B_x)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 183.90/184.42 % 183.90/184.42 fof(conj_1,conjecture, % 183.90/184.42 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,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),c_Com_Ocom_OSKIP),c_Natural_Oevalc(c_Com_Ocom_OSKIP))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 183.90/184.42 % 183.90/184.42 %------------------------------------------------------------------------------ % 183.90/184.42 %------------------------------------------- % 183.90/184.42 % Proof found % 183.90/184.42 % SZS status Theorem for theBenchmark % 183.90/184.42 % SZS output start Proof % 183.90/184.42 %ClaNum:10207(EqnAxiom:2875) % 183.90/184.42 %VarNum:70343(SingletonVarNum:20499) % 183.90/184.42 %MaxLitNum:8 % 183.90/184.42 %MaxfuncDepth:15 % 183.90/184.42 %SharedTerms:1075 % 183.90/184.42 %goalClause: 4570 % 183.90/184.42 %singleGoalClaCount:1 % 183.90/184.42 [2879]P1(a195) % 183.90/184.42 [2880]P2(a870) % 183.90/184.42 [2881]P2(a875) % 183.90/184.42 [2882]P3(a870) % 183.90/184.42 [2883]P3(a878) % 183.90/184.42 [2884]P62(a870) % 183.90/184.42 [2885]P62(a875) % 183.90/184.42 [2886]P62(a1) % 183.90/184.42 [2887]P63(a870) % 183.90/184.42 [2888]P98(a870) % 183.90/184.42 [2889]P98(a875) % 183.90/184.42 [2890]P98(a1) % 183.90/184.42 [2891]P99(a870) % 183.90/184.42 [2892]P99(a875) % 183.90/184.42 [2893]P99(a1) % 183.90/184.42 [2894]P64(a870) % 183.90/184.42 [2895]P64(a875) % 183.90/184.42 [2896]P64(a1) % 183.90/184.42 [2897]P64(a102) % 183.90/184.42 [2898]P96(a870) % 183.90/184.42 [2899]P96(a875) % 183.90/184.42 [2900]P96(a1) % 183.90/184.42 [2901]P103(a1) % 183.90/184.42 [2902]P65(a1) % 183.90/184.42 [2903]P4(a870) % 183.90/184.42 [2904]P66(a875) % 183.90/184.42 [2905]P66(a1) % 183.90/184.42 [2906]P66(a102) % 183.90/184.42 [2907]P104(a870) % 183.90/184.42 [2908]P97(a870) % 183.90/184.42 [2909]P72(a1) % 183.90/184.42 [2910]P67(a875) % 183.90/184.42 [2911]P67(a1) % 183.90/184.42 [2912]P67(a102) % 183.90/184.42 [2913]P134(a875) % 183.90/184.42 [2914]P134(a1) % 183.90/184.42 [2915]P134(a102) % 183.90/184.42 [2916]P68(a875) % 183.90/184.42 [2917]P68(a1) % 183.90/184.42 [2918]P68(a102) % 183.90/184.42 [2919]P69(a875) % 183.90/184.42 [2920]P69(a1) % 183.90/184.42 [2921]P69(a102) % 183.90/184.42 [2922]P70(a875) % 183.90/184.42 [2923]P70(a1) % 183.90/184.42 [2924]P70(a102) % 183.90/184.42 [2925]P109(a875) % 183.90/184.42 [2926]P109(a1) % 183.90/184.42 [2927]P109(a102) % 183.90/184.42 [2928]P139(a875) % 183.90/184.42 [2929]P139(a1) % 183.90/184.42 [2930]P135(a875) % 183.90/184.42 [2931]P135(a1) % 183.90/184.42 [2932]P135(a102) % 183.90/184.42 [2933]P110(a875) % 183.90/184.42 [2934]P110(a1) % 183.90/184.42 [2935]P110(a102) % 183.90/184.42 [2936]P73(a875) % 183.90/184.42 [2937]P73(a1) % 183.90/184.42 [2938]P73(a102) % 183.90/184.42 [2939]P76(a875) % 183.90/184.42 [2940]P76(a1) % 183.90/184.42 [2941]P76(a102) % 183.90/184.42 [2942]P77(a875) % 183.90/184.42 [2943]P77(a1) % 183.90/184.42 [2944]P77(a102) % 183.90/184.42 [2945]P105(a870) % 183.90/184.42 [2946]P105(a875) % 183.90/184.42 [2947]P105(a1) % 183.90/184.42 [2948]P105(a102) % 183.90/184.42 [2949]P114(a1) % 183.90/184.42 [2950]P106(a875) % 183.90/184.42 [2951]P106(a1) % 183.90/184.42 [2952]P106(a102) % 183.90/184.42 [2953]P107(a870) % 183.90/184.42 [2954]P107(a875) % 183.90/184.42 [2955]P107(a1) % 183.90/184.42 [2956]P107(a102) % 183.90/184.42 [2957]P108(a870) % 183.90/184.42 [2958]P108(a875) % 183.90/184.42 [2959]P108(a1) % 183.90/184.42 [2960]P108(a102) % 183.90/184.42 [2961]P79(a875) % 183.90/184.42 [2962]P79(a1) % 183.90/184.42 [2963]P79(a102) % 183.90/184.42 [2964]P80(a875) % 183.90/184.42 [2965]P80(a1) % 183.90/184.42 [2966]P80(a102) % 183.90/184.42 [2967]P81(a875) % 183.90/184.42 [2968]P81(a1) % 183.90/184.42 [2969]P81(a102) % 183.90/184.42 [2970]P82(a1) % 183.90/184.42 [2971]P120(a875) % 183.90/184.42 [2972]P120(a1) % 183.90/184.42 [2973]P120(a102) % 183.90/184.42 [2974]P123(a1) % 183.90/184.42 [2975]P111(a875) % 183.90/184.42 [2976]P111(a1) % 183.90/184.42 [2977]P111(a102) % 183.90/184.42 [2978]P84(a875) % 183.90/184.42 [2979]P84(a1) % 183.90/184.42 [2980]P84(a102) % 183.90/184.42 [2981]P124(a875) % 183.90/184.42 [2982]P124(a1) % 183.90/184.42 [2983]P124(a102) % 183.90/184.42 [2984]P129(a875) % 183.90/184.42 [2985]P129(a1) % 183.90/184.42 [2986]P129(a102) % 183.90/184.42 [2987]P140(a875) % 183.90/184.42 [2988]P140(a1) % 183.90/184.42 [2989]P140(a102) % 183.90/184.42 [2990]P78(a875) % 183.90/184.42 [2991]P78(a1) % 183.90/184.42 [2992]P78(a102) % 183.90/184.42 [2993]P74(a1) % 183.90/184.42 [2994]P136(a1) % 183.90/184.42 [2995]P137(a1) % 183.90/184.42 [2996]P85(a875) % 183.90/184.42 [2997]P85(a1) % 183.90/184.42 [2998]P85(a102) % 183.90/184.42 [2999]P121(a1) % 183.90/184.42 [3000]P122(a1) % 183.90/184.42 [3001]P130(a875) % 183.90/184.42 [3002]P130(a1) % 183.90/184.42 [3003]P130(a102) % 183.90/184.42 [3004]P132(a875) % 183.90/184.42 [3005]P132(a1) % 183.90/184.42 [3006]P132(a102) % 183.90/184.42 [3007]P131(a875) % 183.90/184.42 [3008]P131(a1) % 183.90/184.42 [3009]P131(a102) % 183.90/184.42 [3010]P125(a875) % 183.90/184.42 [3011]P125(a1) % 183.90/184.42 [3012]P125(a102) % 183.90/184.42 [3013]P115(a875) % 183.90/184.42 [3014]P115(a1) % 183.90/184.42 [3015]P115(a102) % 183.90/184.42 [3016]P126(a875) % 183.90/184.42 [3017]P126(a1) % 183.90/184.42 [3018]P126(a102) % 183.90/184.42 [3019]P127(a1) % 183.90/184.42 [3020]P128(a1) % 183.90/184.42 [3021]P100(a875) % 183.90/184.42 [3022]P100(a1) % 183.90/184.42 [3023]P100(a102) % 183.90/184.42 [3024]P141(a875) % 183.90/184.42 [3025]P141(a1) % 183.90/184.42 [3026]P141(a102) % 183.90/184.42 [3027]P138(a1) % 183.90/184.42 [3028]P55(a875) % 183.90/184.42 [3029]P55(a1) % 183.90/184.42 [3030]P55(a102) % 183.90/184.42 [3031]P89(a1) % 183.90/184.42 [3032]P56(a1) % 183.90/184.42 [3033]P83(a1) % 183.90/184.42 [3034]P133(a1) % 183.90/184.42 [3035]P75(a875) % 183.90/184.42 [3036]P75(a1) % 183.90/184.42 [3037]P75(a102) % 183.90/184.42 [3038]P86(a870) % 183.90/184.42 [3039]P86(a1) % 183.90/184.42 [3040]P93(a870) % 183.90/184.42 [3041]P116(a1) % 183.90/184.42 [3042]P113(a1) % 183.90/184.42 [3043]P71(a1) % 183.90/184.42 [3044]P87(a1) % 183.90/184.42 [3045]P90(a1) % 183.90/184.42 [3046]P91(a875) % 183.90/184.42 [3047]P91(a1) % 183.90/184.42 [3048]P91(a102) % 183.90/184.42 [3049]P112(a875) % 183.90/184.42 [3050]P88(a875) % 183.90/184.42 [3051]P88(a1) % 183.90/184.42 [3052]P88(a102) % 183.90/184.42 [3053]P57(a870) % 183.90/184.42 [3054]P57(a878) % 183.90/184.42 [3055]P92(a870) % 183.90/184.42 [3056]P92(a871) % 183.90/184.42 [3057]P92(a872) % 183.90/184.42 [3058]P92(a875) % 183.90/184.42 [3059]P92(a878) % 183.90/184.42 [3060]P92(a1) % 183.90/184.42 [3061]P92(a102) % 183.90/184.42 [3062]P92(a329) % 183.90/184.42 [3063]P142(a878) % 183.90/184.42 [3064]P142(a1) % 183.90/184.42 [3065]P102(a870) % 183.90/184.42 [3066]P102(a871) % 183.90/184.42 [3067]P102(a872) % 183.90/184.42 [3068]P102(a875) % 183.90/184.42 [3069]P102(a878) % 183.90/184.42 [3070]P102(a102) % 183.90/184.42 [3071]P102(a329) % 183.90/184.42 [3072]P101(a878) % 183.90/184.42 [3073]P101(a1) % 183.90/184.42 [3074]P95(a870) % 183.90/184.42 [3094]P37(a875,a252) % 183.90/184.42 [3095]P37(a875,a323) % 183.90/184.42 [4472]~E(a100,a82) % 183.90/184.42 [4473]~P1(a251) % 183.90/184.42 [2876]E(f2(a1),a82) % 183.90/184.42 [2877]E(f103(a102),a3) % 183.90/184.42 [2878]E(f22(a102),a23) % 183.90/184.42 [3075]E(f196(a875),f2(a875)) % 183.90/184.42 [3076]E(f30(a24),f2(a875)) % 183.90/184.42 [3077]E(f104(a875),f245(a875)) % 183.90/184.42 [3078]E(f113(a875),f246(a875)) % 183.90/184.42 [3079]E(f105(a1),f33(a1)) % 183.90/184.42 [3080]E(f83(a251),f2(a875)) % 183.90/184.42 [3081]E(f83(a195),f2(a875)) % 183.90/184.42 [3082]P5(f77(a1)) % 183.90/184.42 [3083]P5(f2(a1)) % 183.90/184.42 [3143]P37(f881(a875,a875),a34) % 183.90/184.42 [3499]E(f326(a875,a875,a252,a252),a34) % 183.90/184.42 [4474]~E(f77(a1),f2(a1)) % 183.90/184.42 [3084]E(f4(f2(a102)),f2(a875)) % 183.90/184.42 [3085]E(f114(f2(a875)),f2(a875)) % 183.90/184.42 [3097]E(f333(f78(a1),a82),a82) % 183.90/184.42 [3100]E(f333(a115,f2(a875)),f77(a875)) % 183.90/184.42 [3101]E(f333(a107,f77(a1)),f77(a875)) % 183.90/184.42 [3102]E(f333(a3,f77(a875)),f77(a102)) % 183.90/184.42 [3104]E(f333(a3,f2(a875)),f2(a102)) % 183.90/184.42 [3106]E(f333(f106(a1),a82),f2(a1)) % 183.90/184.42 [3107]E(f333(f106(a102),a82),f2(a102)) % 183.90/184.42 [3108]E(f333(a107,f2(a1)),f2(a875)) % 183.90/184.42 [3109]E(f333(f197(a870),a251),f2(a875)) % 183.90/184.42 [3110]E(f333(f197(a870),a195),f2(a875)) % 183.90/184.42 [3111]E(f333(f197(a871),a24),f2(a875)) % 183.90/184.42 [3112]E(f333(f106(a875),a82),f2(a875)) % 183.90/184.42 [3116]E(f333(f78(a1),f77(a1)),a100) % 183.90/184.42 [3124]E(f333(f197(a102),f2(a102)),f2(a875)) % 183.90/184.42 [3125]E(f333(f103(a1),f77(a875)),f77(a1)) % 183.90/184.42 [3126]E(f333(f103(a1),f2(a875)),f2(a1)) % 183.90/184.42 [3127]E(f333(f78(a1),f2(a1)),f2(a1)) % 183.90/184.42 [3139]E(f333(a107,f77(a1)),f333(a115,f2(a875))) % 183.90/184.42 [3140]E(f333(f180(a873,a871),a26),a27) % 183.90/184.42 [3141]E(f324(f881(a875,a875),a34),a35) % 183.90/184.42 [3142]E(f325(f881(a875,a875),a34),a36) % 183.90/184.42 [3164]E(f333(f254(a875),f2(a875)),f196(f882(a875,a870))) % 183.90/184.42 [3165]E(f333(f255(a875),f2(a875)),f256(f882(a875,a870))) % 183.90/184.42 [3173]P38(f196(f882(a1,a870))) % 183.90/184.42 [3209]E(f333(f333(f22(a102),f2(a102)),f77(a102)),f2(a102)) % 183.90/184.42 [3290]P1(f333(f333(f248(a1),a100),f2(a1))) % 183.90/184.42 [3315]P1(f333(f333(f248(a1),f2(a1)),f77(a1))) % 183.90/184.42 [3316]P1(f333(f333(f247(a1),f2(a1)),f77(a1))) % 183.90/184.42 [3491]P1(f333(f61(a873),f186(a873,a871,a27))) % 183.90/184.42 [3529]E(f333(f333(f290(a875,a875,a875),a323),f309(a875,a323)),a252) % 183.90/184.42 [3569]P40(a1,a875,a107,f333(f247(a1),f2(a1))) % 183.90/184.42 [3573]E(f333(f333(f41(a875,f882(a875,a870)),f256(f882(a875,a870))),f254(a875)),f256(f882(a875,a870))) % 183.90/184.42 [3574]E(f333(f333(f41(a875,f882(a875,a870)),f256(f882(a875,a870))),f255(a875)),f256(f882(a875,a870))) % 183.90/184.42 [3575]E(f333(f333(f41(a875,f882(a875,a870)),f256(f882(a875,a870))),f302(a875)),f256(f882(a875,a870))) % 183.90/184.42 [3576]E(f333(f333(f42(a875,f882(a875,a870)),f256(f882(a875,a870))),f305(a875)),f196(f882(a875,a870))) % 183.90/184.42 [3592]P25(a875,a1,f103(a1),f256(f882(a875,a870))) % 183.90/184.42 [3605]P40(a875,a1,f103(a1),f333(f16(a870,a875),a195)) % 183.90/184.42 [3743]E(f333(f72(a875,a102,a1,a3),a107),f106(a102)) % 183.90/184.42 [3971]P51(a102,a875,a19,a3,f256(f882(a875,a870))) % 183.90/184.42 [3980]P51(a1,f882(f881(a875,a875),a870),a109,a88,a101) % 183.90/184.42 [4247]E(f273(a1,a1,a1,a1,f33(a1),f78(a1)),a50) % 183.90/184.42 [4497]~E(f333(f106(a1),a100),f333(f106(a1),a82)) % 183.90/184.42 [4498]~P1(f333(a201,f77(a1))) % 183.90/184.42 [4499]~P1(f333(a201,f2(a1))) % 183.90/184.42 [4540]~P1(f333(f333(f248(a1),a82),f2(a1))) % 183.90/184.42 [3156]E(f333(f333(f22(a1),a100),a100),a82) % 183.90/184.42 [3171]E(f333(f103(a1),f333(a115,f2(a875))),f77(a1)) % 183.90/184.42 [3239]E(f333(f37(a878),f256(f882(a878,a870))),f77(a875)) % 183.90/184.42 [3260]P1(f333(a201,f333(f106(a1),a100))) % 183.90/184.42 [3261]P1(f333(f333(f248(a1),a100),a82)) % 183.90/184.42 [3263]P1(f333(f333(f247(a1),a100),a82)) % 183.90/184.42 [3326]E(f333(f333(f311(a875),f2(a875)),f196(f882(a875,a870))),f333(f302(a875),f2(a875))) % 183.90/184.42 [3382]P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),a82))) % 183.90/184.42 [3394]E(f333(f312(a875,a875,a115),f256(f882(a875,a870))),f333(f305(a875),f2(a875))) % 183.90/184.42 [3434]P7(f881(a875,a875),f256(f882(f881(a875,a875),a870)),a111) % 183.90/184.42 [3751]E(f333(f72(a875,a1,a102,f103(a1)),a19),a20) % 183.90/184.42 [3813]P37(a875,f333(f253(f881(a875,a875)),f333(f272(a875,a875,a870),f248(a875)))) % 183.90/184.42 [4529]~P1(f333(a201,f333(f106(a1),a82))) % 183.90/184.42 [4530]~P1(f333(f333(f248(a1),a82),a82)) % 183.90/184.42 [4531]~P1(f333(f333(f248(a1),a82),a100)) % 183.90/184.42 [4532]~P1(f333(f333(f248(a1),a100),a100)) % 183.90/184.42 [4533]~P1(f333(f333(f247(a1),a82),a100)) % 183.90/184.42 [4534]~P1(f333(f333(f90(a1),a82),a100)) % 183.90/184.42 [4535]~P1(f333(f333(f90(a1),a100),a82)) % 183.90/184.42 [4546]~P1(f333(f61(a875),f256(f882(a875,a870)))) % 183.90/184.42 [4547]~P1(f333(f61(a1),f256(f882(a1,a870)))) % 183.90/184.42 [4418]E(f333(f272(a1,a1,a870),f333(f333(f8(f882(a1,a870),f882(a1,a870),a1),f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f248(a1),f2(a1))))),f333(f333(f7(a1,a1,f882(a1,a870)),f333(f333(f8(f882(a1,f882(a1,a870)),f882(a1,f882(a1,a870)),a1),f7(a1,a1,a870)),f333(f333(f8(f882(a1,a1),f882(a1,f882(a1,a870)),a1),f333(f8(a1,f882(a1,a870),a1),a330)),a229))),f77(a1)))),a225) % 183.90/184.42 [4570]~P24(a872,a883,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),a330),a24),f202(a24))),f196(f882(f874(a872),a870)))) % 183.90/184.42 [3472]E(f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100),f333(f78(a1),a100)) % 183.90/184.42 [3512]E(f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100),f333(f333(f22(a1),a82),a100)) % 183.90/184.42 [3676]E(f333(f333(f60(f881(a875,a875)),f256(f882(f881(a875,a875),a870))),a111),a101) % 183.90/184.42 [3705]E(f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f77(a1)) % 183.90/184.42 [3706]E(f333(f106(a102),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f77(a102)) % 183.90/184.42 [3707]E(f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f77(a875)) % 183.90/184.42 [3711]E(f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(a115,f2(a875))) % 183.90/184.42 [4106]E(f333(f333(f113(f882(f881(f881(a875,a875),f881(a875,a875)),a870)),a34),f309(f881(a875,a875),f196(f882(f881(f881(a875,a875),f881(a875,a875)),a870)))),a69) % 183.90/184.42 [4177]E(f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),f77(a875)),f2(a875))),f196(f882(f881(a875,a875),a870))))),f77(a1)) % 183.90/184.42 [4178]E(f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),f2(a875)),f2(a875))),f196(f882(f881(a875,a875),a870))))),f2(a1)) % 183.90/184.42 [4193]E(f333(f253(f881(a875,a875)),f333(f272(a875,a875,a870),f333(f333(f8(a875,f882(a875,a870),a875),f333(f7(a875,a875,a870),a330)),a115))),a323) % 183.90/184.42 [4163]E(f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),f333(a115,f333(a115,f2(a875)))) % 183.90/184.42 [4166]E(f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),f333(f333(f79(a875),f77(a875)),f77(a875))) % 183.90/184.42 [4167]E(f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),f333(f37(a870),f256(f882(a870,a870)))) % 183.90/184.42 [4233]P5(f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))) % 183.90/184.42 [4305]P26(f882(f881(a875,a875),a870),f333(f333(f268(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)),a35),a70)) % 183.90/184.42 [4306]P26(f882(f881(a875,a875),a870),f333(f333(f268(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),a68)) % 183.90/184.42 [4346]E(f333(f333(f113(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),f325(f881(a875,a875),a69)),f333(f333(f311(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f196(f882(f881(a875,a875),a870))),f196(f882(f881(a875,a875),a870)))),f196(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)))),a68) % 183.90/184.42 [4347]E(f333(f333(f113(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),f324(f881(a875,a875),a69)),f333(f333(f311(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f196(f882(f881(a875,a875),a870))),f196(f882(f881(a875,a875),a870)))),f196(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)))),a70) % 183.90/184.42 [4235]E(f333(a107,f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(a115,f333(a115,f2(a875)))) % 183.90/184.42 [4282]E(f333(f103(a1),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))) % 183.90/184.42 [4317]P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.42 [4318]E(f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100)),f333(a115,f333(a115,f333(a115,f2(a875))))) % 183.90/184.42 [4360]P5(f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))) % 183.90/184.42 [4388]E(f333(f103(a1),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))) % 183.90/184.42 [4403]P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100)))) % 183.90/184.42 [3096]P6(x30961,a330) % 183.90/184.42 [3500]P25(a875,a875,a115,x35001) % 183.90/184.42 [3086]P92(f874(x30861)) % 183.90/184.42 [3087]P92(f879(x30871)) % 183.90/184.42 [3088]P92(f876(x30881)) % 183.90/184.42 [3089]P92(f877(x30891)) % 183.90/184.42 [3090]P102(f874(x30901)) % 183.90/184.42 [3091]P102(f879(x30911)) % 183.90/184.42 [3092]P102(f876(x30921)) % 183.90/184.42 [3093]P102(f877(x30931)) % 183.90/184.42 [3113]P37(a1,f108(x31131)) % 183.90/184.42 [3114]P37(a1,f110(x31141)) % 183.90/184.42 [3161]P37(f882(x31611,a870),f308(x31611)) % 183.90/184.42 [3185]E(f257(x31851,x31851,a330),a330) % 183.90/184.42 [3200]E(f44(a1,x32001,x32001),f2(a1)) % 183.90/184.42 [3257]P15(x32571,f882(x32571,a870),f311(x32571)) % 183.90/184.42 [4476]~E(f333(a25,x44761),a24) % 183.90/184.42 [4478]~E(f333(a115,x44781),x44781) % 183.90/184.42 [4488]~E(f333(a115,x44881),f2(a875)) % 183.90/184.42 [3098]E(f333(f197(a875),x30981),x30981) % 183.90/184.42 [3099]E(f333(f106(a1),x30991),x30991) % 183.90/184.42 [3115]E(f333(a88,f334(x31151)),x31151) % 183.90/184.42 [3128]E(f117(x31281,f116(x31281)),f116(x31281)) % 183.90/184.42 [3129]E(f153(x31291,f116(x31291)),f116(x31291)) % 183.90/184.42 [3131]E(f30(f333(a25,x31311)),f2(a875)) % 183.90/184.42 [3136]E(f333(f169(x31361),f116(x31361)),f116(x31361)) % 183.90/184.42 [3137]E(f333(f173(x31371),f116(x31371)),f116(x31371)) % 183.90/184.42 [3138]E(f333(f170(x31381),f116(x31381)),f116(x31381)) % 183.90/184.42 [3144]E(f333(f106(a1),x31441),f333(f105(a1),x31441)) % 183.90/184.42 [3145]E(f333(a88,f333(a109,x31451)),x31451) % 183.90/184.42 [3147]E(f333(a3,f333(a19,x31471)),x31471) % 183.90/184.42 [3148]E(f333(a19,f333(a3,x31481)),x31481) % 183.90/184.42 [3149]P5(f333(f103(a1),x31491)) % 183.90/184.42 [3154]E(f333(f197(f879(x31541)),f209(x31541)),f2(a875)) % 183.90/184.42 [3155]E(f333(f197(f876(x31551)),f116(x31551)),f2(a875)) % 183.90/184.42 [3160]E(f333(f197(a871),f333(a25,x31601)),f2(a875)) % 183.90/184.42 [3169]E(f239(x31691,f209(x31691)),f196(f882(x31691,a870))) % 183.90/184.42 [3176]E(f333(f333(f22(a875),x31761),f2(a875)),x31761) % 183.90/184.42 [3177]E(f333(f333(f79(a875),x31771),f2(a875)),x31771) % 183.90/184.42 [3178]E(f333(f333(f79(a1),x31781),f2(a1)),x31781) % 183.90/184.42 [3179]E(f333(f333(f80(a875),x31791),f77(a875)),x31791) % 183.90/184.42 [3180]E(f333(f333(f80(a1),x31801),f77(a1)),x31801) % 183.90/184.42 [3181]E(f333(f333(f246(a875),x31811),f2(a875)),x31811) % 183.90/184.42 [3182]E(f333(f333(f80(a875),x31821),f2(a875)),f2(a875)) % 183.90/184.42 [3183]E(f333(f333(f38(a1),x31831),f2(a1)),f2(a1)) % 183.90/184.42 [3184]E(f333(f333(f245(a875),x31841),f2(a875)),f2(a875)) % 183.90/184.42 [3191]E(f333(f174(x31911),f116(x31911)),f196(f882(x31911,a870))) % 183.90/184.42 [3195]P1(f333(f138(x31951),f116(x31951))) % 183.90/184.42 [3201]E(f333(f155(x32011,x32011),f5(x32011)),f33(f876(x32011))) % 183.90/184.42 [3202]E(f333(f155(x32021,x32021),f33(x32021)),f33(f876(x32021))) % 183.90/184.42 [3203]E(f333(f210(x32031,x32031),f5(x32031)),f33(f879(x32031))) % 183.90/184.42 [3204]E(f333(f210(x32041,x32041),f33(x32041)),f33(f879(x32041))) % 183.90/184.42 [3205]E(f44(a1,x32051,f2(a1)),x32051) % 183.90/184.42 [3206]E(f333(f247(a875),f333(a115,x32061)),f333(f248(a875),x32061)) % 183.90/184.42 [3207]E(f333(f254(a875),f333(a115,x32071)),f333(f302(a875),x32071)) % 183.90/184.42 [3208]E(f333(f255(a875),f333(a115,x32081)),f333(f305(a875),x32081)) % 183.90/184.42 [3210]E(f44(a1,f2(a1),x32101),f2(a1)) % 183.90/184.42 [3223]E(f333(f333(f79(a875),x32231),f77(a875)),f333(a115,x32231)) % 183.90/184.42 [3233]E(f333(f303(a875,x32331),f2(a875)),f196(f882(a875,a870))) % 183.90/184.42 [3245]E(f304(a875,f2(a875),x32451),f333(f302(a875),x32451)) % 183.90/184.42 [3293]E(f333(f333(f22(a875),f333(a115,x32931)),f77(a875)),x32931) % 183.90/184.42 [3306]E(f46(f2(a1),x33061),f333(f333(f268(a1,a1),f2(a1)),f2(a1))) % 183.90/184.42 [3356]P1(f333(f333(f248(a875),x33561),f333(a115,x33561))) % 183.90/184.42 [3368]P1(f333(f333(f248(a875),f2(a875)),f333(a115,x33681))) % 183.90/184.42 [3662]E(f333(f333(f22(a102),f333(a3,f333(a115,f333(a19,x36621)))),f77(a102)),x36621) % 183.90/184.42 [3735]P1(f333(f333(f247(a1),f333(f78(a1),f333(f103(a1),x37351))),f2(a1))) % 183.90/184.42 [3887]P1(f333(f333(f248(a1),f333(f78(a1),f333(f103(a1),f333(a115,x38871)))),f2(a1))) % 183.90/184.42 [4504]~E(f256(f882(x45041,a870)),f196(f882(x45041,a870))) % 183.90/184.42 [4543]~P1(f333(f333(f248(a875),x45431),f2(a875))) % 183.90/184.42 [4555]~P1(f333(f333(f248(a1),f333(f103(a1),x45551)),f2(a1))) % 183.90/184.42 [3159]E(f182(x31591,f116(f876(x31591))),f116(f876(x31591))) % 183.90/184.42 [3162]E(f333(f333(f80(a1),a82),x31621),a82) % 183.90/184.42 [3163]E(f333(f333(f79(a1),a82),x31631),x31631) % 183.90/184.42 [3166]E(f333(a107,f333(f103(a1),x31661)),x31661) % 183.90/184.42 [3167]E(f333(f333(f22(a1),x31671),a82),x31671) % 183.90/184.42 [3168]E(f333(f333(f79(a1),x31681),a82),x31681) % 183.90/184.42 [3170]E(f333(f333(f22(a875),x31701),x31701),f2(a875)) % 183.90/184.42 [3174]E(f333(f37(a875),f333(f254(a875),x31741)),x31741) % 183.90/184.42 [3175]E(f333(f78(a1),f333(f78(a1),x31751)),x31751) % 183.90/184.42 [3186]E(f333(f333(f79(a875),f2(a875)),x31861),x31861) % 183.90/184.42 [3187]E(f333(f333(f79(a1),f2(a1)),x31871),x31871) % 183.90/184.42 [3188]E(f333(f333(f80(a875),f77(a875)),x31881),x31881) % 183.90/184.42 [3189]E(f333(f333(f80(a1),f77(a1)),x31891),x31891) % 183.90/184.42 [3190]E(f333(f333(f246(a875),f2(a875)),x31901),x31901) % 183.90/184.42 [3196]E(f333(f333(f22(a875),f2(a875)),x31961),f2(a875)) % 183.90/184.42 [3197]E(f333(f333(f80(a875),f2(a875)),x31971),f2(a875)) % 183.90/184.42 [3198]E(f333(f333(f38(a1),f2(a1)),x31981),f2(a1)) % 183.90/184.42 [3199]E(f333(f333(f245(a875),f2(a875)),x31991),f2(a875)) % 183.90/184.42 [3211]E(f126(x32111,f333(f78(a1),x32111)),f133(a1,x32111)) % 183.90/184.42 [3217]E(f333(f303(a875,f2(a875)),x32171),f333(f254(a875),x32171)) % 183.90/184.42 [3218]E(f333(f333(f80(a1),a100),x32181),f333(f78(a1),x32181)) % 183.90/184.42 [3225]E(f333(a107,f333(f106(a1),x32251)),f333(f106(a875),x32251)) % 183.90/184.42 [3226]E(f333(a19,f333(f106(a102),x32261)),f333(f106(a875),x32261)) % 183.90/184.42 [3227]E(f333(f37(a875),f333(f302(a875),x32271)),f333(a115,x32271)) % 183.90/184.42 [3237]E(f333(f333(f79(a875),f77(a875)),x32371),f333(a115,x32371)) % 183.90/184.42 [3241]E(f333(f74(a1),f333(f103(a1),x32411)),f333(f103(a1),x32411)) % 183.90/184.42 [3242]E(f333(f105(a1),f333(f103(a1),x32421)),f333(f103(a1),x32421)) % 183.90/184.42 [3247]E(f333(f37(x32471),f196(f882(x32471,a870))),f2(a875)) % 183.90/184.42 [3249]E(f333(f333(f38(a875),x32491),f333(a115,f2(a875))),x32491) % 183.90/184.42 [3258]E(f44(a875,x32581,f333(a115,f2(a875))),f2(a875)) % 183.90/184.42 [3259]E(f44(a1,x32591,f333(f106(a1),a100)),f2(a1)) % 183.90/184.42 [3275]E(f333(f333(f38(a1),x32751),f333(f106(a1),a100)),f333(f78(a1),x32751)) % 183.90/184.42 [3279]E(f140(a875,f333(f303(a875,x32791),f2(a875))),f116(a875)) % 183.90/184.42 [3280]E(f333(f333(f79(a1),x32801),f77(a1)),f333(f333(f22(a1),x32801),a100)) % 183.90/184.42 [3281]E(f333(f333(f22(a1),x32811),f77(a1)),f333(f333(f79(a1),x32811),a100)) % 183.90/184.42 [3286]P1(f333(f333(f202(a24),x32861),x32861)) % 183.90/184.42 [3287]P1(f333(f333(f247(a875),x32871),x32871)) % 183.90/184.42 [3288]P1(f333(f333(f247(a1),x32881),x32881)) % 183.90/184.42 [3289]P1(f333(f333(f90(a1),x32891),x32891)) % 183.90/184.42 [3294]E(f333(f78(a1),f333(f106(a1),x32941)),f333(f106(a1),f333(f78(a1),x32941))) % 183.90/184.42 [3295]P1(f333(f61(a875),f333(f254(a875),x32951))) % 183.90/184.42 [3296]P1(f333(f61(a875),f333(f302(a875),x32961))) % 183.90/184.42 [3304]E(f162(x33041,f256(f882(x33041,a870))),f256(f882(f876(x33041),a870))) % 183.90/184.42 [3309]P1(f333(f333(f247(a875),f2(a875)),x33091)) % 183.90/184.42 [3319]E(f333(f333(f79(a875),f114(x33191)),f333(a115,f2(a875))),f114(f333(a115,x33191))) % 183.90/184.42 [3320]E(f333(f253(x33201),f333(f16(a870,x33201),a251)),f196(f882(x33201,a870))) % 183.90/184.42 [3321]E(f333(f253(x33211),f333(f16(a870,x33211),a195)),f256(f882(x33211,a870))) % 183.90/184.42 [3325]E(f333(f333(f311(a875),x33251),f333(f254(a875),x33251)),f333(f254(a875),f333(a115,x33251))) % 183.90/184.42 [3337]E(f333(f333(f79(a1),f77(a1)),f333(f103(a1),x33371)),f333(f103(a1),f333(a115,x33371))) % 183.90/184.42 [3339]E(f333(f333(f152(f876(x33391)),f116(x33391)),f116(f876(x33391))),f53(x33391,f116(x33391))) % 183.90/184.42 [3359]E(f196(f882(f881(x33591,x33591),a870)),f265(x33591,f196(f882(x33591,a870)))) % 183.90/184.42 [3360]E(f333(f310(x33601),f256(f882(x33601,a870))),f256(f882(f882(x33601,a870),a870))) % 183.90/184.42 [3361]E(f333(f78(f882(x33611,a870)),f196(f882(x33611,a870))),f256(f882(x33611,a870))) % 183.90/184.42 [3362]E(f333(f78(f882(x33621,a870)),f256(f882(x33621,a870))),f196(f882(x33621,a870))) % 183.90/184.42 [3364]P1(f333(f61(x33641),f196(f882(x33641,a870)))) % 183.90/184.42 [3366]E(f333(f303(a875,x33661),f333(a115,x33661)),f333(f333(f311(a875),x33661),f196(f882(a875,a870)))) % 183.90/184.42 [3367]E(f84(f881(a875,a875),f47(x33671,f2(a875))),f333(f333(f268(a875,a875),f2(a875)),x33671)) % 183.90/184.42 [3381]E(f333(f333(f311(a875),f333(a115,x33811)),f333(f302(a875),x33811)),f333(f302(a875),f333(a115,x33811))) % 183.90/184.42 [3385]P37(x33851,f196(f882(f881(x33851,x33851),a870))) % 183.90/184.42 [3388]P1(f333(f333(f247(a1),f2(a1)),f333(f103(a1),x33881))) % 183.90/184.42 [3396]E(f333(f333(f79(a875),f333(f197(a875),x33961)),f333(a115,f2(a875))),f333(f197(a875),f333(a115,x33961))) % 183.90/184.42 [3507]P38(f333(f312(a875,a1,f103(a1)),x35071)) % 183.90/184.42 [3545]P39(x35451,f196(f882(x35451,a870)),f196(f882(f881(x35451,x35451),a870))) % 183.90/184.42 [3565]E(f333(f333(f268(a1,a1),f333(f106(a1),a100)),f333(f333(f22(a1),x35651),f77(a1))),f49(f333(f106(a1),a100),x35651)) % 183.90/184.42 [3617]P54(x36171,f333(f16(f882(x36171,a870),x36171),f333(f16(a870,x36171),a251))) % 183.90/184.42 [3825]P1(f333(f333(f335(f882(f881(a875,a875),a870)),f334(x38251)),a101)) % 183.90/184.42 [3851]P1(f333(f333(f335(f882(f881(a875,a875),a870)),f333(a109,x38511)),a101)) % 183.90/184.42 [3989]P25(x39891,f882(x39891,a870),f333(f333(f7(x39891,f882(x39891,a870),f882(x39891,a870)),f311(x39891)),f196(f882(x39891,a870))),f256(f882(x39891,a870))) % 183.90/184.42 [4501]~E(f333(f333(f79(a1),x45011),x45011),a100) % 183.90/184.42 [4528]~E(f333(a3,f333(a115,f333(a19,x45281))),f2(a102)) % 183.90/184.42 [4536]~P1(f333(a201,f333(f103(a1),x45361))) % 183.90/184.42 [4539]~P1(f333(f333(f248(a875),x45391),x45391)) % 183.90/184.42 [4548]~P1(f333(f333(f247(a875),f333(a115,x45481)),x45481)) % 183.90/184.42 [3311]E(f333(a107,f333(f78(a1),f333(f103(a1),x33111))),f2(a875)) % 183.90/184.42 [3314]E(f333(f333(f79(a1),f333(f78(a1),x33141)),x33141),f2(a1)) % 183.90/184.42 [3318]E(f333(f37(a1),f333(f303(a1,f2(a1)),x33181)),f333(a107,x33181)) % 183.90/184.42 [3330]E(f333(f333(f258(a875),f333(a115,f2(a875))),x33301),f333(a115,f2(a875))) % 183.90/184.42 [3431]E(f333(f286(x34311),f196(f882(f881(x34311,x34311),a870))),f196(f882(x34311,a870))) % 183.90/184.42 [3439]E(f40(f882(x34391,a870),f196(f882(f882(x34391,a870),a870))),f256(f882(x34391,a870))) % 183.90/184.42 [3440]E(f40(f882(x34401,a870),f256(f882(f882(x34401,a870),a870))),f196(f882(x34401,a870))) % 183.90/184.42 [3441]E(f39(f882(x34411,a870),f196(f882(f882(x34411,a870),a870))),f196(f882(x34411,a870))) % 183.90/184.42 [3442]E(f39(f882(x34421,a870),f256(f882(f882(x34421,a870),a870))),f256(f882(x34421,a870))) % 183.90/184.42 [3489]E(f333(f333(f311(f876(x34891)),f116(x34891)),f196(f882(f876(x34891),a870))),f162(x34891,f196(f882(x34891,a870)))) % 183.90/184.42 [3490]E(f333(f333(f311(f876(x34901)),f116(x34901)),f196(f882(f876(x34901),a870))),f163(x34901,f116(f882(x34901,a870)))) % 183.90/184.42 [3528]E(f333(f333(f79(a875),f4(x35281)),f333(a115,f2(a875))),f4(f333(a3,f333(a115,f333(a19,x35281))))) % 183.90/184.42 [3556]E(f333(f37(a1),f333(f312(a875,a1,f103(a1)),x35561)),f333(f37(a875),x35561)) % 183.90/184.42 [3559]P1(f333(f333(f247(a875),x35591),f333(f333(f80(a875),x35591),x35591))) % 183.90/184.42 [3596]E(f333(f312(a1,a875,a107),f304(a1,f2(a1),f333(f103(a1),x35961))),f333(f302(a875),x35961)) % 183.90/184.42 [3612]E(f333(f333(f38(a875),f333(a115,f2(a875))),f333(f106(a875),x36121)),f333(a107,f333(f333(f38(a1),f77(a1)),f333(f106(a1),x36121)))) % 183.90/184.42 [3614]E(f333(f174(a875),f140(a875,f333(f303(a875,f2(a875)),f333(a115,x36141)))),f333(f302(a875),x36141)) % 183.90/184.42 [3615]E(f333(f333(f79(a875),f333(f197(a102),x36151)),f333(a115,f2(a875))),f333(f197(a102),f333(a3,f333(a115,f333(a19,x36151))))) % 183.90/184.42 [3635]E(f333(f312(a1,a875,a107),f333(f312(a875,a1,f103(a1)),x36351)),x36351) % 183.90/184.42 [3668]E(f333(f333(f311(a875),f2(a875)),f333(f312(a875,a875,a115),f333(f254(a875),x36681))),f333(f254(a875),f333(a115,x36681))) % 183.90/184.42 [3675]P49(x36751,x36751,f309(x36751,f196(f882(f881(x36751,x36751),a870)))) % 183.90/184.42 [3681]P1(f333(a201,f333(f78(a1),f333(f103(a1),f333(a115,x36811))))) % 183.90/184.42 [3692]E(f333(f333(f22(f882(a875,a870)),f333(f255(a875),x36921)),f333(f333(f311(a875),x36921),f196(f882(a875,a870)))),f333(f255(a875),f333(a115,x36921))) % 183.90/184.42 [3708]E(f333(f333(f79(a1),f333(f333(f22(a1),a82),x37081)),f333(f333(f22(a1),a82),x37081)),f333(f333(f22(a1),a82),f333(f333(f79(a1),x37081),x37081))) % 183.90/184.42 [3724]E(f333(f333(f311(f882(x37241,a870)),f196(f882(x37241,a870))),f196(f882(f882(x37241,a870),a870))),f333(f310(x37241),f196(f882(x37241,a870)))) % 183.90/184.42 [3752]E(f333(f333(f22(f882(a875,a870)),f333(f305(a875),x37521)),f333(f333(f311(a875),f333(a115,x37521)),f196(f882(a875,a870)))),f333(f305(a875),f333(a115,x37521))) % 183.90/184.42 [3761]E(f333(f333(f311(f879(x37611)),f209(x37611)),f333(f312(x37611,f879(x37611),f240(x37611)),f256(f882(x37611,a870)))),f256(f882(f879(x37611),a870))) % 183.90/184.42 [3863]E(f333(f106(a875),f333(f333(f79(a1),x38631),x38631)),f333(f333(f85(a875,a875),f333(f106(a875),x38631)),f333(f333(f18(a875,a875,a875),f79(a875)),f5(a875)))) % 183.90/184.42 [4256]P15(x42561,f882(x42561,a870),f333(f333(f8(f882(x42561,a870),f882(f882(x42561,a870),f882(x42561,a870)),x42561),f333(f7(f882(x42561,a870),f882(x42561,a870),f882(x42561,a870)),f22(f882(x42561,a870)))),f333(f333(f7(x42561,f882(x42561,a870),f882(x42561,a870)),f311(x42561)),f196(f882(x42561,a870))))) % 183.90/184.42 [4345]E(f333(f253(f881(a1,a1)),f333(f272(a1,a1,a870),f333(f333(f8(f882(a1,a870),f882(a1,a870),a1),f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),x43451)))),f248(a1)))),f110(x43451)) % 183.90/184.42 [4378]E(f333(f253(f881(a1,a1)),f333(f272(a1,a1,a870),f333(f333(f18(a1,f882(a1,a870),f882(a1,a870)),f333(f333(f8(f882(a870,a870),f882(f882(a1,a870),f882(a1,a870)),a1),f8(a870,a870,a1)),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),x43781)))),f248(a1)))),f108(x43781)) % 183.90/184.42 [4433]E(f333(f253(f881(f882(x44331,a870),f882(x44331,a870))),f333(f272(f882(x44331,a870),f882(x44331,a870),a870),f333(f333(f7(f882(x44331,a870),f882(f882(x44331,a870),a870),f882(f882(x44331,a870),a870)),f333(f333(f8(f882(f882(x44331,a870),f882(a870,a870)),f882(f882(f882(x44331,a870),a870),f882(f882(x44331,a870),a870)),f882(x44331,a870)),f18(f882(x44331,a870),a870,a870)),f333(f333(f8(f882(f882(x44331,a870),a870),f882(f882(x44331,a870),f882(a870,a870)),f882(x44331,a870)),f333(f8(a870,f882(a870,a870),f882(x44331,a870)),a331)),f248(f882(x44331,a870))))),f61(x44331)))),f308(x44331)) % 183.90/184.42 [4552]~P1(f333(f61(f876(x45521)),f256(f882(f876(x45521),a870)))) % 183.90/184.42 [4557]~P1(f333(f333(f90(a1),a100),f333(f333(f79(a1),x45571),x45571))) % 183.90/184.42 [4567]~P1(f333(f333(f247(a1),f2(a1)),f333(f78(a1),f333(f103(a1),f333(a115,x45671))))) % 183.90/184.42 [3466]E(f333(f333(f22(a1),f333(f333(f79(a1),x34661),a100)),a100),x34661) % 183.90/184.42 [3482]E(f333(f174(a875),f140(a875,f333(f303(a875,f2(a875)),x34821))),f333(f254(a875),x34821)) % 183.90/184.42 [3731]E(f333(f333(f79(a1),f333(f333(f79(a1),f77(a1)),x37311)),x37311),f333(f333(f22(a1),f333(f333(f79(a1),x37311),x37311)),a100)) % 183.90/184.42 [3780]E(f333(f288(x37801,x37801),f309(x37801,f196(f882(f881(x37801,x37801),a870)))),f309(x37801,f196(f882(f881(x37801,x37801),a870)))) % 183.90/184.42 [3828]P1(f333(f333(f247(a875),x38281),f333(f333(f80(a875),x38281),f333(f333(f80(a875),x38281),x38281)))) % 183.90/184.42 [4110]P1(f333(f61(a875),f333(f253(a875),f333(f333(f7(a875,a875,a870),f248(a875)),x41101)))) % 183.90/184.42 [4111]P1(f333(f61(a875),f333(f253(a875),f333(f333(f7(a875,a875,a870),f247(a875)),x41111)))) % 183.90/184.42 [4398]E(f333(f253(f881(x43981,x43981)),f333(f333(f8(f882(x43981,a870),a870,f881(x43981,x43981)),f86(x43981)),f333(f333(f7(f881(x43981,x43981),f882(x43981,f881(x43981,x43981)),f882(x43981,a870)),f333(f333(f8(f882(f881(x43981,x43981),a870),f882(f882(x43981,f881(x43981,x43981)),f882(x43981,a870)),f881(x43981,x43981)),f8(f881(x43981,x43981),a870,x43981)),a330)),f333(f333(f18(x43981,x43981,f881(x43981,x43981)),f268(x43981,x43981)),f5(x43981))))),f309(x43981,f196(f882(f881(x43981,x43981),a870)))) % 183.90/184.42 [4554]~E(f333(f333(f22(a1),f333(f333(f79(a1),x45541),x45541)),a100),a82) % 183.90/184.42 [4556]~E(f333(f333(f79(a1),f333(f333(f79(a1),f77(a1)),x45561)),x45561),f2(a1)) % 183.90/184.42 [4564]~P1(f333(f333(f90(a1),f333(f333(f79(a1),x45641),x45641)),a100)) % 183.90/184.42 [3876]E(f333(f333(f79(a1),f333(f333(f22(a1),a100),x38761)),f333(f333(f22(a1),a100),x38761)),f333(f333(f22(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x38761),x38761)),a100))) % 183.90/184.42 [3998]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),a100),x39981)),f333(f333(f22(a1),a100),x39981))),a100),f333(f333(f22(a1),a100),f333(f333(f79(a1),x39981),x39981))) % 183.90/184.42 [4033]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f79(a1),x40331),a100)),f333(f333(f79(a1),x40331),a100))),a100),f333(f333(f79(a1),f333(f333(f79(a1),x40331),x40331)),a100)) % 183.90/184.42 [4072]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),a100),x40721)),f333(f333(f22(a1),a100),x40721))),a100),f333(f333(f22(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x40721),x40721)),a100))) % 183.90/184.42 [4173]E(f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x41731),f2(a875))),f196(f882(f881(a875,a875),a870))))),f333(f103(a1),x41731)) % 183.90/184.42 [4183]E(f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),f338(x41831)),f555(x41831))),f196(f882(f881(a875,a875),a870))))),x41831) % 183.90/184.42 [4218]E(f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x42181)),f333(f312(a875,a1,f103(a1)),f333(f253(a875),f333(f333(f8(a1,a870,a875),x42181),f103(a1))))) % 183.90/184.42 [4264]P38(f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x42641))) % 183.90/184.42 [4285]P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x42851),f196(f882(f881(a875,a875),a870)))),a70)) % 183.90/184.42 [4291]E(f333(f312(a1,a875,a107),f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),f333(f333(f8(a875,a870,a1),x42911),a107)))),f333(f253(a875),x42911)) % 183.90/184.42 [4447]E(f314(a875,f333(f333(f41(f881(a875,a875),f882(a875,a870)),f333(a109,x44471)),f333(f272(a875,a875,f882(a875,a870)),f333(f333(f7(a875,f882(a875,a870),f882(a875,f882(a875,a870))),f333(f333(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))),f333(f333(f8(f882(a875,a875),f882(a875,f882(f882(a875,a870),f882(a875,a870))),a875),f333(f8(a875,f882(f882(a875,a870),f882(a875,a870)),a875),f311(a875))),f22(a875)))),f196(f882(a875,a870)))))),f333(a107,x44471)) % 183.90/184.42 [4569]~P1(f333(f333(f90(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x45691),x45691)),a100))) % 183.90/184.42 [3921]E(f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),x39211),x39211)),a100)),a100),f333(f333(f79(a1),x39211),x39211)) % 183.90/184.42 [3972]E(f333(f333(f22(a1),f333(f333(f22(a1),f333(f333(f79(a1),x39721),x39721)),a100)),a100),f333(f333(f79(a1),f333(f333(f22(a1),x39721),a100)),f333(f333(f22(a1),x39721),a100))) % 183.90/184.42 [4191]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f79(a1),f333(f78(a1),x41911)),a100)),f333(f333(f79(a1),f333(f78(a1),x41911)),a100))),a100),f333(f78(a1),f333(f333(f22(a1),f333(f333(f79(a1),x41911),x41911)),a100))) % 183.90/184.42 [4578]~P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x45781),x45781)),a100)),a82)) % 183.90/184.42 [4236]E(f333(f333(f79(a875),x42361),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(a115,f333(a115,x42361))) % 183.90/184.42 [4237]E(f333(f333(f80(a875),x42371),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f79(a875),x42371),x42371)) % 183.90/184.42 [4238]E(f333(f333(f38(a875),f333(f333(f79(a875),x42381),x42381)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x42381) % 183.90/184.42 [4320]E(f44(a875,f333(a115,f333(a115,x43201)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a875,x43201,f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.42 [4462]E(f333(a88,f333(f333(f41(f881(a875,a875),f882(f881(a875,a875),a870)),f333(a109,x44621)),f333(f272(a875,a875,f882(f881(a875,a875),a870)),f333(f333(f8(f882(a875,f882(f881(a875,a875),a870)),f882(a875,f882(f881(a875,a875),a870)),a875),f333(f8(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870),a875),f287(f881(a875,a875),f881(a875,a875),a111))),f333(f333(f7(a875,f882(f881(a875,a875),a870),f882(a875,f882(f881(a875,a875),a870))),f333(f333(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))),f333(f333(f8(f882(a875,f881(a875,a875)),f882(a875,f882(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),a875),f333(f8(f881(a875,a875),f882(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a875),f311(f881(a875,a875)))),f333(f7(a875,a875,f881(a875,a875)),f268(a875,a875))))),f196(f882(f881(a875,a875),a870))))))),f333(f78(a1),x44621)) % 183.90/184.42 [4315]E(f333(f333(f79(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x43151),f333(a115,f333(a115,x43151))) % 183.90/184.42 [4316]E(f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x43161),f333(f333(f79(a875),x43161),x43161)) % 183.90/184.42 [4350]E(f333(f333(f38(a875),f333(a115,f333(a115,x43501))),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(a115,f333(f333(f38(a875),x43501),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.42 [4404]E(f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44041),f333(a115,f333(a115,f333(a115,x44041)))) % 183.90/184.42 [4470]E(f333(f272(a1,a1,f881(a1,a1)),f333(f333(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f333(f333(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))),f333(f333(f8(f882(a1,f881(a1,a1)),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f333(f18(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f333(f333(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f99(f881(a1,a1))),f333(f333(f8(a1,a870,a1),f333(f247(a1),f2(a1))),f333(f333(f7(a1,a1,a1),f22(a1)),x44701))))),f333(f333(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f333(f333(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f882(a1,a1),a1),f79(a1)),f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f77(a1))))),f333(f333(f7(a1,a1,a1),f22(a1)),x44701))))),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))),f43(x44701)) % 183.90/184.42 [3132]P92(f880(x31321,x31322)) % 183.90/184.42 [3133]P92(f881(x31331,x31332)) % 183.90/184.42 [3134]P102(f880(x31341,x31342)) % 183.90/184.42 [3135]P102(f881(x31351,x31352)) % 183.90/184.42 [3152]P14(a1,f181(x31521,x31522)) % 183.90/184.42 [3153]P37(x31531,f154(x31531,x31532)) % 183.90/184.42 [3219]P31(x32191,x32192,f116(x32191)) % 183.90/184.42 [3253]P39(x32531,x32532,f265(x32531,x32532)) % 183.90/184.42 [3254]P49(x32541,x32541,f265(x32541,x32542)) % 183.90/184.42 [3531]P25(x35311,x35311,f5(x35311),x35312) % 183.90/184.42 [3532]P25(x35321,x35321,f33(x35321),x35322) % 183.90/184.42 [3540]P32(x35401,x35402,f116(x35401),f116(x35401)) % 183.90/184.42 [3541]P25(x35411,f879(x35411),f240(x35411),x35412) % 183.90/184.42 [3550]P25(f876(x35501),f876(x35501),f170(x35501),x35502) % 183.90/184.42 [4481]~E(f32(x44811,x44812),a24) % 183.90/184.42 [4482]~E(f31(x44821,x44822),a24) % 183.90/184.42 [4511]~P33(x45111,x45112,f116(x45111)) % 183.90/184.42 [4512]~P35(x45121,x45122,f116(x45121)) % 183.90/184.42 [3117]E(f333(f5(x31171),x31172),x31172) % 183.90/184.42 [3118]E(f333(f253(x31181),x31182),x31182) % 183.90/184.42 [3120]E(f333(f33(x31201),x31202),x31202) % 183.90/184.42 [3130]E(f333(f199(x31301),x31302),f118(x31301)) % 183.90/184.42 [3150]E(f84(x31501,f333(a330,x31502)),x31502) % 183.90/184.42 [3151]E(f89(x31511,f333(a330,x31512)),x31512) % 183.90/184.42 [3172]E(f333(f137(x31721,x31722),f116(x31721)),f116(x31721)) % 183.90/184.42 [3192]E(f309(x31921,f309(x31921,x31922)),f309(x31921,x31922)) % 183.90/184.42 [3193]E(f153(x31931,f153(x31931,x31932)),f153(x31931,x31932)) % 183.90/184.42 [3214]E(f333(f333(f135(x32141),x32142),f116(x32141)),x32142) % 183.90/184.42 [3220]E(f175(x32201,x32202,f116(x32201)),x32202) % 183.90/184.42 [3221]E(f175(x32211,f116(x32211),x32212),x32212) % 183.90/184.42 [3222]E(f171(x32221,f2(a875),x32222),f116(x32221)) % 183.90/184.42 [3228]E(f333(f333(f177(x32281),x32282),f116(x32281)),f116(x32281)) % 183.90/184.42 [3229]E(f333(f333(f139(x32291),x32292),f116(x32291)),f116(x32291)) % 183.90/184.42 [3231]E(f156(x32311,x32312,f116(x32311)),f2(a875)) % 183.90/184.42 [3232]E(f241(x32321,x32322,f209(x32321)),f2(a875)) % 183.90/184.42 [3234]E(f172(x32341,x32342,f116(x32341)),f116(x32341)) % 183.90/184.42 [3235]E(f179(x32351,x32352,f116(x32351)),f116(x32351)) % 183.90/184.42 [3236]E(f178(x32361,f116(x32361),x32362),f116(x32361)) % 183.90/184.42 [3240]E(f333(f174(x32401),f153(x32401,x32402)),f333(f174(x32401),x32402)) % 183.90/184.42 [3243]E(f333(f264(x32431,x32431),f265(x32431,x32432)),x32432) % 183.90/184.42 [3244]E(f333(f266(x32441,x32441),f265(x32441,x32442)),x32442) % 183.90/184.42 [3252]E(f333(f288(x32521,x32521),f265(x32521,x32522)),f265(x32521,x32522)) % 183.90/184.42 [3267]E(f309(f876(x32671),f158(x32671,x32672)),f159(x32671,f309(x32671,x32672))) % 183.90/184.42 [3269]P1(f333(f138(a1),f181(x32691,x32692))) % 183.90/184.42 [3277]E(f333(f264(x32771,x32771),f309(x32771,x32772)),f256(f882(x32771,a870))) % 183.90/184.42 [3278]E(f333(f266(x32781,x32781),f309(x32781,x32782)),f256(f882(x32781,a870))) % 183.90/184.42 [3282]P1(f333(f138(x32821),f153(x32821,x32822))) % 183.90/184.42 [3284]P1(f333(f161(x32841,x32842),f116(x32841))) % 183.90/184.42 [3292]E(f333(f174(a1),f181(x32921,x32922)),f304(a1,x32921,x32922)) % 183.90/184.42 [3307]P50(x33071,f196(f882(x33071,a870)),x33072) % 183.90/184.42 [3312]E(f333(f271(a1,a1),f45(x33121,x33122)),f44(a1,x33121,x33122)) % 183.90/184.42 [3313]E(f333(f303(a875,x33131),f333(a115,x33132)),f304(a875,x33131,x33132)) % 183.90/184.42 [3329]E(f333(f333(f152(x33291),x33292),f116(x33291)),f141(x33291,x33292,f116(x33291))) % 183.90/184.42 [3341]E(f304(a875,f333(a115,x33411),x33412),f306(a875,x33411,x33412)) % 183.90/184.42 [3344]P39(x33441,f256(f882(x33441,a870)),f309(x33441,x33442)) % 183.90/184.42 [3408]E(f333(f333(f22(a875),x34081),f333(a115,x34082)),f333(f37(a875),f307(a875,x34082,x34081))) % 183.90/184.42 [3467]E(f168(x34671,x34672,f116(x34671)),f333(f333(f268(f876(x34671),f876(x34671)),f116(x34671)),f116(x34671))) % 183.90/184.42 [3487]E(f333(f272(x34871,x34872,f881(x34871,x34872)),f268(x34871,x34872)),f33(f881(x34871,x34872))) % 183.90/184.42 [3492]P1(f333(f333(f335(f876(x34921)),f116(x34921)),f162(x34921,x34922))) % 183.90/184.42 [3493]E(f333(f197(f876(x34931)),f117(x34931,x34932)),f333(f333(f22(a875),f333(f197(f876(x34931)),x34932)),f77(a875))) % 183.90/184.42 [3501]P1(f333(f61(a875),f307(a875,x35011,x35012))) % 183.90/184.42 [3502]P1(f333(f61(a875),f306(a875,x35021,x35022))) % 183.90/184.42 [3503]P1(f333(f61(a875),f304(a875,x35031,x35032))) % 183.90/184.42 [3504]P1(f333(f61(a1),f307(a1,x35041,x35042))) % 183.90/184.42 [3505]P1(f333(f61(a1),f306(a1,x35051,x35052))) % 183.90/184.42 [3506]P1(f333(f61(a1),f304(a1,x35061,x35062))) % 183.90/184.42 [3611]E(f333(f312(a875,a875,a115),f304(a875,x36111,x36112)),f304(a875,f333(a115,x36111),f333(a115,x36112))) % 183.90/184.42 [3632]E(f333(f333(f290(x36321,x36321,x36321),f309(x36321,x36322)),f309(x36321,x36322)),f309(x36321,x36322)) % 183.90/184.42 [3666]E(f333(f333(f268(a1,a1),f333(f333(f38(a1),x36661),x36662)),f44(a1,x36661,x36662)),f45(x36661,x36662)) % 183.90/184.42 [3667]E(f333(f333(f268(a102,a102),f333(f333(f38(a102),x36671),x36672)),f44(a102,x36671,x36672)),f21(x36671,x36672)) % 183.90/184.42 [3696]E(f333(f333(f268(a875,a875),f333(f333(f38(a875),x36961),x36962)),f44(a875,x36961,x36962)),f84(f881(a875,a875),f47(x36961,x36962))) % 183.90/184.42 [3748]P1(f333(f333(f248(a875),f333(f333(f22(a875),x37481),x37482)),f333(a115,x37481))) % 183.90/184.42 [3850]E(f333(f333(f79(a1),f333(f333(f80(a1),x38501),f333(f333(f38(a1),x38502),x38501))),f44(a1,x38502,x38501)),x38502) % 183.90/184.42 [3854]E(f333(f333(f41(a875,f882(f881(f876(x38541),f876(x38541)),a870)),f256(f882(a875,a870))),f144(x38541,x38542)),f146(x38541,x38542)) % 183.90/184.42 [4085]P1(f333(f333(f335(f881(f876(x40851),f876(x40851))),f333(f333(f268(f876(x40851),f876(x40851)),f116(x40851)),f116(x40851))),f159(x40851,x40852))) % 183.90/184.42 [4203]E(f269(x42031,x42031,x42031,a330,f269(x42031,x42031,x42031,x42032,a330)),x42032) % 183.90/184.42 [4249]E(f273(x42491,x42491,x42492,x42492,f5(x42491),f5(x42492)),f33(f881(x42491,x42492))) % 183.90/184.42 [4251]E(f273(x42511,x42511,x42512,x42512,f33(x42511),f33(x42512)),f33(f881(x42511,x42512))) % 183.90/184.42 [4490]~E(f333(f240(x44901),x44902),f209(x44901)) % 183.90/184.42 [3212]E(f333(f244(x32121),f333(f240(x32121),x32122)),x32122) % 183.90/184.42 [3213]E(f333(f170(x32131),f333(f170(x32131),x32132)),x32132) % 183.90/184.42 [3215]E(f333(f333(f139(x32151),f2(a875)),x32152),x32152) % 183.90/184.42 [3230]E(f333(f333(f177(x32301),f2(a875)),x32302),f116(x32301)) % 183.90/184.42 [3238]E(f333(f333(f135(x32381),f116(x32381)),x32382),x32382) % 183.90/184.42 [3246]E(f333(f197(f879(x32461)),f333(f240(x32461),x32462)),f2(a875)) % 183.90/184.42 [3248]E(f39(f882(x32481,a870),f333(f310(x32481),x32482)),x32482) % 183.90/184.42 [3250]E(f333(f174(x32501),f333(f169(x32501),x32502)),f333(f174(x32501),x32502)) % 183.90/184.42 [3251]E(f333(f174(x32511),f333(f170(x32511),x32512)),f333(f174(x32511),x32512)) % 183.90/184.42 [3256]E(f333(f333(f22(a102),x32561),x32562),f333(f333(a23,x32561),x32562)) % 183.90/184.42 [3271]E(f333(f333(f79(a875),x32711),x32712),f333(f333(f79(a875),x32712),x32711)) % 183.90/184.42 [3272]E(f333(f333(f79(a1),x32721),x32722),f333(f333(f79(a1),x32722),x32721)) % 183.90/184.42 [3273]E(f333(f333(f80(a875),x32731),x32732),f333(f333(f80(a875),x32732),x32731)) % 183.90/184.42 [3274]E(f333(f333(f80(a1),x32741),x32742),f333(f333(f80(a1),x32742),x32741)) % 183.90/184.42 [3299]E(f333(f333(f191(x32991,x32991),f2(a875)),x32992),f33(x32991)) % 183.90/184.42 [3300]E(f333(f197(f876(x33001)),f333(f169(x33001),x33002)),f333(f197(f876(x33001)),x33002)) % 183.90/184.42 [3301]E(f333(f197(f876(x33011)),f333(f170(x33011),x33012)),f333(f197(f876(x33011)),x33012)) % 183.90/184.42 [3302]E(f178(x33021,x33022,f196(f882(a875,a870))),f116(x33021)) % 183.90/184.42 [3303]E(f333(f333(f155(x33031,x33031),f5(x33031)),x33032),x33032) % 183.90/184.42 [3305]E(f333(f267(a1,a1),f45(x33051,x33052)),f333(f333(f38(a1),x33051),x33052)) % 183.90/184.42 [3322]E(f333(f197(f876(x33221)),f153(x33221,x33222)),f333(f37(x33221),f333(f174(x33221),x33222))) % 183.90/184.42 [3323]E(f30(f31(x33231,x33232)),f333(f333(f79(a875),f30(x33232)),f333(a115,f2(a875)))) % 183.90/184.42 [3324]E(f333(f286(x33241),f333(f288(x33241,x33241),x33242)),f333(f286(x33241),x33242)) % 183.90/184.42 [3328]P1(f333(f61(x33281),f333(f174(x33281),x33282))) % 183.90/184.42 [3336]E(f333(f333(f79(a1),x33361),f333(f78(a1),x33362)),f333(f333(f22(a1),x33361),x33362)) % 183.90/184.42 [3343]P24(x33431,x33432,f196(f882(f874(x33431),a870))) % 183.90/184.42 [3345]E(f333(f312(x33451,x33451,f5(x33451)),x33452),x33452) % 183.90/184.42 [3346]E(f333(f312(x33461,x33461,f33(x33461)),x33462),x33462) % 183.90/184.42 [3347]E(f333(f313(x33471,x33471,f5(x33471)),x33472),x33472) % 183.90/184.42 [3348]E(f333(f313(x33481,x33481,f33(x33481)),x33482),x33482) % 183.90/184.42 [3349]P1(f333(f256(f882(x33491,a870)),x33492)) % 183.90/184.42 [3351]E(f333(f37(a875),f333(f303(a875,x33511),x33512)),f333(f333(f22(a875),x33512),x33511)) % 183.90/184.42 [3352]E(f333(f303(a875,f333(a115,x33521)),x33522),f307(a875,x33521,x33522)) % 183.90/184.42 [3365]E(f333(f333(f311(x33651),x33652),f196(f882(x33651,a870))),f333(f253(x33651),f333(a330,x33652))) % 183.90/184.42 [3369]E(f333(f333(f311(x33691),x33692),f196(f882(x33691,a870))),f239(x33691,f333(f240(x33691),x33692))) % 183.90/184.42 [3371]E(f309(x33711,f333(f288(x33711,x33711),x33712)),f333(f288(x33711,x33711),f309(x33711,x33712))) % 183.90/184.42 [3376]E(f333(f333(f79(a875),f333(a115,x33761)),x33762),f333(f333(f79(a875),x33761),f333(a115,x33762))) % 183.90/184.42 [3377]E(f333(f333(f22(a875),f333(a115,x33771)),f333(a115,x33772)),f333(f333(f22(a875),x33771),x33772)) % 183.90/184.42 [3383]E(f54(x33831,f2(a875),x33832),f333(f333(f152(f876(x33831)),f116(x33831)),f116(f876(x33831)))) % 183.90/184.42 [3384]E(f333(f37(a875),f306(a875,x33841,x33842)),f333(f333(f22(a875),x33842),x33841)) % 183.90/184.42 [3393]P37(x33931,f333(f333(f289(a875,x33931),a252),x33932)) % 183.90/184.42 [3395]P14(a875,f140(a875,f333(f303(a875,x33951),x33952))) % 183.90/184.42 [3397]P1(f333(f61(a875),f333(f303(a875,x33971),x33972))) % 183.90/184.42 [3398]P1(f333(f61(a1),f333(f303(a1,x33981),x33982))) % 183.90/184.42 [3401]E(f333(f288(f876(x34011),f876(x34011)),f158(x34011,x34012)),f158(x34011,f333(f288(x34011,x34011),x34012))) % 183.90/184.42 [3402]E(f333(f197(a871),f31(x34021,x34022)),f333(f333(f79(a875),f333(f197(a871),x34022)),f333(a115,f2(a875)))) % 183.90/184.42 [3404]E(f333(f303(a1,x34041),f333(f333(f79(a1),x34042),f77(a1))),f304(a1,x34041,x34042)) % 183.90/184.42 [3407]E(f333(f333(f38(a1),f333(f78(a1),x34071)),f333(f78(a1),x34072)),f333(f333(f38(a1),x34071),x34072)) % 183.90/184.42 [3415]E(f186(x34151,x34152,f333(f16(f879(x34152),x34151),f209(x34152))),f196(f882(x34151,a870))) % 183.90/184.42 [3416]E(f188(x34161,x34162,f333(f16(f879(x34162),x34161),f209(x34162))),f196(f882(x34162,a870))) % 183.90/184.42 [3417]E(f333(f333(f191(f881(x34171,x34171),a870),f77(a875)),x34172),x34172) % 183.90/184.42 [3419]E(f333(f333(f113(f882(x34191,a870)),x34192),f196(f882(x34191,a870))),x34192) % 183.90/184.42 [3420]E(f333(f333(f22(f882(x34201,a870)),x34202),f196(f882(x34201,a870))),x34202) % 183.90/184.42 [3421]E(f333(f333(f104(f882(x34211,a870)),x34212),f256(f882(x34211,a870))),x34212) % 183.90/184.42 [3422]E(f333(f267(a875,a875),f84(f881(a875,a875),f47(x34221,x34222))),f333(f333(f38(a875),x34221),x34222)) % 183.90/184.42 [3429]E(f315(x34291,f333(a20,x34292),f333(f78(a1),f333(a20,x34292))),f333(f333(f318(a1),x34291),x34292)) % 183.90/184.42 [3430]E(f304(a1,f333(f333(f79(a1),x34301),f77(a1)),x34302),f306(a1,x34301,x34302)) % 183.90/184.42 [3435]E(f333(f271(a875,a875),f84(f881(a875,a875),f47(x34351,x34352))),f44(a875,x34351,x34352)) % 183.90/184.42 [3443]E(f316(x34431,f333(a20,x34432),f333(f78(a1),f333(a20,x34432))),f317(a1,x34431,x34432)) % 183.90/184.42 [3446]P1(f333(f333(f335(x34461),x34462),f256(f882(x34461,a870)))) % 183.90/184.42 [3451]E(f333(f333(f22(a875),f333(a115,x34511)),x34512),f333(f37(a875),f304(a875,x34512,x34511))) % 183.90/184.42 [3478]E(f333(f333(f113(f882(x34781,a870)),x34782),f256(f882(x34781,a870))),f256(f882(x34781,a870))) % 183.90/184.42 [3479]E(f333(f333(f22(f882(x34791,a870)),x34792),f256(f882(x34791,a870))),f196(f882(x34791,a870))) % 183.90/184.42 [3480]E(f333(f333(f104(f882(x34801,a870)),x34802),f196(f882(x34801,a870))),f196(f882(x34801,a870))) % 183.90/184.42 [3496]E(f44(a1,f333(f103(a1),x34961),f333(f103(a1),x34962)),f333(f103(a1),f44(a875,x34961,x34962))) % 183.90/184.42 [3497]E(f44(a1,f333(f78(a1),x34971),f333(f78(a1),x34972)),f333(f78(a1),f44(a1,x34971,x34972))) % 183.90/184.42 [3508]E(f333(f197(f876(x35081)),f333(f173(x35081),x35082)),f333(f333(f22(a875),f333(f197(f876(x35081)),x35082)),f77(a875))) % 183.90/184.42 [3533]E(f333(f333(f38(a1),f44(a1,x35331,x35332)),x35332),f2(a1)) % 183.90/184.42 [3543]E(f333(a3,f44(a875,f333(a19,x35431),f333(a19,x35432))),f44(a102,x35431,x35432)) % 183.90/184.42 [3578]E(f333(a3,f333(f333(f22(a875),f333(a19,x35781)),f333(a19,x35782))),f333(f333(f22(a102),x35781),x35782)) % 183.90/184.42 [3579]E(f333(a3,f333(f333(f79(a875),f333(a19,x35791)),f333(a19,x35792))),f333(f333(f79(a102),x35791),x35792)) % 183.90/184.42 [3580]E(f333(a3,f333(f333(f80(a875),f333(a19,x35801)),f333(a19,x35802))),f333(f333(f80(a102),x35801),x35802)) % 183.90/184.42 [3581]E(f333(a3,f333(f333(f38(a875),f333(a19,x35811)),f333(a19,x35812))),f333(f333(f38(a102),x35811),x35812)) % 183.90/184.42 [3590]E(f333(f312(a875,a875,a115),f333(f303(a875,x35901),x35902)),f333(f303(a875,f333(a115,x35901)),f333(a115,x35902))) % 183.90/184.42 [3616]P1(f333(f47(x36161,x36162),f84(f881(a875,a875),f47(x36161,x36162)))) % 183.90/184.42 [3638]E(f333(f333(f79(a875),f333(f333(f79(a875),f30(x36381)),f30(x36382))),f333(a115,f2(a875))),f30(f32(x36381,x36382))) % 183.90/184.42 [3639]E(f44(a875,f333(a115,f44(a875,x36391,x36392)),x36392),f44(a875,f333(a115,x36391),x36392)) % 183.90/184.42 [3653]E(f333(f333(f42(f882(x36531,a870),f882(x36531,a870)),x36532),f5(f882(x36531,a870))),f40(f882(x36531,a870),x36532)) % 183.90/184.42 [3654]E(f333(f333(f41(f882(x36541,a870),f882(x36541,a870)),x36542),f5(f882(x36541,a870))),f39(f882(x36541,a870),x36542)) % 183.90/184.42 [3655]E(f333(f312(f876(x36551),f882(x36551,a870),f174(x36551)),f333(f174(f876(x36551)),f53(x36551,x36552))),f333(f310(x36551),f333(f174(x36551),x36552))) % 183.90/184.42 [3659]P1(f333(f333(f335(f882(x36591,a870)),x36592),f333(f310(x36591),x36592))) % 183.90/184.42 [3665]E(f44(a1,f333(f78(a1),f44(a1,x36651,x36652)),x36652),f44(a1,f333(f78(a1),x36651),x36652)) % 183.90/184.42 [3677]P1(f333(f333(f247(f882(x36771,a870)),x36772),f256(f882(x36771,a870)))) % 183.90/184.42 [3679]E(f333(f333(f290(x36791,x36791,x36791),f309(x36791,x36792)),f309(x36791,f309(x36791,x36792))),f309(x36791,x36792)) % 183.90/184.42 [3680]E(f333(f333(f113(f882(x36801,a870)),f333(f266(x36801,x36801),x36802)),f333(f264(x36801,x36801),x36802)),f333(f286(x36801),x36802)) % 183.90/184.42 [3701]E(f320(x37011,x37012,f256(f882(x37011,a870)),f256(f882(x37012,a870))),f256(f882(f880(x37011,x37012),a870))) % 183.90/184.42 [3753]P1(f333(f333(f247(a875),f44(a875,x37531,x37532)),x37531)) % 183.90/184.42 [3778]P1(f333(f333(f247(a1),f333(f78(a1),f333(f103(a1),x37781))),f333(f103(a1),x37782))) % 183.90/184.42 [3804]P1(f333(f333(f335(f882(x38041,a870)),f196(f882(x38041,a870))),f333(f310(x38041),x38042))) % 183.90/184.42 [3809]E(f309(x38091,f333(f333(f290(x38091,x38091,x38091),x38092),f309(x38091,x38092))),f309(x38091,x38092)) % 183.90/184.42 [3812]E(f333(f333(f290(x38121,x38121,x38121),f309(x38121,x38122)),x38122),f333(f333(f290(x38121,x38121,x38121),x38122),f309(x38121,x38122))) % 183.90/184.42 [3814]E(f333(a107,f333(f333(f79(a1),f333(f333(f22(a1),x38141),x38142)),f77(a1))),f333(f37(a1),f304(a1,x38142,x38141))) % 183.90/184.42 [3829]E(f333(f264(x38291,x38291),f333(f333(f290(x38291,x38291,x38291),x38292),f309(x38291,x38292))),f333(f264(x38291,x38291),x38292)) % 183.90/184.42 [3830]E(f333(f266(x38301,x38301),f333(f333(f290(x38301,x38301,x38301),x38302),f309(x38301,x38302))),f333(f266(x38301,x38301),x38302)) % 183.90/184.42 [3846]E(f333(f333(f79(a875),f333(f333(f79(a875),f333(f197(a871),x38461)),f333(f197(a871),x38462))),f333(a115,f2(a875))),f333(f197(a871),f32(x38461,x38462))) % 183.90/184.42 [3849]E(f333(f143(f876(x38491),f876(x38491),f135(x38491),f116(x38491)),f171(f876(x38491),x38492,f116(x38491))),f116(x38491)) % 183.90/184.42 [3858]P25(a875,a875,f333(f333(f7(a875,a875,a875),f79(a875)),x38581),x38582) % 183.90/184.42 [3860]P14(a875,f333(f170(a875),f333(f333(f155(f876(x38601),a875),f197(f876(x38601))),f182(x38601,x38602)))) % 183.90/184.42 [3907]P1(f333(f333(f248(a1),f333(f78(a1),f333(f103(a1),f333(a115,x39071)))),f333(f103(a1),x39072))) % 183.90/184.42 [3953]E(f333(f143(f876(x39531),x39531,f333(f7(x39531,f876(x39531),f876(x39531)),f152(x39531)),f116(x39531)),x39532),f333(f170(x39531),x39532)) % 183.90/184.42 [4005]P1(f333(f333(f247(f882(f881(f876(x40051),f876(x40051)),a870)),f159(x40051,x40052)),f309(f876(x40051),f158(x40051,x40052)))) % 183.90/184.42 [4037]P1(f333(f47(x40371,x40372),f333(f333(f268(a875,a875),f333(f333(f38(a875),x40371),x40372)),f44(a875,x40371,x40372)))) % 183.90/184.42 [4048]P1(f333(f333(f247(f882(f881(f876(x40481),f876(x40481)),a870)),f158(x40481,f309(x40481,x40482))),f309(f876(x40481),f158(x40481,x40482)))) % 183.90/184.42 [4275]E(f333(f333(f274(f881(a102,a102),a102,f881(a102,a102),f881(x42751,f881(a102,a102))),f278(f333(f167(a102),f333(f333(f155(f881(a102,x42751),a102),f267(a102,x42751)),x42752)))),f333(f333(f8(x42751,f882(f881(a102,a102),f881(x42751,f881(a102,a102))),a102),f268(x42751,f881(a102,a102))),f279(x42751,x42752))),f277(x42751,x42752)) % 183.90/184.42 [4386]E(f333(f242(a875,f881(x43861,f877(x43861)),f2(a875),f333(f272(x43861,f877(x43861),a875),f333(f16(f882(f877(x43861),a875),x43861),f333(f333(f7(f877(x43861),a875,a875),f333(f333(f8(a875,f882(a875,a875),f877(x43861)),f79(a875)),f197(f877(x43861)))),f77(a875))))),f333(f136(x43861),x43862)),f333(f197(f877(x43861)),x43862)) % 183.90/184.42 [4461]E(f333(f272(f882(f881(x44611,x44611),a870),f882(f881(x44611,x44611),a870),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f333(f333(f7(f882(f881(x44611,x44611),a870),f882(f882(f881(x44611,x44611),a870),f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870))),f882(f882(f881(x44611,x44611),a870),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870))))),f333(f333(f8(f882(f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870)),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f882(f882(f882(f881(x44611,x44611),a870),f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870))),f882(f882(f881(x44611,x44611),a870),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870))))),f882(f881(x44611,x44611),a870)),f8(f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870)),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870))),f882(f881(x44611,x44611),a870))),f333(f333(f8(f882(f882(x44612,x44611),f882(f882(f881(x44612,x44612),a870),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f882(f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870)),f882(f882(x44612,x44611),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f882(f881(x44611,x44611),a870)),f18(f882(x44612,x44611),f882(f881(x44612,x44612),a870),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f333(f333(f8(f882(f882(x44612,x44611),f882(f881(x44612,x44612),a870)),f882(f882(x44612,x44611),f882(f882(f881(x44612,x44612),a870),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f882(f881(x44611,x44611),a870)),f333(f8(f882(f881(x44612,x44612),a870),f882(f882(f881(x44612,x44612),a870),f881(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870))),f882(x44612,x44611)),f268(f882(f881(x44612,x44612),a870),f882(f881(x44612,x44612),a870)))),f289(x44611,x44612))))),f289(x44611,x44612))),f73(x44611,x44612)) % 183.90/184.42 [4537]~E(f333(f310(x45371),x45372),f196(f882(f882(x45371,a870),a870))) % 183.90/184.42 [4551]~P1(f333(f333(f335(x45511),x45512),f196(f882(x45511,a870)))) % 183.90/184.42 [4561]~P1(f333(f333(f248(f882(x45611,a870)),x45612),f196(f882(x45611,a870)))) % 183.90/184.42 [3354]E(f333(f333(f22(a875),x33541),f333(f333(f79(a875),x33541),x33542)),f2(a875)) % 183.90/184.42 [3357]E(f333(f333(f113(f882(x33571,a870)),x33572),x33572),x33572) % 183.90/184.42 [3358]E(f333(f333(f104(f882(x33581,a870)),x33582),x33582),x33582) % 183.90/184.42 [3386]E(f333(f333(f22(f882(x33861,a870)),x33862),x33862),f196(f882(x33861,a870))) % 183.90/184.42 [3389]E(f333(f144(x33891,x33892),f2(a875)),f196(f882(f881(f876(x33891),f876(x33891)),a870))) % 183.90/184.42 [3390]E(f333(f333(f79(a875),x33901),f333(a115,x33902)),f333(a115,f333(f333(f79(a875),x33901),x33902))) % 183.90/184.42 [3403]E(f203(f333(f103(a1),x34031),f333(f103(a1),x34032)),f333(f103(a1),f333(f333(f22(a875),x34031),x34032))) % 183.90/184.42 [3406]E(f333(f333(f38(a1),f333(f78(a1),x34061)),x34062),f333(f333(f38(a1),x34061),f333(f78(a1),x34062))) % 183.90/184.42 [3410]E(f333(f37(a1),f333(f303(a1,x34101),x34102)),f333(a107,f333(f333(f22(a1),x34102),x34101))) % 183.90/184.42 [3413]E(f333(f333(f79(a875),f333(a115,x34131)),x34132),f333(a115,f333(f333(f79(a875),x34131),x34132))) % 183.90/184.42 [3418]E(f333(f78(f882(x34181,a870)),f333(f78(f882(x34181,a870)),x34182)),x34182) % 183.90/184.42 [3432]E(f182(x34321,f333(f333(f152(f876(x34321)),f116(x34321)),x34322)),f182(x34321,x34322)) % 183.90/184.42 [3436]E(f333(f333(f79(a875),x34361),f333(f333(f80(a875),x34361),x34362)),f333(f333(f80(a875),x34361),f333(a115,x34362))) % 183.90/184.42 [3444]E(f333(f333(a23,f333(a3,x34441)),f333(a3,x34442)),f333(a3,f333(f333(f22(a875),x34441),x34442))) % 183.90/184.42 [3458]E(f333(f333(f80(a1),f333(f78(a1),x34581)),x34582),f333(f78(a1),f333(f333(f80(a1),x34581),x34582))) % 183.90/184.42 [3460]E(f333(f333(f258(a1),f333(f103(a1),x34601)),x34602),f333(f103(a1),f333(f333(f258(a875),x34601),x34602))) % 183.90/184.42 [3461]E(f333(f333(f79(a102),f333(a3,x34611)),f333(a3,x34612)),f333(a3,f333(f333(f79(a875),x34611),x34612))) % 183.90/184.42 [3462]E(f333(f333(f80(a102),f333(a3,x34621)),f333(a3,x34622)),f333(a3,f333(f333(f80(a875),x34621),x34622))) % 183.90/184.42 [3463]E(f333(f333(f245(a875),f333(a115,x34631)),f333(a115,x34632)),f333(a115,f333(f333(f245(a875),x34631),x34632))) % 183.90/184.42 [3464]E(f333(f333(f246(a875),f333(a115,x34641)),f333(a115,x34642)),f333(a115,f333(f333(f246(a875),x34641),x34642))) % 183.90/184.42 [3470]E(f333(f174(a875),f140(a875,f333(f303(a875,x34701),x34702))),f333(f303(a875,x34701),x34702)) % 183.90/184.42 [3471]E(f314(x34711,f333(f333(f311(x34711),x34712),f196(f882(x34711,a870)))),x34712) % 183.90/184.42 [3476]E(f333(f264(x34761,x34762),f196(f882(f881(x34761,x34762),a870))),f196(f882(x34762,a870))) % 183.90/184.42 [3477]E(f333(f266(x34771,x34772),f196(f882(f881(x34771,x34772),a870))),f196(f882(x34771,a870))) % 183.90/184.42 [3481]E(f333(a107,f333(f333(f22(a1),x34811),x34812)),f333(f37(a1),f306(a1,x34812,x34811))) % 183.90/184.42 [3486]E(f333(f333(f79(a875),x34861),f333(f333(f80(a875),x34862),x34861)),f333(f333(f80(a875),f333(a115,x34862)),x34861)) % 183.90/184.42 [3488]E(f333(f333(f60(x34881),f196(f882(x34881,a870))),x34882),f196(f882(f882(x34881,a870),a870))) % 183.90/184.42 [3498]E(f333(f197(f876(a875)),f140(a875,f333(f303(a875,x34981),x34982))),f333(f333(f22(a875),x34982),x34981)) % 183.90/184.42 [3513]E(f333(f333(f113(f882(x35131,a870)),f196(f882(x35131,a870))),x35132),x35132) % 183.90/184.42 [3514]E(f333(f333(f104(f882(x35141,a870)),f256(f882(x35141,a870))),x35142),x35142) % 183.90/184.42 [3517]E(f333(f333(f79(a1),f333(f78(a1),x35171)),f333(f78(a1),x35172)),f333(f78(a1),f333(f333(f79(a1),x35171),x35172))) % 183.90/184.42 [3520]E(f333(f333(f79(a1),f333(f103(a1),x35201)),f333(f103(a1),x35202)),f333(f103(a1),f333(f333(f79(a875),x35201),x35202))) % 183.90/184.42 [3521]E(f333(f333(f79(a1),f333(f106(a1),x35211)),f333(f106(a1),x35212)),f333(f106(a1),f333(f333(f79(a1),x35211),x35212))) % 183.90/184.42 [3523]E(f333(f333(f80(a1),f333(f103(a1),x35231)),f333(f103(a1),x35232)),f333(f103(a1),f333(f333(f80(a875),x35231),x35232))) % 183.90/184.42 [3524]E(f333(f333(f80(a1),f333(f106(a1),x35241)),f333(f106(a1),x35242)),f333(f106(a1),f333(f333(f80(a1),x35241),x35242))) % 183.90/184.42 [3525]E(f333(f333(f38(a1),f333(f103(a1),x35251)),f333(f103(a1),x35252)),f333(f103(a1),f333(f333(f38(a875),x35251),x35252))) % 183.90/184.42 [3544]E(f333(f333(f6(x35441,a875),f333(f16(a875,x35441),f77(a875))),x35442),f333(f37(x35441),x35442)) % 183.90/184.42 [3551]E(f333(f78(a1),f44(a1,f333(f78(a1),x35511),x35512)),f44(a1,x35511,f333(f78(a1),x35512))) % 183.90/184.42 [3553]E(f333(f174(a1),f181(x35531,f333(f333(f22(a1),x35532),f77(a1)))),f333(f303(a1,x35531),x35532)) % 183.90/184.42 [3557]P1(f333(f333(f247(a875),x35571),f333(f333(f79(a875),x35572),x35571))) % 183.90/184.42 [3558]P1(f333(f333(f247(a875),x35581),f333(f333(f79(a875),x35581),x35582))) % 183.90/184.42 [3561]E(f333(f333(f113(f882(x35611,a870)),f256(f882(x35611,a870))),x35612),f256(f882(x35611,a870))) % 183.90/184.42 [3562]E(f333(f333(f22(f882(x35621,a870)),f196(f882(x35621,a870))),x35622),f196(f882(x35621,a870))) % 183.90/184.42 [3563]E(f333(f333(f104(f882(x35631,a870)),f196(f882(x35631,a870))),x35632),f196(f882(x35631,a870))) % 183.90/184.42 [3570]E(f333(f333(f268(a1,a1),x35701),f333(f78(a1),x35702)),f333(a50,f333(f333(f268(a1,a1),x35701),x35702))) % 183.90/184.42 [3571]E(f333(f303(a1,f333(f333(f79(a1),x35711),f77(a1))),x35712),f307(a1,x35711,x35712)) % 183.90/184.42 [3582]E(f333(f333(f80(a875),x35821),f333(f333(f38(a875),x35822),x35821)),f333(f333(f22(a875),x35822),f44(a875,x35822,x35821))) % 183.90/184.42 [3583]E(f333(f333(f80(a1),x35831),f333(f333(f38(a1),x35832),x35831)),f333(f333(f22(a1),x35832),f44(a1,x35832,x35831))) % 183.90/184.42 [3587]E(f333(f174(a1),f181(f333(f333(f79(a1),x35871),f77(a1)),x35872)),f306(a1,x35871,x35872)) % 183.90/184.42 [3591]P1(f333(f333(f247(f882(x35911,a870)),x35912),x35912)) % 183.90/184.42 [3594]E(f333(f333(f113(f882(x35941,a870)),x35942),f333(f78(f882(x35941,a870)),x35942)),f256(f882(x35941,a870))) % 183.90/184.42 [3595]E(f333(f333(f104(f882(x35951,a870)),x35952),f333(f78(f882(x35951,a870)),x35952)),f196(f882(x35951,a870))) % 183.90/184.42 [3603]E(f333(f333(f22(a875),f333(f333(f22(a875),x36031),f77(a875))),x36032),f333(f333(f22(a875),x36031),f333(a115,x36032))) % 183.90/184.42 [3608]E(f333(f333(f22(f882(x36081,a870)),f256(f882(x36081,a870))),x36082),f333(f78(f882(x36081,a870)),x36082)) % 183.90/184.42 [3609]E(f333(f333(f22(a1),f333(f106(a1),x36091)),f333(f106(a1),x36092)),f333(f106(a1),f333(f333(f79(a1),x36091),f333(f78(a1),x36092)))) % 183.90/184.42 [3622]E(f333(f174(a875),f140(a875,f333(f303(a875,x36221),f333(a115,x36222)))),f304(a875,x36221,x36222)) % 183.90/184.42 [3630]P1(f333(f333(f333(f333(a204,a24),x36301),x36302),x36301)) % 183.90/184.42 [3636]E(f333(f197(f876(f876(x36361))),f53(x36361,x36362)),f333(f333(f258(a875),f333(a115,f333(a115,f2(a875)))),f333(f197(f876(x36361)),x36362))) % 183.90/184.42 [3657]E(f333(f333(f191(f881(x36571,x36571),a870),f2(a875)),x36572),f309(x36571,f196(f882(f881(x36571,x36571),a870)))) % 183.90/184.42 [3661]P1(f333(f138(a875),f140(a875,f333(f303(a875,x36611),x36612)))) % 183.90/184.42 [3678]E(f333(f312(a1,a875,a107),f304(a1,f333(f103(a1),x36781),f333(f103(a1),x36782))),f304(a875,x36781,x36782)) % 183.90/184.42 [3688]E(f193(a875,f2(a875),f5(a875),f333(f333(f22(a875),x36881),x36882)),f333(f333(f22(a875),x36881),f333(a115,x36882))) % 183.90/184.42 [3689]E(f333(a107,f333(f333(f22(a1),x36891),f333(f333(f79(a1),x36892),f77(a1)))),f333(f37(a1),f307(a1,x36892,x36891))) % 183.90/184.42 [3725]E(f333(f333(f155(a875,a875),a115),f140(a875,f333(f303(a875,x37251),x37252))),f140(a875,f333(f303(a875,f333(a115,x37251)),f333(a115,x37252)))) % 183.90/184.42 [3733]E(f333(f174(a1),f181(f333(f333(f79(a1),x37331),f77(a1)),f333(f333(f22(a1),x37332),f77(a1)))),f307(a1,x37331,x37332)) % 183.90/184.42 [3744]P1(f333(f333(f247(f882(x37441,a870)),f196(f882(x37441,a870))),x37442)) % 183.90/184.42 [3749]E(f84(x37491,f333(f333(f7(x37491,x37491,a870),a330),x37492)),x37492) % 183.90/184.42 [3750]E(f89(x37501,f333(f333(f7(x37501,x37501,a870),a330),x37502)),x37502) % 183.90/184.42 [3754]E(f333(f174(a875),f140(a875,f333(f303(a875,f333(a115,x37541)),f333(a115,x37542)))),f306(a875,x37541,x37542)) % 183.90/184.42 [3781]E(f333(f333(f270(x37811,x37812),f256(f882(x37811,a870))),f333(f16(f882(x37812,a870),x37811),f256(f882(x37812,a870)))),f256(f882(f881(x37811,x37812),a870))) % 183.90/184.42 [3816]E(f333(f253(x38161),f333(f333(f8(a870,a870,x38161),a328),x38162)),f333(f78(f882(x38161,a870)),f333(f253(x38161),x38162))) % 183.90/184.42 [3819]E(f333(f253(x38191),f333(f333(f7(x38191,x38191,a870),a330),x38192)),f333(f333(f311(x38191),x38192),f196(f882(x38191,a870)))) % 183.90/184.42 [3826]E(f333(f333(f79(a1),f333(f333(f22(a1),x38261),x38262)),f333(f333(f22(a1),x38261),x38262)),f333(f333(f22(a1),f333(f333(f79(a1),x38261),x38261)),f333(f333(f79(a1),x38262),x38262))) % 183.90/184.42 [3827]E(f333(f333(f79(a1),f333(f333(f79(a1),x38271),x38271)),f333(f333(f79(a1),x38272),x38272)),f333(f333(f79(a1),f333(f333(f79(a1),x38271),x38272)),f333(f333(f79(a1),x38271),x38272))) % 183.90/184.42 [3843]P1(f333(f333(f247(a875),f333(f37(x38431),f333(f174(x38431),x38432))),f333(f197(f876(x38431)),x38432))) % 183.90/184.42 [3844]P1(f333(f333(f247(a875),f333(f197(f876(x38441)),f153(x38441,x38442))),f333(f197(f876(x38441)),x38442))) % 183.90/184.42 [3855]E(f333(f253(x38551),f333(f333(f7(x38551,f882(x38551,a870),a870),f335(x38551)),x38552)),x38552) % 183.90/184.42 [3871]E(f333(f333(f177(x38711),f333(f333(f22(a875),f333(f197(f876(x38711)),x38712)),f77(a875))),x38712),f117(x38711,x38712)) % 183.90/184.42 [3894]E(f193(a875,f2(a875),f333(f333(f8(a875,a875,a875),a115),f333(f245(a875),x38941)),x38942),f333(f333(f245(a875),f333(a115,x38941)),x38942)) % 183.90/184.42 [3898]E(f39(f882(x38981,a870),f333(f312(f882(f881(x38981,x38981),a870),f882(x38981,a870),f286(x38981)),x38982)),f333(f286(x38981),f39(f882(f881(x38981,x38981),a870),x38982))) % 183.90/184.42 [3899]E(f193(a875,f333(a115,x38991),f333(f333(f8(a875,a875,a875),a115),f333(f246(a875),x38991)),x38992),f333(f333(f246(a875),f333(a115,x38991)),x38992)) % 183.90/184.42 [3901]E(f333(f333(f268(a1,a1),f333(f333(f38(a1),f333(f74(a1),x39011)),f333(f74(a1),x39012))),f44(a1,f333(f74(a1),x39011),f333(f74(a1),x39012))),f52(x39011,x39012)) % 183.90/184.42 [3924]P1(f333(f333(f247(f882(f882(x39241,a870),a870)),x39242),f333(f310(x39241),f39(f882(x39241,a870),x39242)))) % 183.90/184.42 [3958]E(f333(f333(f41(x39581,f882(x39581,a870)),x39582),f333(f333(f7(x39581,f882(x39581,a870),f882(x39581,a870)),f311(x39581)),f196(f882(x39581,a870)))),x39582) % 183.90/184.42 [3959]E(f333(f333(f290(x39591,x39591,x39591),f333(f288(x39591,x39591),x39592)),f309(x39591,f333(f288(x39591,x39591),x39592))),f333(f288(x39591,x39591),f333(f333(f290(x39591,x39591,x39591),x39592),f309(x39591,x39592)))) % 183.90/184.42 [4028]E(f333(f174(x40281),f333(f143(f876(x40281),f876(x40281),f135(x40281),f116(x40281)),x40282)),f333(f333(f41(f876(x40281),f882(x40281,a870)),f333(f174(f876(x40281)),x40282)),f174(x40281))) % 183.90/184.42 [4061]E(f333(f333(f113(f882(f881(x40611,x40611),a870)),f309(x40611,f196(f882(f881(x40611,x40611),a870)))),f333(f333(f290(x40611,x40611,x40611),f309(x40611,x40612)),x40612)),f309(x40611,x40612)) % 183.90/184.42 [4095]E(f333(f333(f184(x40951,x40951),x40952),x40952),f333(f333(f155(x40951,f881(x40951,x40951)),f333(f333(f18(x40951,x40951,f881(x40951,x40951)),f268(x40951,x40951)),f5(x40951))),x40952)) % 183.90/184.42 [4212]E(f333(f143(a875,f876(x42121),f333(f7(f876(x42121),a875,a875),f333(f333(f8(a875,f882(a875,a875),f876(x42121)),f246(a875)),f197(f876(x42121)))),f2(a875)),f333(f170(f876(x42121)),x42122)),f333(f197(f876(f876(x42121))),f182(x42121,x42122))) % 183.90/184.42 [4290]E(f333(f333(f289(f881(a875,f876(x42901)),f876(x42901)),f326(a875,f876(x42901),a252,f146(x42901,x42902))),f333(f333(f18(f876(x42901),f876(x42901),f881(a875,f876(x42901))),f333(f333(f8(a875,f882(f876(x42901),f881(a875,f876(x42901))),f876(x42901)),f268(a875,f876(x42901))),f197(f876(x42901)))),f5(f876(x42901)))),f147(x42901,x42902)) % 183.90/184.42 [4420]E(f333(f253(x44201),f333(f333(f8(f882(f882(x44201,a870),a870),a870,x44201),f87(f882(x44201,a870))),f333(f333(f8(f882(f882(x44201,a870),a870),f882(f882(x44201,a870),a870),x44201),f333(f18(f882(x44201,a870),a870,a870),f333(f333(f8(a870,f882(a870,a870),f882(x44201,a870)),a336),f333(f333(f7(f882(x44201,a870),f882(f882(x44201,a870),a870),a870),f335(f882(x44201,a870))),x44202)))),f335(x44201)))),f40(f882(x44201,a870),x44202)) % 183.90/184.42 [4562]~P1(f333(f333(f248(a1),f333(f103(a1),x45621)),f333(f78(a1),f333(f103(a1),x45622)))) % 183.90/184.42 [4579]~P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x45791),x45791)),a100)),f333(f333(f79(a1),x45792),x45792))) % 183.90/184.42 [3484]E(f333(f333(f22(a875),f333(f333(f79(a875),x34841),x34842)),x34842),x34841) % 183.90/184.42 [3485]E(f333(f333(f22(a875),f333(f333(f79(a875),x34851),x34852)),x34851),x34852) % 183.90/184.42 [3552]E(f333(f333(f79(a875),f333(f333(f22(a875),x35521),x35522)),x35522),f333(f333(f246(a875),x35521),x35522)) % 183.90/184.42 [3664]E(f333(f333(f80(a875),f333(f333(f38(a875),x36641),x36642)),x36642),f333(f333(f22(a875),x36641),f44(a875,x36641,x36642))) % 183.90/184.42 [3693]E(f333(f174(a875),f140(a875,f333(f303(a875,f333(a115,x36931)),x36932))),f307(a875,x36931,x36932)) % 183.90/184.42 [3700]E(f333(f103(a1),f228(f333(a107,f333(f74(a1),x37001)),f333(a107,f333(f74(a1),x37002)))),f333(f333(a229,x37001),x37002)) % 183.90/184.42 [3702]E(f333(f333(f113(f882(x37021,a870)),f333(f78(f882(x37021,a870)),x37022)),x37022),f256(f882(x37021,a870))) % 183.90/184.42 [3703]E(f333(f333(f104(f882(x37031,a870)),f333(f78(f882(x37031,a870)),x37032)),x37032),f196(f882(x37031,a870))) % 183.90/184.42 [3721]P1(f333(f333(f247(a875),f333(f333(f22(a875),x37211),x37212)),x37211)) % 183.90/184.42 [3722]P1(f333(f333(f247(a875),f333(f333(f38(a875),x37221),x37222)),x37221)) % 183.90/184.42 [3746]P1(f333(f333(f248(a875),x37461),f333(a115,f333(f333(f79(a875),x37462),x37461)))) % 183.90/184.42 [3747]P1(f333(f333(f248(a875),x37471),f333(a115,f333(f333(f79(a875),x37471),x37472)))) % 183.90/184.42 [3765]E(f333(f333(f80(a875),f333(a107,f333(f74(a1),x37651))),f333(a107,f333(f74(a1),x37652))),f333(a107,f333(f74(a1),f333(f333(f80(a1),x37651),x37652)))) % 183.90/184.42 [3777]P1(f333(f333(f247(a1),f2(a1)),f333(f333(f258(a1),f333(f74(a1),x37771)),x37772))) % 183.90/184.42 [3848]E(f333(f287(f876(x38481),f876(x38481),f159(x38481,x38482)),f333(f333(f311(f876(x38481)),f116(x38481)),f196(f882(f876(x38481),a870)))),f333(f333(f311(f876(x38481)),f116(x38481)),f196(f882(f876(x38481),a870)))) % 183.90/184.42 [3869]E(f333(f333(f113(f882(f881(x38691,x38691),a870)),f309(x38691,x38692)),f309(x38691,f196(f882(f881(x38691,x38691),a870)))),f309(x38691,x38692)) % 183.90/184.42 [3884]E(f333(f333(f38(a1),f333(f106(a1),f333(f333(f79(a1),x38841),x38841))),f333(f106(a1),f333(f333(f79(a1),x38842),x38842))),f333(f333(f38(a1),f333(f106(a1),x38841)),f333(f106(a1),x38842))) % 183.90/184.42 [3948]E(f333(f333(f258(a1),x39481),f333(f106(a875),f333(f333(f79(a1),x39482),x39482))),f333(f333(f85(a1,a1),f333(f333(f258(a1),x39481),f333(f106(a875),x39482))),f333(f333(f18(a1,a1,a1),f80(a1)),f5(a1)))) % 183.90/184.42 [3954]E(f333(f253(f882(x39541,a870)),f333(f333(f7(f882(x39541,a870),f882(x39541,a870),a870),f247(f882(x39541,a870))),x39542)),f333(f310(x39541),x39542)) % 183.90/184.42 [3969]E(f333(f333(f155(a1,a875),a107),f333(f333(f135(a1),f333(f333(f155(a875,a1),f103(a1)),x39691)),f333(f333(f155(a875,a1),f103(a1)),x39692))),f333(f333(f135(a875),x39691),x39692)) % 183.90/184.42 [4004]E(f333(f312(a1,a1,f333(f333(f7(a1,a1,a1),f79(a1)),x40041)),f333(f303(a1,f2(a1)),f333(f333(f22(a1),x40042),x40041))),f333(f303(a1,x40041),x40042)) % 183.90/184.42 [4006]P41(x40061,f333(f333(f22(f882(f881(x40061,x40061),a870)),x40062),f309(x40061,f196(f882(f881(x40061,x40061),a870))))) % 183.90/184.42 [4026]E(f333(f197(f876(x40261)),f333(f143(f876(x40261),f876(x40261),f135(x40261),f116(x40261)),x40262)),f333(f167(a875),f333(f333(f155(f876(x40261),a875),f197(f876(x40261))),x40262))) % 183.90/184.42 [4031]P39(x40311,f256(f882(x40311,a870)),f333(f333(f113(f882(f881(x40311,x40311),a870)),x40312),f309(x40311,f196(f882(f881(x40311,x40311),a870))))) % 183.90/184.42 [4075]E(f193(a875,f2(a875),f333(f333(f8(a875,a875,a875),a115),f333(f333(f7(a875,a875,a875),f245(a875)),x40751)),x40752),f333(f333(f245(a875),x40752),f333(a115,x40751))) % 183.90/184.42 [4078]E(f193(a875,f333(a115,x40781),f333(f333(f8(a875,a875,a875),a115),f333(f333(f7(a875,a875,a875),f246(a875)),x40781)),x40782),f333(f333(f246(a875),x40782),f333(a115,x40781))) % 183.90/184.42 [4081]E(f333(f312(x40811,f876(x40811),f333(f333(f7(x40811,f876(x40811),f876(x40811)),f152(x40811)),f116(x40811))),x40812),f176(x40811,x40812,f333(f333(f311(f876(x40811)),f116(x40811)),f196(f882(f876(x40811),a870))))) % 183.90/184.42 [4082]E(f333(f333(f113(f882(f881(x40821,x40821),a870)),f333(f333(f290(x40821,x40821,x40821),x40822),f309(x40821,x40822))),f309(x40821,f196(f882(f881(x40821,x40821),a870)))),f309(x40821,x40822)) % 183.90/184.42 [4090]P1(f333(f333(f247(f882(f881(x40901,x40901),a870)),f265(x40901,x40902)),f333(f333(f270(x40901,x40901),x40902),f333(f16(f882(x40901,a870),x40901),x40902)))) % 183.90/184.42 [4093]E(f333(f312(a1,a875,a107),f333(f333(f113(f882(a1,a870)),f333(f312(a875,a1,f103(a1)),x40931)),f333(f312(a875,a1,f103(a1)),x40932))),f333(f333(f113(f882(a875,a870)),x40931),x40932)) % 183.90/184.42 [4094]E(f333(f312(a1,a875,a107),f333(f333(f104(f882(a1,a870)),f333(f312(a875,a1,f103(a1)),x40941)),f333(f312(a875,a1,f103(a1)),x40942))),f333(f333(f104(f882(a875,a870)),x40941),x40942)) % 183.90/184.42 [4098]E(f333(f253(x40981),f333(f333(f8(a870,a870,x40981),a328),f333(f333(f7(x40981,f882(x40981,a870),a870),f335(x40981)),x40982))),f333(f78(f882(x40981,a870)),x40982)) % 183.90/184.42 [4125]E(f333(f143(f876(x41251),f876(x41251),f135(x41251),f116(x41251)),f333(f333(f155(f876(x41251),f876(x41251)),f170(x41251)),f333(f170(f876(x41251)),x41252))),f333(f170(x41251),f333(f143(f876(x41251),f876(x41251),f135(x41251),f116(x41251)),x41252))) % 183.90/184.42 [4154]E(f333(f333(f41(a875,f882(f881(x41541,x41541),a870)),f256(f882(a875,a870))),f333(f333(f7(a875,f882(f881(x41541,x41541),a870),f882(f881(x41541,x41541),a870)),f191(f881(x41541,x41541),a870)),x41542)),f309(x41541,x41542)) % 183.90/184.42 [4174]E(f84(x41741,f333(f333(f8(f882(x41741,a870),a870,x41741),f333(a330,x41742)),f333(f333(f7(x41741,f882(x41741,a870),f882(x41741,a870)),f311(x41741)),f196(f882(x41741,a870))))),f314(x41741,x41742)) % 183.90/184.42 [4182]E(f333(f197(f876(x41821)),f153(x41821,f333(f143(f876(x41821),f876(x41821),f135(x41821),f116(x41821)),x41822))),f333(f37(x41821),f333(f333(f41(f876(x41821),f882(x41821,a870)),f333(f174(f876(x41821)),x41822)),f174(x41821)))) % 183.90/184.42 [4198]E(f333(f333(f113(f882(f881(x41981,x41981),a870)),x41982),f333(f333(f290(x41981,x41981,x41981),f333(f333(f290(x41981,x41981,x41981),x41982),f309(x41981,x41982))),x41982)),f333(f333(f290(x41981,x41981,x41981),x41982),f309(x41981,x41982))) % 183.90/184.42 [4222]P1(f333(f333(f247(f882(f881(x42221,x42221),a870)),f333(f333(f290(x42221,x42221,x42221),x42222),f309(x42221,x42222))),f333(f333(f270(x42221,x42221),f333(f286(x42221),x42222)),f333(f16(f882(x42221,a870),x42221),f333(f286(x42221),x42222))))) % 183.90/184.42 [4265]E(f333(f253(f876(x42651)),f333(f333(f7(f876(x42651),f882(x42651,a870),a870),f333(f333(f8(f882(x42651,a870),f882(f882(x42651,a870),a870),f876(x42651)),f247(f882(x42651,a870))),f174(x42651))),x42652)),f162(x42651,x42652)) % 183.90/184.42 [4277]E(f333(f157(f876(x42771),x42771,f116(x42771),f333(f333(f8(f876(x42771),f882(f876(x42771),f876(x42771)),x42771),f333(f7(f876(x42771),f876(x42771),f876(x42771)),f135(x42771))),f333(f333(f7(x42771,f876(x42771),f876(x42771)),f152(x42771)),f116(x42771)))),x42772),f333(f169(x42771),x42772)) % 183.90/184.42 [4319]P25(f882(x43191,x43192),f882(f881(x43191,x43192),a870),f333(f333(f8(f882(f881(x43191,x43192),a870),f882(f881(x43191,x43192),a870),f882(x43191,x43192)),f253(f881(x43191,x43192))),f333(f333(f8(f882(x43191,f882(x43192,a870)),f882(f881(x43191,x43192),a870),f882(x43191,x43192)),f272(x43191,x43192,a870)),f333(f8(x43192,f882(x43192,a870),x43191),f333(f7(x43192,x43192,a870),a330)))),f256(f882(f882(x43191,x43192),a870))) % 183.90/184.42 [4324]E(f44(a1,f333(f106(a1),f333(f333(f79(a1),x43241),x43241)),f333(f106(a1),f333(f333(f79(a1),x43242),x43242))),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a1,f333(f106(a1),x43241),f333(f106(a1),x43242)))) % 183.90/184.42 [4367]E(f333(f333(f41(x43671,f882(f881(x43671,x43671),a870)),x43672),f333(f333(f7(x43671,f882(f881(x43671,x43671),a870),f882(f881(x43671,x43671),a870)),f333(f333(f8(f881(x43671,x43671),f882(f882(f881(x43671,x43671),a870),f882(f881(x43671,x43671),a870)),x43671),f311(f881(x43671,x43671))),f333(f333(f18(x43671,x43671,f881(x43671,x43671)),f268(x43671,x43671)),f5(x43671)))),f196(f882(f881(x43671,x43671),a870)))),f265(x43671,x43672)) % 183.90/184.42 [4375]E(f214(x43751,f333(f333(f268(a1,a1),f333(f78(a1),f333(f333(f72(f881(a1,a1),a1,x43751,f267(a1,a1)),f224(x43751)),x43752))),f333(f333(f72(f881(a1,a1),a1,x43751,f271(a1,a1)),f224(x43751)),x43752))),f232(x43751,x43752)) % 183.90/184.42 [4456]E(f333(f253(f882(x44561,a870)),f333(f333(f8(f882(f882(x44561,a870),a870),a870,f882(x44561,a870)),f86(f882(x44561,a870))),f333(f333(f7(f882(x44561,a870),f882(f882(x44561,a870),a870),f882(f882(x44561,a870),a870)),f333(f333(f8(f882(f882(x44561,a870),f882(a870,a870)),f882(f882(f882(x44561,a870),a870),f882(f882(x44561,a870),a870)),f882(x44561,a870)),f18(f882(x44561,a870),a870,a870)),f333(f333(f8(f882(f882(x44561,a870),a870),f882(f882(x44561,a870),f882(a870,a870)),f882(x44561,a870)),f333(f8(a870,f882(a870,a870),f882(x44561,a870)),a331)),f333(f333(f7(f882(x44561,a870),f882(f882(x44561,a870),f882(x44561,a870)),f882(f882(x44561,a870),a870)),f333(f333(f8(f882(f882(x44561,a870),a870),f882(f882(f882(x44561,a870),f882(x44561,a870)),f882(f882(x44561,a870),a870)),f882(x44561,a870)),f8(f882(x44561,a870),a870,f882(x44561,a870))),a330)),f78(f882(x44561,a870)))))),f333(f333(f8(f882(f882(x44561,a870),a870),a870,f882(x44561,a870)),f333(f335(f882(x44561,a870)),x44562)),f310(x44561))))),f333(f310(x44561),f333(f78(f882(x44561,a870)),x44562))) % 183.90/184.42 [4559]~E(f333(f333(f79(a1),x45591),x45591),f333(f333(f22(a1),f333(f333(f79(a1),x45592),x45592)),a100)) % 183.90/184.42 [4565]~P1(f333(f333(f248(a875),f333(f333(f79(a875),x45651),x45652)),x45652)) % 183.90/184.42 [4566]~P1(f333(f333(f248(a875),f333(f333(f79(a875),x45661),x45662)),x45661)) % 183.90/184.42 [3782]E(f333(f333(f22(a875),x37821),f333(f333(f80(a875),f333(f333(f38(a875),x37821),x37822)),x37822)),f44(a875,x37821,x37822)) % 183.90/184.42 [3783]E(f333(f333(f22(a1),x37831),f333(f333(f80(a1),f333(f333(f38(a1),x37831),x37832)),x37832)),f44(a1,x37831,x37832)) % 183.90/184.42 [3817]E(f333(f333(f155(a875,x38171),f333(f166(x38171),x38172)),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(x38171)),x38172)))),x38172) % 183.90/184.42 [3880]E(f333(f287(x38801,x38801,f309(x38801,f196(f882(f881(x38801,x38801),a870)))),x38802),x38802) % 183.90/184.42 [4009]E(f309(x40091,f333(f333(f113(f882(f881(x40091,x40091),a870)),x40092),f309(x40091,f196(f882(f881(x40091,x40091),a870))))),f309(x40091,x40092)) % 183.90/184.42 [4010]E(f309(x40101,f333(f333(f22(f882(f881(x40101,x40101),a870)),x40102),f309(x40101,f196(f882(f881(x40101,x40101),a870))))),f309(x40101,x40102)) % 183.90/184.42 [4064]E(f333(f333(f22(a1),f333(f333(f22(a1),f333(f333(f79(a1),x40641),x40641)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x40642),x40642)),a100)),f333(f333(f79(a1),f333(f333(f22(a1),x40641),x40642)),f333(f333(f22(a1),x40641),x40642))) % 183.90/184.42 [4103]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f79(a1),x41031),x41032)),f333(f333(f79(a1),x41031),x41032))),a100),f333(f333(f79(a1),f333(f333(f79(a1),x41031),x41031)),f333(f333(f22(a1),f333(f333(f79(a1),x41032),x41032)),a100))) % 183.90/184.42 [4129]E(f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),x41291),x41291)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x41292),x41292)),a100)),f333(f333(f79(a1),f333(f333(f79(a1),x41291),f333(f333(f22(a1),x41292),a100))),f333(f333(f79(a1),x41291),f333(f333(f22(a1),x41292),a100)))) % 183.90/184.42 [4139]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),x41391),x41392)),f333(f333(f22(a1),x41391),x41392))),a100),f333(f333(f22(a1),f333(f333(f22(a1),f333(f333(f79(a1),x41391),x41391)),a100)),f333(f333(f79(a1),x41392),x41392))) % 183.90/184.42 [4140]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f79(a1),x41401),x41402)),f333(f333(f79(a1),x41401),x41402))),a100),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),x41401),x41401)),a100)),f333(f333(f79(a1),x41402),x41402))) % 183.90/184.42 [4195]E(f333(f103(a1),f333(f333(f38(a875),f333(f333(f80(a875),f333(a107,f333(f74(a1),x41951))),f333(a107,f333(f74(a1),x41952)))),f228(f333(a107,f333(f74(a1),x41951)),f333(a107,f333(f74(a1),x41952))))),f230(x41951,x41952)) % 183.90/184.42 [4242]E(f333(f333(f274(f881(a102,a102),a102,f881(a102,a102),f881(x42421,f881(a102,a102))),f278(f333(a3,f333(f197(f876(x42421)),x42422)))),f333(f333(f8(x42421,f882(f881(a102,a102),f881(x42421,f881(a102,a102))),a102),f268(x42421,f881(a102,a102))),f333(f333(f8(a875,x42421,a102),f333(f166(x42421),x42422)),a19))),f284(x42421,x42422)) % 183.90/184.42 [4325]E(f333(f143(a875,f876(x43251),f333(f7(f876(x43251),a875,a875),f333(f333(f8(a875,f882(a875,a875),f876(x43251)),f246(a875)),f197(f876(x43251)))),f2(a875)),f333(f170(f876(x43251)),f182(x43251,x43252))),f333(f197(f876(f876(x43251))),f333(f137(f876(x43251),f333(f333(f8(a870,a870,f876(x43251)),a328),f333(f333(f7(f876(x43251),f876(x43251),a870),a330),f116(x43251)))),x43252))) % 183.90/184.42 [4331]E(f333(f333(f41(a875,f882(x43311,a870)),f256(f882(a875,a870))),f333(f333(f7(a875,f882(a875,f882(x43311,a870)),f882(x43311,a870)),f333(f333(f8(f882(a875,a870),f882(f882(a875,f882(x43311,a870)),f882(x43311,a870)),a875),f41(a875,f882(x43311,a870))),f303(a875,f2(a875)))),x43312)),f333(f333(f41(a875,f882(x43311,a870)),f256(f882(a875,a870))),x43312)) % 183.90/184.42 [4351]P1(f333(f61(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),x43511)),f333(f333(f7(a875,a875,a870),f248(a875)),x43512))))) % 183.90/184.42 [4467]E(f333(f253(f881(f876(x44671),f876(x44671))),f333(f272(f876(x44671),f876(x44671),a870),f333(f333(f18(f876(x44671),f882(f876(x44671),a870),f882(f876(x44671),a870)),f333(f333(f8(f882(f876(x44671),f882(a870,a870)),f882(f882(f876(x44671),a870),f882(f876(x44671),a870)),f876(x44671)),f18(f876(x44671),a870,a870)),f333(f333(f8(f882(f876(x44671),a870),f882(f876(x44671),f882(a870,a870)),f876(x44671)),f333(f8(a870,f882(a870,a870),f876(x44671)),a332)),f333(f333(f7(f876(x44671),f882(f876(x44671),a875),f882(f876(x44671),a870)),f333(f333(f8(f882(a875,a870),f882(f882(f876(x44671),a875),f882(f876(x44671),a870)),f876(x44671)),f8(a875,a870,f876(x44671))),f333(f333(f8(a875,f882(a875,a870),f876(x44671)),f248(a875)),f197(f876(x44671))))),f197(f876(x44671)))))),f333(f333(f18(f876(x44671),f882(f876(x44671),a870),f882(f876(x44671),a870)),f333(f333(f8(f882(f876(x44671),f882(a870,a870)),f882(f882(f876(x44671),a870),f882(f876(x44671),a870)),f876(x44671)),f18(f876(x44671),a870,a870)),f333(f333(f8(f882(f876(x44671),a870),f882(f876(x44671),f882(a870,a870)),f876(x44671)),f333(f8(a870,f882(a870,a870),f876(x44671)),a331)),f333(f333(f7(f876(x44671),f882(f876(x44671),a875),f882(f876(x44671),a870)),f333(f333(f8(f882(a875,a870),f882(f882(f876(x44671),a875),f882(f876(x44671),a870)),f876(x44671)),f8(a875,a870,f876(x44671))),f333(f333(f8(a875,f882(a875,a870),f876(x44671)),a330),f197(f876(x44671))))),f197(f876(x44671)))))),f333(f333(f7(f876(x44671),f882(f881(f876(x44671),f876(x44671)),a870),f882(f876(x44671),a870)),f333(f333(f8(f882(f876(x44671),f882(f882(f881(f876(x44671),f876(x44671)),a870),a870)),f882(f882(f881(f876(x44671),f876(x44671)),a870),f882(f876(x44671),a870)),f876(x44671)),f7(f876(x44671),f882(f881(f876(x44671),f876(x44671)),a870),a870)),f333(f333(f8(f882(f876(x44671),f881(f876(x44671),f876(x44671))),f882(f876(x44671),f882(f882(f881(f876(x44671),f876(x44671)),a870),a870)),f876(x44671)),f333(f8(f881(f876(x44671),f876(x44671)),f882(f882(f881(f876(x44671),f876(x44671)),a870),a870),f876(x44671)),f335(f881(f876(x44671),f876(x44671))))),f268(f876(x44671),f876(x44671))))),f146(x44671,x44672)))))),f147(x44671,x44672)) % 183.90/184.42 [4572]~P1(f333(f333(f90(a1),f333(f333(f79(a1),x45721),x45721)),f333(f333(f22(a1),f333(f333(f79(a1),x45722),x45722)),a100))) % 183.90/184.42 [4132]E(f333(f333(f79(a1),f333(f333(f79(a1),f333(f333(f80(a1),x41321),x41322)),f333(f333(f80(a1),x41321),x41322))),x41322),f333(f333(f80(a1),f333(f333(f22(a1),f333(f333(f79(a1),x41321),x41321)),a100)),x41322)) % 183.90/184.42 [4240]E(f333(a107,f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x42401),x42402)),f196(f882(f881(a875,a875),a870)))))),f333(f333(f22(a875),x42401),x42402)) % 183.90/184.42 [4245]E(f333(f333(f290(x42451,x42451,x42451),f333(f333(f113(f882(f881(x42451,x42451),a870)),x42452),f309(x42451,f196(f882(f881(x42451,x42451),a870))))),f309(x42451,f333(f333(f113(f882(f881(x42451,x42451),a870)),x42452),f309(x42451,f196(f882(f881(x42451,x42451),a870)))))),f309(x42451,x42452)) % 183.90/184.42 [4283]E(f279(x42831,f333(f137(f881(a102,x42831),f333(f272(a102,x42831,a870),f333(f333(f8(a870,f882(x42831,a870),a102),f16(a870,x42831)),f333(f248(a102),f2(a102))))),x42832)),f279(x42831,x42832)) % 183.90/184.42 [4284]E(f277(x42841,f333(f137(f881(a102,x42841),f333(f272(a102,x42841,a870),f333(f333(f8(a870,f882(x42841,a870),a102),f16(a870,x42841)),f333(f248(a102),f2(a102))))),x42842)),f277(x42841,x42842)) % 183.90/184.42 [4286]E(f333(f78(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x42861),x42862)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x42862),x42861)),f196(f882(f881(a875,a875),a870)))))) % 183.90/184.42 [4343]E(f333(f333(f289(f876(a875),x43431),f146(a875,a252)),f333(f333(f7(x43431,f876(f882(x43431,a875)),f876(a875)),f333(f333(f8(f882(f882(x43431,a875),a875),f882(f876(f882(x43431,a875)),f876(a875)),x43431),f155(f882(x43431,a875),a875)),f333(f7(f882(x43431,a875),x43431,a875),f5(f882(x43431,a875))))),x43432)),f154(x43431,x43432)) % 183.90/184.42 [4364]E(f333(f333(f85(a1,a875),f333(f106(a1),f333(f333(f79(a1),x43641),a100))),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f2(a875))),f333(f333(f8(a875,a875,a1),a115),f333(f333(f8(a875,a875,a1),f333(f245(a875),x43642)),a107)))),f333(f333(f245(a875),f333(a115,x43642)),f333(f106(a875),x43641))) % 183.90/184.42 [4365]E(f333(f333(f85(a1,a875),f333(f106(a1),f333(f333(f79(a1),x43651),a100))),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f333(a115,x43652))),f333(f333(f8(a875,a875,a1),a115),f333(f333(f8(a875,a875,a1),f333(f246(a875),x43652)),a107)))),f333(f333(f246(a875),f333(a115,x43652)),f333(f106(a875),x43651))) % 183.90/184.42 [4385]E(f333(f143(f876(x43851),f876(x43851),f135(x43851),f116(x43851)),f333(f333(f155(f876(x43851),f876(x43851)),f157(f876(x43851),x43851,f116(x43851),f333(f333(f8(f876(x43851),f882(f876(x43851),f876(x43851)),x43851),f16(f876(x43851),f876(x43851))),f333(f333(f7(x43851,f876(x43851),f876(x43851)),f152(x43851)),f116(x43851))))),x43852)),f333(f333(f155(f876(x43851),x43851),f142(x43851)),f333(f137(f876(x43851),f333(f333(f8(a870,a870,f876(x43851)),a328),f333(f333(f7(f876(x43851),f876(x43851),a870),a330),f116(x43851)))),x43852))) % 183.90/184.43 [4448]E(f333(f272(a1,a1,a870),f333(f333(f7(a1,f882(a1,a870),f882(a1,a870)),f333(f333(f8(f882(a1,f882(a870,a870)),f882(f882(a1,a870),f882(a1,a870)),a1),f18(a1,a870,a870)),f333(f333(f8(f882(a1,a870),f882(a1,f882(a870,a870)),a1),f333(f8(a870,f882(a870,a870),a1),a331)),f333(f333(f8(f882(a1,a1),f882(a1,a870),a1),f333(f8(a1,a870,a1),f333(a330,x44481))),f333(f333(f8(a1,f882(a1,a1),a1),f79(a1)),f333(f80(a1),x44482)))))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),f333(a336,f333(f333(f248(a1),f2(a1)),x44482))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),f333(f333(f7(a1,a1,a870),f248(a1)),x44482))))),f333(f333(f8(a870,a870,a1),f333(a336,f333(a328,f333(f333(f248(a1),f2(a1)),x44482)))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f248(a1),x44482))),f333(f333(f7(a1,a1,a870),f247(a1)),f2(a1))))))),f48(x44481,x44482)) % 183.90/184.43 [4450]E(f333(f253(x44501),f333(f333(f8(f882(a875,a870),a870,x44501),f86(a875)),f333(f333(f7(x44501,f882(a875,a870),f882(a875,a870)),f333(f333(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),x44501),f18(a875,a870,a870)),f333(f333(f8(f882(a875,a870),f882(a875,f882(a870,a870)),x44501),f333(f8(a870,f882(a870,a870),a875),a331)),f333(f333(f7(x44501,f882(a875,x44501),f882(a875,a870)),f333(f333(f8(f882(x44501,a870),f882(f882(a875,x44501),f882(a875,a870)),x44501),f8(x44501,a870,a875)),a330)),f333(f166(x44501),x44502))))),f333(f333(f7(a875,a875,a870),f248(a875)),f333(f197(f876(x44501)),x44502))))),f333(f174(x44501),x44502)) % 183.90/184.43 [4255]E(f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),x42551),a100)),x42552)),f333(f333(f22(a1),f333(f333(f79(a1),x42551),a100)),x42552))),a100),f333(f333(f22(a1),f333(f333(f79(a1),x42551),x42551)),f333(f333(f22(a1),f333(f333(f79(a1),x42552),x42552)),a100))) % 183.90/184.43 [4380]E(f333(f143(f876(f876(x43801)),f876(f876(x43801)),f135(f876(x43801)),f116(f876(x43801))),f333(f333(f155(f876(x43801),f876(f876(x43801))),f157(f876(f876(x43801)),x43801,f116(f876(x43801)),f333(f16(f882(f876(x43801),f876(f876(x43801))),x43801),f333(f333(f7(f876(x43801),f876(f876(x43801)),f876(f876(x43801))),f152(f876(x43801))),f116(f876(x43801)))))),x43802)),f333(f333(f155(f876(x43801),f876(x43801)),f173(x43801)),f333(f137(f876(x43801),f333(f333(f8(a870,a870,f876(x43801)),a328),f333(f333(f7(f876(x43801),f876(x43801),a870),a330),f116(x43801)))),x43802))) % 183.90/184.43 [4391]E(f333(f333(f85(a1,a875),f333(f106(a1),f333(f333(f79(a1),x43911),a100))),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f2(a875))),f333(f333(f8(a875,a875,a1),a115),f333(f333(f7(a1,a875,a875),f333(f333(f8(a875,f882(a875,a875),a1),f245(a875)),a107)),x43912)))),f333(f333(f245(a875),f333(f106(a875),x43911)),f333(a115,x43912))) % 183.90/184.43 [4392]E(f333(f333(f85(a1,a875),f333(f106(a1),f333(f333(f79(a1),x43921),a100))),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f333(a115,x43922))),f333(f333(f8(a875,a875,a1),a115),f333(f333(f7(a1,a875,a875),f333(f333(f8(a875,f882(a875,a875),a1),f246(a875)),a107)),x43922)))),f333(f333(f246(a875),f333(f106(a875),x43921)),f333(a115,x43922))) % 183.90/184.43 [4379]E(f333(f272(x43791,x43791,a870),f333(f333(f18(x43791,a870,f882(x43791,a870)),f333(f333(f8(f882(x43791,f882(a870,a870)),f882(a870,f882(x43791,a870)),x43791),f7(x43791,a870,a870)),f333(f333(f8(f882(x43791,a870),f882(x43791,f882(a870,a870)),x43791),f333(f8(a870,f882(a870,a870),x43791),a331)),a330))),x43792)),f265(x43791,x43792)) % 183.90/184.43 [4426]E(f333(f333(f38(a875),x44261),f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44262)),f333(f333(f38(a875),x44261),f333(a115,f333(a115,f333(a115,x44262))))) % 183.90/184.43 [4427]E(f44(a875,x44271,f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44272)),f44(a875,x44271,f333(a115,f333(a115,f333(a115,x44272))))) % 183.90/184.43 [4428]E(f44(a875,f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44281),x44282),f44(a875,f333(a115,f333(a115,f333(a115,x44281))),x44282)) % 183.90/184.43 [4441]E(f125(f333(x44411,f333(f333(f80(a102),f333(f106(a102),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44412))),f333(f212(x44411),x44412)) % 183.90/184.43 [4442]E(f333(f333(f38(a875),f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),x44421)),x44422),f333(f333(f38(a875),f333(a115,f333(a115,f333(a115,x44421)))),x44422)) % 183.90/184.43 [4491]~E(f32(x44911,x44912),f333(a25,x44913)) % 183.90/184.43 [4492]~E(f31(x44921,x44922),f333(a25,x44923)) % 183.90/184.43 [4493]~E(f333(a25,x44931),f32(x44932,x44933)) % 183.90/184.43 [4494]~E(f333(a25,x44941),f31(x44942,x44943)) % 183.90/184.43 [4507]~E(f29(x45071,x45072,x45073),a24) % 183.90/184.43 [4508]~E(f28(x45081,x45082,x45083),a24) % 183.90/184.43 [3194]E(f333(f200(x31941,x31942),x31943),f122(x31941,x31942)) % 183.90/184.43 [3216]E(f333(f211(x32161,x32162),x32163),f333(f127(x32161),x32162)) % 183.90/184.43 [3297]E(f333(f333(f155(x32971,x32972),x32973),f116(x32971)),f116(x32972)) % 183.90/184.43 [3298]E(f333(f333(f210(x32981,x32982),x32983),f209(x32981)),f209(x32982)) % 183.90/184.43 [3338]E(f333(f192(x33381,x33382,x33383),f2(a875)),x33382) % 183.90/184.43 [3340]E(f333(f333(f184(x33401,x33402),x33403),f116(x33402)),f116(f881(x33401,x33402))) % 183.90/184.43 [3355]E(f333(f197(f876(x33551)),f171(x33551,x33552,x33553)),x33552) % 183.90/184.43 [3375]E(f84(x33751,f62(x33751,x33752,x33753)),f333(f63(x33751,x33752),x33753)) % 183.90/184.43 [3379]E(f257(x33791,x33792,f257(x33792,x33791,x33793)),x33793) % 183.90/184.43 [3399]E(f333(f170(x33991),f171(x33991,x33992,x33993)),f171(x33991,x33992,x33993)) % 183.90/184.43 [3428]E(f141(x34281,x34282,f153(x34281,x34283)),f153(x34281,f141(x34281,x34282,x34283))) % 183.90/184.43 [3447]E(f333(f267(f876(x34471),f876(x34471)),f168(x34471,x34472,x34473)),f333(f137(x34471,x34472),x34473)) % 183.90/184.43 [3494]E(f333(f333(f152(x34941),x34942),f171(x34941,x34943,x34942)),f171(x34941,f333(a115,x34943),x34942)) % 183.90/184.43 [3526]E(f193(x35261,x35262,x35263,f2(a875)),x35262) % 183.90/184.43 [3527]E(f17(x35271,x35272,x35273,f2(a102)),x35272) % 183.90/184.43 [3534]E(f164(x35341,x35342,x35343,f116(x35341)),f116(x35342)) % 183.90/184.43 [3535]E(f165(x35351,x35352,x35353,f116(x35351)),f116(x35352)) % 183.90/184.43 [3542]E(f333(f333(f166(x35421),f333(f333(f152(x35421),x35422),x35423)),f2(a875)),x35422) % 183.90/184.43 [3572]E(f59(x35721,x35722,f116(x35721),x35723),f116(f881(x35721,x35722))) % 183.90/184.43 [3593]P25(x35931,x35932,x35933,f196(f882(x35931,a870))) % 183.90/184.43 [3755]E(f333(f72(x37551,x37552,x37551,x37553),f33(x37551)),x37553) % 183.90/184.43 [3939]P1(f333(f333(f335(f881(x39391,x39391)),f333(f333(f268(x39391,x39391),x39392),x39392)),f309(x39391,x39393))) % 183.90/184.43 [4573]~P1(f333(f333(f335(f881(f876(x45731),f876(x45731))),f333(f333(f268(f876(x45731),f876(x45731)),x45732),f116(x45731))),f146(x45731,x45733))) % 183.90/184.43 [4574]~P1(f333(f333(f335(f881(f876(x45741),f876(x45741))),f333(f333(f268(f876(x45741),f876(x45741)),x45742),f116(x45741))),f148(x45741,x45743))) % 183.90/184.43 [4575]~P1(f333(f333(f335(f881(f876(x45751),f876(x45751))),f333(f333(f268(f876(x45751),f876(x45751)),x45752),f116(x45751))),f158(x45751,x45753))) % 183.90/184.43 [4576]~P1(f333(f333(f335(f881(f876(x45761),f876(x45761))),f333(f333(f268(f876(x45761),f876(x45761)),f116(x45761)),x45762)),f146(x45761,x45763))) % 183.90/184.43 [4577]~P1(f333(f333(f335(f881(f876(x45771),f876(x45771))),f333(f333(f268(f876(x45771),f876(x45771)),f116(x45771)),x45772)),f158(x45771,x45773))) % 183.90/184.43 [3270]E(f333(f333(f213(x32701),x32702),x32703),f214(x32701,f227(x32702,x32703))) % 183.90/184.43 [3327]E(f333(f288(x33271,x33272),f333(f288(x33272,x33271),x33273)),x33273) % 183.90/184.43 [3350]E(f333(f333(f184(x33501,x33502),f116(x33501)),x33503),f116(f881(x33501,x33502))) % 183.90/184.43 [3353]E(f178(x33531,x33532,f333(f254(a875),x33533)),f333(f333(f177(x33531),x33533),x33532)) % 183.90/184.43 [3372]E(f153(x33721,f333(f137(x33721,x33722),x33723)),f333(f137(x33721,x33722),f153(x33721,x33723))) % 183.90/184.43 [3373]E(f333(f264(x33731,x33732),f333(f288(x33732,x33731),x33733)),f333(f266(x33732,x33731),x33733)) % 183.90/184.43 [3374]E(f333(f266(x33741,x33742),f333(f288(x33742,x33741),x33743)),f333(f264(x33742,x33741),x33743)) % 183.90/184.43 [3391]E(f333(f137(x33911,x33912),f333(f170(x33911),x33913)),f333(f170(x33911),f333(f137(x33911,x33912),x33913))) % 183.90/184.43 [3405]E(f333(f333(f139(x34051),x34052),f333(f173(x34051),x34053)),f333(f333(f139(x34051),f333(a115,x34052)),x34053)) % 183.90/184.43 [3423]E(f30(f28(x34231,x34232,x34233)),f333(f333(f79(a875),f30(x34233)),f333(a115,f2(a875)))) % 183.90/184.43 [3424]E(f333(f312(x34241,x34242,x34243),f196(f882(x34241,a870))),f196(f882(x34242,a870))) % 183.90/184.43 [3425]E(f333(f313(x34251,x34252,x34253),f196(f882(x34252,a870))),f196(f882(x34251,a870))) % 183.90/184.43 [3426]E(f333(f313(x34261,x34262,x34263),f256(f882(x34262,a870))),f256(f882(x34261,a870))) % 183.90/184.43 [3427]E(f333(f287(x34271,x34272,x34273),f196(f882(x34271,a870))),f196(f882(x34272,a870))) % 183.90/184.43 [3456]E(f333(f333(f311(x34561),x34562),f333(f174(x34561),x34563)),f333(f174(x34561),f141(x34561,x34562,x34563))) % 183.90/184.43 [3468]E(f241(x34681,x34682,f333(f240(x34681),x34683)),f333(f333(f79(a875),f333(x34682,x34683)),f333(a115,f2(a875)))) % 183.90/184.43 [3546]E(f333(f197(a871),f28(x35461,x35462,x35463)),f333(f333(f79(a875),f333(f197(a871),x35463)),f333(a115,f2(a875)))) % 183.90/184.43 [3547]E(f333(f312(f881(x35471,x35472),x35472,f271(x35471,x35472)),x35473),f333(f264(x35471,x35472),x35473)) % 183.90/184.43 [3548]E(f333(f312(f881(x35481,x35482),x35481,f267(x35481,x35482)),x35483),f333(f266(x35481,x35482),x35483)) % 183.90/184.43 [3564]E(f333(f174(x35641),f171(x35641,f333(a115,x35642),x35643)),f333(f333(f311(x35641),x35643),f196(f882(x35641,a870)))) % 183.90/184.43 [3621]E(f333(f333(f268(x36211,x36212),f333(f267(x36211,x36212),x36213)),f333(f271(x36211,x36212),x36213)),x36213) % 183.90/184.43 [3628]E(f333(f197(f877(x36281)),f128(x36281,x36282,x36283)),f333(f333(f79(a875),f333(f197(f877(x36281)),x36283)),f333(a115,f2(a875)))) % 183.90/184.43 [3631]E(f333(f333(f272(x36311,x36312,x36311),f16(x36311,x36312)),x36313),f333(f267(x36311,x36312),x36313)) % 183.90/184.43 [3651]E(f187(x36511,x36512,x36513,f333(f16(f879(x36512),x36511),f209(x36512))),x36513) % 183.90/184.43 [3652]E(f187(x36521,x36522,f333(f16(f879(x36522),x36521),f209(x36522)),x36523),x36523) % 183.90/184.43 [3709]E(f30(f29(x37091,x37092,x37093)),f333(f333(f79(a875),f333(f333(f79(a875),f30(x37092)),f30(x37093))),f333(a115,f2(a875)))) % 183.90/184.43 [3760]E(f333(f72(x37601,x37601,x37602,f33(x37601)),x37603),x37603) % 183.90/184.43 [3768]E(f333(f333(f135(x37681),f171(x37681,x37682,x37683)),f333(f333(f152(x37681),x37683),f116(x37681))),f333(f333(f152(x37681),x37683),f171(x37681,x37682,x37683))) % 183.90/184.43 [3872]E(f333(f197(a871),f29(x38721,x38722,x38723)),f333(f333(f79(a875),f333(f333(f79(a875),f333(f197(a871),x38722)),f333(f197(a871),x38723))),f333(a115,f2(a875)))) % 183.90/184.43 [3949]P1(f333(f333(f247(f882(x39491,a870)),f333(f174(x39491),f333(f137(x39491,x39492),x39493))),f333(f174(x39491),x39493))) % 183.90/184.43 [3994]P1(f333(f333(f247(f882(x39941,a870)),f333(f174(x39941),f333(f333(f177(x39941),x39942),x39943))),f333(f174(x39941),x39943))) % 183.90/184.43 [3995]P1(f333(f333(f247(f882(x39951,a870)),f333(f174(x39951),f333(f333(f139(x39951),x39952),x39953))),f333(f174(x39951),x39953))) % 183.90/184.43 [4000]P1(f333(f333(f247(f882(x40001,a870)),f333(f174(x40001),f178(x40001,x40002,x40003))),f333(f174(x40001),x40002))) % 183.90/184.43 [4001]P1(f333(f333(f247(f882(x40011,a870)),f333(f174(x40011),f172(x40011,x40012,x40013))),f333(f174(x40011),x40013))) % 183.90/184.43 [4024]P25(f881(x40241,x40242),f881(x40242,x40241),f333(f272(x40241,x40242,f881(x40242,x40241)),f333(f7(x40242,x40241,f881(x40242,x40241)),f268(x40242,x40241))),x40243) % 183.90/184.43 [4036]E(f333(f333(f333(f191(f876(x40361),f876(x40361)),f44(a875,x40362,f333(f197(f876(x40361)),x40363))),f169(x40361)),x40363),f333(f333(f333(f191(f876(x40361),f876(x40361)),x40362),f169(x40361)),x40363)) % 183.90/184.43 [4079]P1(f333(f333(f335(f881(f876(x40791),f876(x40791))),f333(f333(f268(f876(x40791),f876(x40791)),x40792),x40792)),f159(x40791,f309(x40791,x40793)))) % 183.90/184.43 [4225]E(f84(f881(x42251,x42252),f333(f333(f18(f881(x42251,x42252),x42252,a870),f333(f333(f8(x42251,f882(x42252,a870),f881(x42251,x42252)),x42253),f267(x42251,x42252))),f271(x42251,x42252))),f84(f881(x42251,x42252),f333(f272(x42251,x42252,a870),x42253))) % 183.90/184.43 [4226]E(f89(f881(x42261,x42262),f333(f333(f18(f881(x42261,x42262),x42262,a870),f333(f333(f8(x42261,f882(x42262,a870),f881(x42261,x42262)),x42263),f267(x42261,x42262))),f271(x42261,x42262))),f89(f881(x42261,x42262),f333(f272(x42261,x42262,a870),x42263))) % 183.90/184.43 [4262]E(f333(f333(f289(f881(a875,x42621),x42621),f326(a875,x42621,a252,x42622)),f333(f333(f18(x42621,x42621,f881(a875,x42621)),f333(f333(f8(a875,f882(x42621,f881(a875,x42621)),x42621),f268(a875,x42621)),x42623)),f5(x42621))),f327(x42621,x42623,x42622)) % 183.90/184.43 [4327]E(f333(f273(x43271,x43271,x43272,x43272,f5(x43271),f5(x43272)),x43273),x43273) % 183.90/184.43 [4402]E(f333(f143(f876(f876(x44021)),f876(f876(x44021)),f135(f876(x44021)),f116(f876(x44021))),f333(f333(f155(f876(x44021),f876(f876(x44021))),f333(f333(f7(f876(x44021),f876(x44021),f876(f876(x44021))),f333(f333(f8(f882(x44021,f876(x44021)),f882(f876(x44021),f876(f876(x44021))),f876(x44021)),f155(x44021,f876(x44021))),f333(f7(x44021,f876(x44021),f876(x44021)),f152(x44021)))),x44022)),f54(x44021,x44023,x44022))),f54(x44021,f333(a115,x44023),x44022)) % 183.90/184.43 [4463]E(f333(f242(a875,f881(x44631,f877(x44631)),f2(a875),f333(f272(x44631,f877(x44631),a875),f333(f333(f7(x44631,a875,f882(f877(x44631),a875)),f333(f333(f8(f882(f877(x44631),f882(a875,a875)),f882(a875,f882(f877(x44631),a875)),x44631),f7(f877(x44631),a875,a875)),f333(f333(f8(f882(f877(x44631),a875),f882(f877(x44631),f882(a875,a875)),x44631),f333(f8(a875,f882(a875,a875),f877(x44631)),f79(a875))),f333(f333(f7(x44631,f882(f877(x44631),a875),f882(f877(x44631),a875)),f333(f333(f8(f882(a875,a875),f882(f882(f877(x44631),a875),f882(f877(x44631),a875)),x44631),f8(a875,a875,f877(x44631))),f333(f333(f8(a875,f882(a875,a875),x44631),f79(a875)),x44632))),f130(x44631,x44632))))),f77(a875)))),f333(f136(x44631),x44633)),f333(f130(x44631,x44632),x44633)) % 183.90/184.43 [4466]E(f333(f333(f85(a1,x44661),f230(f333(f333(f72(f881(a1,a1),a1,x44661,f271(a1,a1)),f224(x44661)),x44662),f333(f333(f72(f881(a1,a1),a1,x44661,f271(a1,a1)),f224(x44661)),x44663))),f333(f333(f18(a1,a1,x44661),f333(f333(f8(a1,f882(a1,x44661),a1),f213(x44661)),f333(f333(f18(a1,a1,a1),f333(f333(f8(a1,f882(a1,a1),a1),f79(a1)),f333(f333(f8(a1,a1,a1),f333(f80(a1),f333(f333(f72(f881(a1,a1),a1,x44661,f267(a1,a1)),f224(x44661)),x44662))),f333(f333(f7(a1,a1,a1),f38(a1)),f333(f333(f72(f881(a1,a1),a1,x44661,f271(a1,a1)),f224(x44661)),x44662))))),f333(f333(f8(a1,a1,a1),f333(f80(a1),f333(f333(f72(f881(a1,a1),a1,x44661,f267(a1,a1)),f224(x44661)),x44663))),f333(f333(f7(a1,a1,a1),f38(a1)),f333(f333(f72(f881(a1,a1),a1,x44661,f271(a1,a1)),f224(x44661)),x44663)))))),f5(a1))),f235(x44661,x44662,x44663)) % 183.90/184.43 [4503]~E(f333(f333(f152(x45031),x45032),x45033),x45033) % 183.90/184.43 [4510]~E(f333(f333(f152(x45101),x45102),x45103),f116(x45101)) % 183.90/184.43 [4526]~E(f333(f333(f311(x45261),x45262),x45263),f196(f882(x45261,a870))) % 183.90/184.43 [4549]~E(f333(f312(x45491,f882(x45491,a870),x45492),x45493),f333(f310(x45491),x45493)) % 183.90/184.43 [3332]E(f333(f333(f160(x33321,f116(x33321)),x33322),x33323),f116(x33321)) % 183.90/184.43 [3333]E(f333(f142(x33331),f333(f333(f152(x33331),x33332),x33333)),x33332) % 183.90/184.43 [3334]E(f333(f173(x33341),f333(f333(f152(x33341),x33342),x33343)),x33343) % 183.90/184.43 [3378]E(f333(f333(f139(x33781),f77(a875)),f333(f333(f152(x33781),x33782),x33783)),x33783) % 183.90/184.43 [3412]E(f117(x34121,f333(f333(f139(x34121),x34122),x34123)),f333(f333(f139(x34121),x34122),f117(x34121,x34123))) % 183.90/184.43 [3414]E(f333(f333(f160(x34141,x34142),x34143),f333(f333(f166(x34141),x34142),x34143)),x34142) % 183.90/184.43 [3438]E(f333(f333(f311(x34381),x34382),f333(f333(f311(x34381),x34382),x34383)),f333(f333(f311(x34381),x34382),x34383)) % 183.90/184.43 [3449]E(f333(f333(f180(x34491,x34492),f116(f881(x34491,x34492))),x34493),f209(x34492)) % 183.90/184.43 [3452]E(f333(f333(f311(x34521),x34522),f333(f174(x34521),x34523)),f333(f174(x34521),f333(f333(f152(x34521),x34522),x34523))) % 183.90/184.43 [3454]E(f333(f333(f139(x34541),x34542),f333(f173(x34541),x34543)),f333(f173(x34541),f333(f333(f139(x34541),x34542),x34543))) % 183.90/184.43 [3465]E(f333(f333(f177(x34651),f77(a875)),f333(f333(f152(x34651),x34652),x34653)),f333(f333(f152(x34651),x34652),f116(x34651))) % 183.90/184.43 [3511]E(f333(f63(x35111,x35112),f333(f333(f311(x35111),x35113),f196(f882(x35111,a870)))),x35113) % 183.90/184.43 [3554]E(f333(f333(f79(a875),x35541),f333(f333(f79(a875),x35542),x35543)),f333(f333(f79(a875),x35542),f333(f333(f79(a875),x35541),x35543))) % 183.90/184.43 [3555]E(f333(f333(f79(a1),x35551),f333(f333(f79(a1),x35552),x35553)),f333(f333(f79(a1),x35552),f333(f333(f79(a1),x35551),x35553))) % 183.90/184.43 [3560]E(f333(f333(f270(x35601,x35602),f196(f882(x35601,a870))),x35603),f196(f882(f881(x35601,x35602),a870))) % 183.90/184.43 [3585]E(f333(f333(f113(f882(x35851,a870)),x35852),x35853),f333(f333(f113(f882(x35851,a870)),x35853),x35852)) % 183.90/184.43 [3586]E(f333(f333(f104(f882(x35861,a870)),x35862),x35863),f333(f333(f104(f882(x35861,a870)),x35863),x35862)) % 183.90/184.43 [3588]E(f333(f333(f135(x35881),x35882),f333(f333(f152(x35881),x35883),f116(x35881))),f333(f169(x35881),f333(f333(f152(x35881),x35883),x35882))) % 183.90/184.43 [3589]E(f333(f333(f135(x35891),f333(f170(x35891),x35892)),f333(f170(x35891),x35893)),f333(f170(x35891),f333(f333(f135(x35891),x35893),x35892))) % 183.90/184.43 [3599]E(f333(f173(x35991),f333(f333(f177(x35991),f333(a115,x35992)),x35993)),f333(f333(f177(x35991),x35992),f333(f173(x35991),x35993))) % 183.90/184.43 [3606]P1(f333(f333(f335(x36061),x36062),f333(f333(f311(x36061),x36062),x36063))) % 183.90/184.43 [3610]E(f333(f333(f42(x36101,f882(x36102,a870)),f196(f882(x36101,a870))),x36103),f256(f882(x36102,a870))) % 183.90/184.43 [3613]E(f333(f287(x36131,x36131,f265(x36131,x36132)),x36133),f333(f333(f104(f882(x36131,a870)),x36132),x36133)) % 183.90/184.43 [3627]E(f333(f197(f876(x36271)),f333(f333(f152(x36271),x36272),x36273)),f333(f333(f79(a875),f333(f197(f876(x36271)),x36273)),f333(a115,f2(a875)))) % 183.90/184.43 [3633]E(f117(x36331,f333(f333(f135(x36331),x36332),f333(f333(f152(x36331),x36333),f116(x36331)))),x36332) % 183.90/184.43 [3634]E(f145(x36341,f333(f333(f135(x36341),x36342),f333(f333(f152(x36341),x36343),f116(x36341)))),x36343) % 183.90/184.43 [3640]E(f333(f333(f135(x36401),f333(f333(f177(x36401),x36402),x36403)),f333(f333(f139(x36401),x36402),x36403)),x36403) % 183.90/184.43 [3649]E(f333(f333(f22(a875),f333(f333(f79(a875),x36491),x36492)),f333(f333(f79(a875),x36493),x36492)),f333(f333(f22(a875),x36491),x36493)) % 183.90/184.43 [3650]E(f333(f333(f22(a875),f333(f333(f79(a875),x36501),x36502)),f333(f333(f79(a875),x36501),x36503)),f333(f333(f22(a875),x36502),x36503)) % 183.90/184.43 [3658]E(f333(f333(f135(x36581),f333(f170(x36581),x36582)),f333(f333(f152(x36581),x36583),f116(x36581))),f333(f170(x36581),f333(f333(f152(x36581),x36583),x36582))) % 183.90/184.43 [3660]E(f333(f333(f79(a875),f333(f197(f876(x36601)),x36602)),f333(f197(f876(x36601)),x36603)),f333(f197(f876(x36601)),f333(f333(f135(x36601),x36602),x36603))) % 183.90/184.43 [3663]E(f333(f333(f79(a875),f333(f197(f876(x36631)),x36632)),f333(f197(f876(x36631)),x36633)),f333(f197(f876(x36631)),f175(x36631,x36632,x36633))) % 183.90/184.43 [3671]E(f333(f333(f113(f882(x36711,a870)),f333(f174(x36711),x36712)),f333(f174(x36711),x36713)),f333(f174(x36711),f333(f333(f135(x36711),x36712),x36713))) % 183.90/184.43 [3672]E(f44(a875,f333(f333(f80(a875),x36721),x36722),f333(f333(f80(a875),x36721),x36723)),f333(f333(f80(a875),x36721),f44(a875,x36722,x36723))) % 183.90/184.43 [3685]E(f333(f333(f177(x36851),f333(f333(f22(a875),x36852),f77(a875))),f333(f173(x36851),x36853)),f333(f173(x36851),f333(f333(f177(x36851),x36852),x36853))) % 183.90/184.43 [3690]E(f333(f333(f104(f882(x36901,a870)),x36902),f333(f78(f882(x36901,a870)),x36903)),f333(f333(f22(f882(x36901,a870)),x36902),x36903)) % 183.90/184.43 [3691]E(f333(f333(f22(f882(x36911,a870)),x36912),f333(f78(f882(x36911,a870)),x36913)),f333(f333(f104(f882(x36911,a870)),x36912),x36913)) % 183.90/184.43 [3713]E(f333(f333(f270(x37131,x37132),x37133),f333(f16(f882(x37132,a870),x37131),f196(f882(x37132,a870)))),f196(f882(f881(x37131,x37132),a870))) % 183.90/184.43 [3715]E(f333(f333(f22(a875),f333(f333(f80(a875),x37151),x37152)),f333(f333(f80(a875),x37151),x37153)),f333(f333(f80(a875),x37151),f333(f333(f22(a875),x37152),x37153))) % 183.90/184.43 [3716]E(f333(f333(f79(a875),f333(f333(f80(a875),x37161),x37162)),f333(f333(f80(a875),x37161),x37163)),f333(f333(f80(a875),x37161),f333(f333(f79(a875),x37162),x37163))) % 183.90/184.43 [3717]E(f333(f333(f22(a1),f333(f333(f80(a1),x37171),x37172)),f333(f333(f80(a1),x37171),x37173)),f333(f333(f80(a1),x37171),f333(f333(f22(a1),x37172),x37173))) % 183.90/184.43 [3718]E(f333(f333(f79(a1),f333(f333(f80(a1),x37181),x37182)),f333(f333(f80(a1),x37181),x37183)),f333(f333(f80(a1),x37181),f333(f333(f79(a1),x37182),x37183))) % 183.90/184.43 [3719]E(f333(f333(f80(a1),f333(f333(f258(a1),x37191),x37192)),f333(f333(f258(a1),x37191),x37193)),f333(f333(f258(a1),x37191),f333(f333(f79(a875),x37192),x37193))) % 183.90/184.43 [3734]E(f333(f333(f41(x37341,f882(x37342,a870)),x37343),f333(f16(f882(x37342,a870),x37341),f196(f882(x37342,a870)))),f196(f882(x37342,a870))) % 183.90/184.43 [3736]E(f44(a875,f333(f333(f80(a875),x37361),x37362),f333(f333(f80(a875),x37363),x37362)),f333(f333(f80(a875),f44(a875,x37361,x37363)),x37362)) % 183.90/184.43 [3740]E(f44(a1,f333(f333(f22(a1),x37401),f44(a1,x37402,x37403)),x37403),f44(a1,f333(f333(f22(a1),x37401),x37402),x37403)) % 183.90/184.43 [3741]E(f44(a1,f333(f333(f80(a1),x37411),f44(a1,x37412,x37413)),x37413),f44(a1,f333(f333(f80(a1),x37411),x37412),x37413)) % 183.90/184.43 [3742]P1(f333(f333(f247(f882(x37421,a870)),x37422),f333(f333(f311(x37421),x37423),x37422))) % 183.90/184.43 [3745]E(f333(f312(f881(x37451,x37452),x37451,f267(x37451,x37452)),f333(f174(f881(x37451,x37452)),x37453)),f186(x37451,x37452,f333(f180(x37451,x37452),x37453))) % 183.90/184.43 [3796]P1(f333(f61(x37961),f186(x37961,x37962,f333(f180(x37961,x37962),x37963)))) % 183.90/184.43 [3821]E(f333(f333(f42(f882(x38211,a870),f882(x38211,a870)),x38212),f333(f113(f882(x38211,a870)),x38213)),f333(f333(f113(f882(x38211,a870)),x38213),f40(f882(x38211,a870),x38212))) % 183.90/184.43 [3822]E(f333(f333(f41(f882(x38221,a870),f882(x38221,a870)),x38222),f333(f104(f882(x38221,a870)),x38223)),f333(f333(f104(f882(x38221,a870)),x38223),f39(f882(x38221,a870),x38222))) % 183.90/184.43 [3833]E(f333(f174(x38331),f333(f333(f333(f191(f876(x38331),f876(x38331)),x38332),f169(x38331)),x38333)),f333(f174(x38331),x38333)) % 183.90/184.43 [3837]E(f333(f333(f177(x38371),f333(f197(f876(x38371)),f179(x38371,x38372,x38373))),x38373),f179(x38371,x38372,x38373)) % 183.90/184.43 [3838]E(f186(x38381,x38382,f333(f333(f8(x38382,f879(x38382),x38381),f240(x38382)),x38383)),f256(f882(x38381,a870))) % 183.90/184.43 [3842]E(f333(f197(f876(x38421)),f333(f333(f333(f191(f876(x38421),f876(x38421)),x38422),f169(x38421)),x38423)),f333(f197(f876(x38421)),x38423)) % 183.90/184.43 [3845]E(f333(f333(f272(x38451,x38452,x38452),f333(f16(f882(x38452,x38452),x38451),f5(x38452))),x38453),f333(f271(x38451,x38452),x38453)) % 183.90/184.43 [3852]E(f44(a1,f333(f333(f22(a1),f44(a1,x38521,x38522)),x38523),x38522),f44(a1,f333(f333(f22(a1),x38521),x38523),x38522)) % 183.90/184.43 [3853]E(f44(a1,f333(f333(f258(a1),f44(a1,x38531,x38532)),x38533),x38532),f44(a1,f333(f333(f258(a1),x38531),x38533),x38532)) % 183.90/184.43 [3856]E(f333(f333(f41(f882(f881(x38561,x38562),a870),f882(x38562,a870)),x38563),f264(x38561,x38562)),f333(f264(x38561,x38562),f39(f882(f881(x38561,x38562),a870),x38563))) % 183.90/184.43 [3857]E(f333(f333(f41(f882(f881(x38571,x38572),a870),f882(x38571,a870)),x38573),f266(x38571,x38572)),f333(f266(x38571,x38572),f39(f882(f881(x38571,x38572),a870),x38573))) % 183.90/184.43 [3885]E(f333(f72(x38851,x38851,x38851,x38852),f333(f333(f191(x38851,x38851),x38853),x38852)),f333(f333(f191(x38851,x38851),f333(a115,x38853)),x38852)) % 183.90/184.43 [3895]E(f242(f879(x38951),x38952,f209(x38951),f333(f333(f8(x38951,f879(x38951),x38952),f240(x38951)),x38953)),f333(f210(x38952,x38951),x38953)) % 183.90/184.43 [3902]E(f333(f333(f139(x39021),f333(f333(f22(a875),f333(f197(f876(x39021)),x39022)),x39023)),f333(f170(x39021),x39022)),f333(f170(x39021),f333(f333(f177(x39021),x39023),x39022))) % 183.90/184.43 [3903]E(f333(f333(f177(x39031),f333(f333(f22(a875),f333(f197(f876(x39031)),x39032)),x39033)),f333(f170(x39031),x39032)),f333(f170(x39031),f333(f333(f139(x39031),x39033),x39032))) % 183.90/184.43 [3906]E(f333(f333(f79(a875),f333(f167(a875),f333(f333(f155(x39061,a875),x39062),x39063))),f333(f197(f876(x39061)),x39063)),f156(x39061,x39062,x39063)) % 183.90/184.43 [3925]E(f333(f169(x39251),f333(f333(f333(f191(f876(x39251),f876(x39251)),x39252),f169(x39251)),x39253)),f333(f333(f333(f191(f876(x39251),f876(x39251)),f333(a115,x39252)),f169(x39251)),x39253)) % 183.90/184.43 [3940]P1(f333(f333(f247(a875),f333(f197(f876(x39401)),f333(f137(x39401,x39402),x39403))),f333(f197(f876(x39401)),x39403))) % 183.90/184.43 [3957]E(f333(f333(f113(f882(f882(x39571,a870),a870)),f333(f310(x39571),x39572)),f333(f312(f882(x39571,a870),f882(x39571,a870),f333(f311(x39571),x39573)),f333(f310(x39571),x39572))),f333(f310(x39571),f333(f333(f311(x39571),x39573),x39572))) % 183.90/184.43 [3976]P24(x39761,x39762,f333(f333(f311(f874(x39761)),f333(f333(f333(f91(x39761),x39763),a24),x39763)),f196(f882(f874(x39761),a870)))) % 183.90/184.43 [3991]P1(f333(f333(f247(a875),f333(f197(f876(x39911)),f179(x39911,x39912,x39913))),f333(f197(f876(x39911)),x39913))) % 183.90/184.43 [3999]E(f333(f266(x39991,x39992),f333(f253(f881(x39991,x39992)),f333(f272(x39991,x39992,a870),x39993))),f333(f253(x39991),f333(f333(f8(f882(x39992,a870),a870,x39991),f86(x39992)),x39993))) % 183.90/184.43 [4011]E(f333(f312(a875,a875,f333(f333(f7(a875,a875,a875),f79(a875)),x40111)),f304(a875,x40112,x40113)),f304(a875,f333(f333(f79(a875),x40112),x40111),f333(f333(f79(a875),x40113),x40111))) % 183.90/184.43 [4014]P1(f333(f61(f879(x40141)),f333(f312(x40142,f879(x40141),f333(f180(x40142,x40141),x40143)),f256(f882(x40142,a870))))) % 183.90/184.43 [4027]E(f333(f312(a875,a875,f333(f333(f7(a875,a875,a875),f79(a875)),x40271)),f333(f303(a875,x40272),x40273)),f333(f303(a875,f333(f333(f79(a875),x40272),x40271)),f333(f333(f79(a875),x40273),x40271))) % 183.90/184.43 [4045]E(f333(f333(f184(x40451,x40452),f333(f333(f155(f881(x40451,x40452),x40451),f267(x40451,x40452)),x40453)),f333(f333(f155(f881(x40451,x40452),x40452),f271(x40451,x40452)),x40453)),x40453) % 183.90/184.43 [4050]E(f333(f333(f79(a875),f333(f333(f80(a875),x40501),f44(a875,f333(f333(f38(a875),x40502),x40501),x40503))),f44(a875,x40502,x40501)),f44(a875,x40502,f333(f333(f80(a875),x40501),x40503))) % 183.90/184.43 [4065]E(f333(f333(f135(x40651),x40652),f333(f143(f876(x40651),f876(x40651),f135(x40651),f116(x40651)),x40653)),f333(f143(f876(x40651),f876(x40651),f135(x40651),x40652),x40653)) % 183.90/184.43 [4083]P1(f333(f333(f335(f881(x40831,x40831)),f333(f333(f268(x40831,x40831),x40832),x40832)),f333(f333(f191(f881(x40831,x40831),a870),f2(a875)),x40833))) % 183.90/184.43 [4089]E(f333(f253(x40891),f333(f333(f8(f882(x40892,a870),a870,x40891),f86(x40892)),f333(f7(x40892,x40891,a870),x40893))),f333(f264(x40892,x40891),f333(f253(f881(x40892,x40891)),f333(f272(x40892,x40891,a870),x40893)))) % 183.90/184.43 [4107]E(f333(f333(f113(f882(x41071,a870)),f333(f333(f41(a875,f882(x41071,a870)),f304(a875,f77(a875),x41072)),x41073)),f333(x41073,f2(a875))),f333(f333(f41(a875,f882(x41071,a870)),f333(f302(a875),x41072)),x41073)) % 183.90/184.43 [4122]E(f333(f143(f876(x41221),f876(x41221),f135(x41221),f116(x41221)),f333(f333(f155(f876(x41221),f876(x41221)),f137(x41221,x41222)),x41223)),f333(f137(x41221,x41222),f333(f143(f876(x41221),f876(x41221),f135(x41221),f116(x41221)),x41223))) % 183.90/184.43 [4127]E(f333(f271(f876(x41271),f876(x41271)),f168(x41271,x41272,x41273)),f333(f137(x41271,f333(f72(a870,a870,x41271,a328),x41272)),x41273)) % 183.90/184.43 [4145]E(f333(f333(f42(x41451,f882(x41452,a870)),f256(f882(x41451,a870))),f333(f333(f8(f882(x41452,a870),f882(x41452,a870),x41451),f253(x41452)),f333(f7(x41452,x41451,a870),x41453))),f333(f253(x41452),f333(f333(f8(f882(x41451,a870),a870,x41452),f87(x41451)),x41453))) % 183.90/184.43 [4176]E(f333(f333(f79(a1),f333(f333(f79(a1),f333(f333(f80(a1),x41761),f333(f333(f38(a1),x41762),x41761))),f44(a1,x41762,x41761))),x41763),f333(f333(f79(a1),x41762),x41763)) % 183.90/184.43 [4214]E(f333(f333(f79(a1),f333(f333(f79(a1),f333(f333(f80(a1),f333(f333(f38(a1),x42141),x42142)),x42142)),f44(a1,x42141,x42142))),x42143),f333(f333(f79(a1),x42141),x42143)) % 183.90/184.43 [4243]E(f84(f881(x42431,x42432),f333(f272(x42431,x42432,a870),f333(f333(f8(f882(x42432,f881(x42431,x42432)),f882(x42432,a870),x42431),f333(f8(f881(x42431,x42432),a870,x42432),x42433)),f268(x42431,x42432)))),f84(f881(x42431,x42432),x42433)) % 183.90/184.43 [4244]E(f89(f881(x42441,x42442),f333(f272(x42441,x42442,a870),f333(f333(f8(f882(x42442,f881(x42441,x42442)),f882(x42442,a870),x42441),f333(f8(f881(x42441,x42442),a870,x42442),x42443)),f268(x42441,x42442)))),f89(f881(x42441,x42442),x42443)) % 183.90/184.43 [4272]P1(f333(f333(f247(f882(x42721,a870)),f39(f882(x42721,a870),f333(f333(f104(f882(f882(x42721,a870),a870)),x42722),x42723))),f333(f333(f104(f882(x42721,a870)),f39(f882(x42721,a870),x42722)),f39(f882(x42721,a870),x42723)))) % 183.90/184.43 [4273]E(f333(f170(x42731),f333(f333(f333(f191(f876(x42731),f876(x42731)),f333(f333(f22(a875),f333(f197(f876(x42731)),x42732)),f44(a875,x42733,f333(f197(f876(x42731)),x42732)))),f169(x42731)),x42732)),f333(f333(f333(f191(f876(x42731),f876(x42731)),x42733),f169(x42731)),f333(f170(x42731),x42732))) % 183.90/184.43 [4287]E(f333(f253(x42871),f333(f333(f8(a870,a870,x42871),a328),f333(f333(f7(x42871,f879(x42872),a870),f333(f333(f8(f879(x42872),f882(f879(x42872),a870),x42871),a330),x42873)),f209(x42872)))),f186(x42871,x42872,x42873)) % 183.90/184.43 [4312]P1(f333(f333(f247(a875),f333(f197(f876(x43121)),f333(f333(f139(x43121),f333(f197(f876(x43121)),f179(x43121,x43122,x43123))),x43123))),f333(f197(f876(x43121)),x43123))) % 183.90/184.43 [4353]E(f333(f253(x43531),f333(f333(f8(f882(x43532,a870),a870,x43531),f86(x43532)),f333(f333(f8(f879(x43531),f882(x43532,a870),x43531),f333(f7(x43532,f879(x43531),a870),f333(f333(f8(f879(x43531),f882(f879(x43531),a870),x43532),a330),x43533))),f240(x43531)))),f188(x43532,x43531,x43533)) % 183.90/184.43 [4563]~P1(f333(f62(x45631,x45632,f196(f882(x45631,a870))),x45633)) % 183.90/184.43 [4571]~P1(f333(f333(f335(f881(x45711,x45711)),f333(f333(f268(x45711,x45711),x45712),x45713)),f154(x45711,f116(f882(x45711,a875))))) % 183.90/184.43 [3600]E(f333(f197(f876(x36001)),f333(f333(f177(x36001),x36002),x36003)),f333(f333(f245(a875),f333(f197(f876(x36001)),x36003)),x36002)) % 183.90/184.43 [3601]E(f333(f197(f876(x36011)),f333(f333(f139(x36011),x36012),x36013)),f333(f333(f22(a875),f333(f197(f876(x36011)),x36013)),x36012)) % 183.90/184.43 [3626]E(f333(f197(f876(f876(x36261))),f54(x36261,x36262,x36263)),f333(f333(f258(a875),f333(f197(f876(x36261)),x36263)),x36262)) % 183.90/184.43 [3642]E(f333(f333(f38(a875),f333(f333(f38(a875),x36421),x36422)),x36423),f333(f333(f38(a875),x36421),f333(f333(f80(a875),x36422),x36423))) % 183.90/184.43 [3643]E(f333(f333(f22(a875),f333(f333(f22(a875),x36431),x36432)),x36433),f333(f333(f22(a875),x36431),f333(f333(f79(a875),x36432),x36433))) % 183.90/184.43 [3644]E(f333(f333(f79(a875),f333(f333(f79(a875),x36441),x36442)),x36443),f333(f333(f79(a875),x36441),f333(f333(f79(a875),x36442),x36443))) % 183.90/184.43 [3645]E(f333(f333(f79(a1),f333(f333(f79(a1),x36451),x36452)),x36453),f333(f333(f79(a1),x36451),f333(f333(f79(a1),x36452),x36453))) % 183.90/184.43 [3646]E(f333(f333(f80(a875),f333(f333(f80(a875),x36461),x36462)),x36463),f333(f333(f80(a875),x36461),f333(f333(f80(a875),x36462),x36463))) % 183.90/184.43 [3647]E(f333(f333(f80(a1),f333(f333(f80(a1),x36471),x36472)),x36473),f333(f333(f80(a1),x36471),f333(f333(f80(a1),x36472),x36473))) % 183.90/184.43 [3648]E(f333(f333(f258(a1),f333(f333(f258(a1),x36481),x36482)),x36483),f333(f333(f258(a1),x36481),f333(f333(f80(a875),x36482),x36483))) % 183.90/184.43 [3669]E(f163(x36691,f333(f333(f152(f882(x36691,a870)),x36692),x36693)),f176(x36691,x36692,f163(x36691,x36693))) % 183.90/184.43 [3714]E(f333(f333(f22(a875),f333(f333(f22(a875),x37141),x37142)),x37143),f333(f333(f22(a875),f333(f333(f22(a875),x37141),x37143)),x37142)) % 183.90/184.43 [3720]E(f333(f240(f881(x37201,f877(x37201))),f333(f333(f268(x37201,f877(x37201)),x37202),x37203)),f333(f136(x37201),f128(x37201,x37202,x37203))) % 183.90/184.43 [3723]E(f333(f333(f104(f882(x37231,a870)),x37232),f333(f333(f22(f882(x37231,a870)),x37233),x37232)),f196(f882(x37231,a870))) % 183.90/184.43 [3727]E(f333(f333(f155(a875,x37271),f333(f16(x37271,a875),x37272)),f140(a875,f333(f303(a875,f2(a875)),x37273))),f171(x37271,x37273,x37272)) % 183.90/184.43 [3766]E(f40(f882(x37661,a870),f333(f333(f311(f882(x37661,a870)),x37662),x37663)),f333(f333(f104(f882(x37661,a870)),x37662),f40(f882(x37661,a870),x37663))) % 183.90/184.43 [3767]E(f39(f882(x37671,a870),f333(f333(f311(f882(x37671,a870)),x37672),x37673)),f333(f333(f113(f882(x37671,a870)),x37672),f39(f882(x37671,a870),x37673))) % 183.90/184.43 [3769]E(f171(x37691,f333(f197(f876(x37691)),f333(f137(x37691,f333(a330,x37692)),x37693)),x37692),f333(f137(x37691,f333(a330,x37692)),x37693)) % 183.90/184.43 [3771]E(f333(f333(f22(a875),f333(f333(f80(a875),x37711),x37712)),f333(f333(f80(a875),x37713),x37712)),f333(f333(f80(a875),f333(f333(f22(a875),x37711),x37713)),x37712)) % 183.90/184.43 [3772]E(f333(f333(f79(a875),f333(f333(f80(a875),x37721),x37722)),f333(f333(f80(a875),x37723),x37722)),f333(f333(f80(a875),f333(f333(f79(a875),x37721),x37723)),x37722)) % 183.90/184.43 [3773]E(f333(f333(f22(a1),f333(f333(f80(a1),x37731),x37732)),f333(f333(f80(a1),x37733),x37732)),f333(f333(f80(a1),f333(f333(f22(a1),x37731),x37733)),x37732)) % 183.90/184.43 [3774]E(f333(f333(f79(a1),f333(f333(f80(a1),x37741),x37742)),f333(f333(f80(a1),x37743),x37742)),f333(f333(f80(a1),f333(f333(f79(a1),x37741),x37743)),x37742)) % 183.90/184.43 [3776]E(f333(f333(f245(a875),f333(f333(f22(a875),x37761),x37762)),f333(f333(f22(a875),x37763),x37762)),f333(f333(f22(a875),f333(f333(f245(a875),x37761),x37763)),x37762)) % 183.90/184.43 [3799]E(f333(f333(f104(f882(f876(x37991),a870)),f161(x37991,x37992)),f161(x37991,x37993)),f161(x37991,f333(f333(f104(f882(x37991,a870)),x37992),x37993))) % 183.90/184.43 [3801]E(f333(f333(f113(f882(x38011,a870)),x38012),f333(f333(f113(f882(x38011,a870)),x38012),x38013)),f333(f333(f113(f882(x38011,a870)),x38012),x38013)) % 183.90/184.43 [3802]E(f333(f333(f113(f882(x38021,a870)),x38022),f333(f333(f22(f882(x38021,a870)),x38023),x38022)),f333(f333(f113(f882(x38021,a870)),x38022),x38023)) % 183.90/184.43 [3803]E(f333(f333(f104(f882(x38031,a870)),x38032),f333(f333(f104(f882(x38031,a870)),x38032),x38033)),f333(f333(f104(f882(x38031,a870)),x38032),x38033)) % 183.90/184.43 [3815]E(f333(f333(f290(x38151,x38152,x38152),x38153),f309(x38152,f196(f882(f881(x38152,x38152),a870)))),x38153) % 183.90/184.43 [3818]E(f333(f333(f113(f882(x38181,a870)),f333(f333(f311(x38181),x38182),f196(f882(x38181,a870)))),x38183),f333(f333(f311(x38181),x38182),x38183)) % 183.90/184.43 [3836]E(f333(f333(f22(a875),f333(f333(f22(a875),f333(a115,x38361)),x38362)),f333(a115,x38363)),f333(f333(f22(a875),f333(f333(f22(a875),x38361),x38362)),x38363)) % 183.90/184.43 [3866]E(f333(f333(f104(f882(f882(x38661,a870),a870)),f333(f310(x38661),x38662)),f333(f310(x38661),x38663)),f333(f310(x38661),f333(f333(f104(f882(x38661,a870)),x38662),x38663))) % 183.90/184.43 [3870]E(f333(f333(f113(f882(x38701,a870)),f333(f78(f882(x38701,a870)),x38702)),x38703),f333(f78(f882(x38701,a870)),f333(f333(f22(f882(x38701,a870)),x38702),x38703))) % 183.90/184.43 [3882]E(f333(f333(f311(x38821),x38822),f333(f333(f22(f882(x38821,a870)),x38823),f333(f333(f311(x38821),x38822),f196(f882(x38821,a870))))),f333(f333(f311(x38821),x38822),x38823)) % 183.90/184.43 [3892]P1(f333(f333(f247(f882(x38921,a870)),x38922),f333(f333(f113(f882(x38921,a870)),x38923),x38922))) % 183.90/184.43 [3893]P1(f333(f333(f247(f882(x38931,a870)),x38932),f333(f333(f113(f882(x38931,a870)),x38932),x38933))) % 183.90/184.43 [3896]E(f333(f333(f104(f882(x38961,a870)),f333(f78(f882(x38961,a870)),x38962)),f333(f78(f882(x38961,a870)),x38963)),f333(f78(f882(x38961,a870)),f333(f333(f113(f882(x38961,a870)),x38962),x38963))) % 183.90/184.43 [3897]E(f333(f333(f113(f882(x38971,a870)),f333(f78(f882(x38971,a870)),x38972)),f333(f78(f882(x38971,a870)),x38973)),f333(f78(f882(x38971,a870)),f333(f333(f104(f882(x38971,a870)),x38972),x38973))) % 183.90/184.43 [3911]P1(f333(f333(f247(f882(x39111,a870)),f333(f174(x39111),x39112)),f333(f174(x39111),f333(f333(f152(x39111),x39113),x39112)))) % 183.90/184.43 [3922]E(f333(f333(f113(f882(x39221,a870)),f333(f333(f22(f882(x39221,a870)),x39222),x39223)),f333(f333(f104(f882(x39221,a870)),x39222),x39223)),x39222) % 183.90/184.43 [3978]E(f333(f333(f6(x39781,a1),f333(f333(f8(a875,a1,x39781),f103(a1)),x39782)),x39783),f333(f103(a1),f333(f333(f6(x39781,a875),x39782),x39783))) % 183.90/184.43 [3979]E(f333(f333(f9(x39791,a1),f333(f333(f8(a875,a1,x39791),f103(a1)),x39792)),x39793),f333(f103(a1),f333(f333(f9(x39791,a875),x39792),x39793))) % 183.90/184.43 [4029]E(f333(f333(f135(x40291),f179(x40291,x40292,x40293)),f333(f333(f139(x40291),f333(f197(f876(x40291)),f179(x40291,x40292,x40293))),x40293)),x40293) % 183.90/184.43 [4034]E(f333(f78(f882(f881(x40341,x40342),a870)),f333(f333(f270(x40341,x40342),x40343),f333(f16(f882(x40342,a870),x40341),f256(f882(x40342,a870))))),f333(f333(f270(x40341,x40342),f333(f78(f882(x40341,a870)),x40343)),f333(f16(f882(x40342,a870),x40341),f256(f882(x40342,a870))))) % 183.90/184.43 [4035]E(f333(f78(f882(f881(x40351,x40352),a870)),f333(f333(f270(x40351,x40352),f256(f882(x40351,a870))),f333(f16(f882(x40352,a870),x40351),x40353))),f333(f333(f270(x40351,x40352),f256(f882(x40351,a870))),f333(f16(f882(x40352,a870),x40351),f333(f78(f882(x40352,a870)),x40353)))) % 183.90/184.43 [4059]E(f119(f879(x40591),f333(f242(f877(f879(x40591)),f877(f879(x40591)),f129(x40591),f5(f877(f879(x40591)))),x40592),f124(x40591,x40593)),f124(x40591,f128(f879(f877(f879(x40591))),x40592,x40593))) % 183.90/184.43 [4084]E(f333(f333(f41(f882(x40841,a870),f882(x40841,a870)),x40842),f333(f333(f7(f882(x40841,a870),f882(x40841,a870),f882(x40841,a870)),f104(f882(x40841,a870))),x40843)),f333(f333(f104(f882(x40841,a870)),f39(f882(x40841,a870),x40842)),x40843)) % 183.90/184.43 [4091]E(f333(f143(f876(x40911),f876(x40911),f135(x40911),f116(x40911)),f333(f333(f152(f876(x40911)),x40912),x40913)),f333(f333(f135(x40911),x40912),f333(f143(f876(x40911),f876(x40911),f135(x40911),f116(x40911)),x40913))) % 183.90/184.43 [4113]E(f333(f333(f311(f882(x41131,a870)),f333(f287(x41131,x41131,x41132),f333(f333(f311(x41131),x41133),f196(f882(x41131,a870))))),f196(f882(f882(x41131,a870),a870))),f333(f333(f60(x41131),f333(f333(f311(x41131),x41133),f196(f882(x41131,a870)))),x41132)) % 183.90/184.43 [4123]E(f333(f333(f79(a875),f333(f333(f80(a875),x41231),f333(f333(f38(a875),x41232),x41233))),f333(f333(f38(a875),f333(f333(f80(a875),x41231),f44(a875,x41232,x41233))),x41233)),f333(f333(f38(a875),f333(f333(f80(a875),x41231),x41232)),x41233)) % 183.90/184.43 [4124]E(f333(f333(f79(a1),f333(f333(f80(a1),x41241),f333(f333(f38(a1),x41242),x41243))),f333(f333(f38(a1),f333(f333(f80(a1),x41241),f44(a1,x41242,x41243))),x41243)),f333(f333(f38(a1),f333(f333(f80(a1),x41241),x41242)),x41243)) % 183.90/184.43 [4161]E(f333(f333(f22(f882(x41611,a870)),f333(f174(x41611),x41612)),f333(f333(f311(x41611),x41613),f196(f882(x41611,a870)))),f333(f174(x41611),f333(f137(x41611,f333(f333(f8(a870,a870,x41611),a328),f333(a330,x41613))),x41612))) % 183.90/184.43 [4211]E(f333(f333(f135(x42111),f333(f143(f876(x42111),f876(x42111),f135(x42111),f116(x42111)),x42112)),f333(f143(f876(x42111),f876(x42111),f135(x42111),f116(x42111)),x42113)),f333(f143(f876(x42111),f876(x42111),f135(x42111),f116(x42111)),f333(f333(f135(f876(x42111)),x42112),x42113))) % 183.90/184.43 [4216]E(f333(f333(f268(f876(x42161),f876(x42161)),f333(f137(x42161,x42162),x42163)),f333(f137(x42161,f333(f72(a870,a870,x42161,a328),x42162)),x42163)),f168(x42161,x42162,x42163)) % 183.90/184.43 [4219]E(f333(f333(f79(a875),f333(f333(f79(a875),f333(f333(f38(a875),x42191),x42192)),f333(f333(f38(a875),x42193),x42192))),f333(f333(f38(a875),f333(f333(f79(a875),f44(a875,x42191,x42192)),f44(a875,x42193,x42192))),x42192)),f333(f333(f38(a875),f333(f333(f79(a875),x42191),x42193)),x42192)) % 183.90/184.43 [4220]E(f333(f333(f79(a1),f333(f333(f79(a1),f333(f333(f38(a1),x42201),x42202)),f333(f333(f38(a1),x42203),x42202))),f333(f333(f38(a1),f333(f333(f79(a1),f44(a1,x42201,x42202)),f44(a1,x42203,x42202))),x42202)),f333(f333(f38(a1),f333(f333(f79(a1),x42201),x42203)),x42202)) % 183.90/184.43 [4276]E(f333(f333(f104(f882(f876(x42761),a870)),f333(f333(f7(f876(x42761),f882(f876(x42761),a870),a870),f335(f876(x42761))),f162(x42761,x42762))),f333(f333(f7(f876(x42761),f882(f876(x42761),a870),a870),f335(f876(x42761))),f162(x42761,x42763))),f161(x42761,f333(f333(f104(f882(x42761,a870)),f333(f333(f7(x42761,f882(x42761,a870),a870),f335(x42761)),x42762)),f333(f333(f7(x42761,f882(x42761,a870),a870),f335(x42761)),x42763)))) % 183.90/184.43 [4289]E(f333(f253(x42891),f333(f333(f18(x42891,a870,a870),f333(f333(f8(a870,f882(a870,a870),x42891),a332),f333(f333(f7(x42891,x42891,a870),a330),x42892))),f333(f333(f7(x42891,f882(x42891,a870),a870),f335(x42891)),x42893))),f333(f333(f311(x42891),x42892),x42893)) % 183.90/184.43 [4309]E(f333(f333(f85(f876(f876(x43091)),f876(f876(x43091))),f53(x43091,x43092)),f333(f333(f18(f876(f876(x43091)),f876(f876(x43091)),f876(f876(x43091))),f333(f333(f8(f876(f876(x43091)),f882(f876(f876(x43091)),f876(f876(x43091))),f876(f876(x43091))),f135(f876(x43091))),f333(f155(f876(x43091),f876(x43091)),f333(f152(x43091),x43093)))),f5(f876(f876(x43091))))),f53(x43091,f333(f333(f152(x43091),x43093),x43092))) % 183.90/184.43 [4313]E(f333(f253(x43131),f333(f333(f18(x43131,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43131),a332),f333(f333(f7(x43131,f882(x43131,a870),a870),f335(x43131)),x43132))),f333(f333(f7(x43131,f882(x43131,a870),a870),f335(x43131)),x43133))),f333(f333(f113(f882(x43131,a870)),x43132),x43133)) % 183.90/184.43 [4314]E(f333(f253(x43141),f333(f333(f18(x43141,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43141),a331),f333(f333(f7(x43141,f882(x43141,a870),a870),f335(x43141)),x43142))),f333(f333(f7(x43141,f882(x43141,a870),a870),f335(x43141)),x43143))),f333(f333(f104(f882(x43141,a870)),x43142),x43143)) % 183.90/184.43 [4405]E(f333(f333(f41(x44051,f882(f882(x44051,a870),a870)),x44052),f333(f333(f7(x44051,f882(f882(x44051,a870),a870),f882(f882(x44051,a870),a870)),f333(f333(f8(f882(x44051,a870),f882(f882(f882(x44051,a870),a870),f882(f882(x44051,a870),a870)),x44051),f311(f882(x44051,a870))),f333(f333(f8(f882(x44051,a870),f882(x44051,a870),x44051),f287(x44051,x44051,x44053)),f333(f333(f7(x44051,f882(x44051,a870),f882(x44051,a870)),f311(x44051)),f196(f882(x44051,a870)))))),f196(f882(f882(x44051,a870),a870)))),f333(f333(f60(x44051),x44052),x44053)) % 183.90/184.43 [4407]E(f333(f333(f213(x44071),f333(f333(f80(a1),f333(f333(f72(f881(a1,a1),a1,x44071,f267(a1,a1)),f224(x44071)),x44072)),f333(f333(f72(f881(a1,a1),a1,x44071,f267(a1,a1)),f224(x44071)),x44073))),f333(f333(f80(a1),f333(f333(f72(f881(a1,a1),a1,x44071,f271(a1,a1)),f224(x44071)),x44072)),f333(f333(f72(f881(a1,a1),a1,x44071,f271(a1,a1)),f224(x44071)),x44073))),f233(x44071,x44072,x44073)) % 183.90/184.43 [4410]E(f333(f253(f876(x44101)),f333(f333(f18(f876(x44101),a870,a870),f333(f333(f8(a870,f882(a870,a870),f876(x44101)),a331),f333(f333(f7(f876(x44101),a875,a870),f333(f333(f8(a875,f882(a875,a870),f876(x44101)),a330),f197(f876(x44101)))),x44102))),f333(f333(f7(f876(x44101),f882(x44101,a870),a870),f333(f333(f8(f882(x44101,a870),f882(f882(x44101,a870),a870),f876(x44101)),f247(f882(x44101,a870))),f174(x44101))),f333(f174(x44101),x44103)))),f333(f174(f876(x44101)),f54(x44101,x44102,x44103))) % 183.90/184.43 [3789]E(f44(a875,f333(f333(f79(a875),f333(f333(f80(a875),x37891),x37892)),x37893),x37892),f44(a875,x37893,x37892)) % 183.90/184.43 [3835]E(f140(a875,f333(f303(a875,f333(f333(f79(a875),x38351),x38352)),x38353)),f333(f333(f139(a875),x38352),f140(a875,f333(f303(a875,x38351),x38353)))) % 183.90/184.43 [3881]E(f333(f333(f79(a1),f333(f103(a1),x38811)),f333(f333(f79(a1),f333(f103(a1),x38812)),x38813)),f333(f333(f79(a1),f333(f103(a1),f333(f333(f79(a875),x38811),x38812))),x38813)) % 183.90/184.43 [3888]E(f333(f333(f113(f882(x38881,a870)),f333(f333(f22(f882(x38881,a870)),x38882),x38883)),x38883),f333(f333(f113(f882(x38881,a870)),x38882),x38883)) % 183.90/184.43 [3889]E(f333(f333(f22(f882(x38891,a870)),f333(f333(f22(f882(x38891,a870)),x38892),x38893)),x38893),f333(f333(f22(f882(x38891,a870)),x38892),x38893)) % 183.90/184.43 [3912]E(f333(f333(f290(x39121,x39121,x39122),f309(x39121,f196(f882(f881(x39121,x39121),a870)))),x39123),x39123) % 183.90/184.43 [3919]E(f333(f333(f113(f882(x39191,a870)),f333(f286(x39191),x39192)),f333(f286(x39191),x39193)),f333(f286(x39191),f333(f333(f113(f882(f881(x39191,x39191),a870)),x39192),x39193))) % 183.90/184.43 [3930]E(f277(x39301,f333(f333(f152(f881(a102,x39301)),f333(f333(f268(a102,x39301),f2(a102)),x39302)),x39303)),f277(x39301,x39303)) % 183.90/184.43 [3933]E(f333(f333(f104(f882(x39331,a870)),f40(f882(x39331,a870),x39332)),f40(f882(x39331,a870),x39333)),f40(f882(x39331,a870),f333(f333(f113(f882(f882(x39331,a870),a870)),x39332),x39333))) % 183.90/184.43 [3934]E(f333(f333(f113(f882(x39341,a870)),f39(f882(x39341,a870),x39342)),f39(f882(x39341,a870),x39343)),f39(f882(x39341,a870),f333(f333(f113(f882(f882(x39341,a870),a870)),x39342),x39343))) % 183.90/184.43 [3970]E(f333(f333(f290(x39701,x39701,x39701),f333(f333(f191(f881(x39701,x39701),a870),x39702),x39703)),x39703),f333(f333(f191(f881(x39701,x39701),a870),f333(a115,x39702)),x39703)) % 183.90/184.43 [4020]P1(f333(f333(f247(f882(x40201,a870)),f333(f333(f22(f882(x40201,a870)),x40202),x40203)),x40202)) % 183.90/184.43 [4021]P1(f333(f333(f247(f882(x40211,a870)),f333(f333(f104(f882(x40211,a870)),x40212),x40213)),x40213)) % 183.90/184.43 [4022]P1(f333(f333(f247(f882(x40221,a870)),f333(f333(f104(f882(x40221,a870)),x40222),x40223)),x40222)) % 183.90/184.43 [4047]E(f309(x40471,f333(f333(f113(f882(f881(x40471,x40471),a870)),f309(x40471,x40472)),f309(x40471,x40473))),f309(x40471,f333(f333(f113(f882(f881(x40471,x40471),a870)),x40472),x40473))) % 183.90/184.43 [4051]E(f39(f882(x40511,a870),f333(f333(f311(f882(x40511,a870)),x40512),f333(f333(f311(f882(x40511,a870)),x40513),f196(f882(f882(x40511,a870),a870))))),f333(f333(f113(f882(x40511,a870)),x40512),x40513)) % 183.90/184.43 [4052]E(f40(f882(x40521,a870),f333(f333(f311(f882(x40521,a870)),x40522),f333(f333(f311(f882(x40521,a870)),x40523),f196(f882(f882(x40521,a870),a870))))),f333(f333(f104(f882(x40521,a870)),x40522),x40523)) % 183.90/184.43 [4058]E(f333(f333(f290(x40581,x40581,x40581),f333(f333(f191(f881(x40581,x40581),a870),x40582),x40583)),x40583),f333(f333(f290(x40581,x40581,x40581),x40583),f333(f333(f191(f881(x40581,x40581),a870),x40582),x40583))) % 183.90/184.43 [4128]E(f333(f333(f113(f882(x41281,a870)),f333(f253(x41281),f333(f333(f7(x41281,x41281,a870),a330),x41282))),x41283),f333(f333(f311(x41281),x41282),x41283)) % 183.90/184.43 [4130]E(f333(a107,f333(f333(f6(x41301,a1),f333(f333(f8(a875,a1,x41301),f103(a1)),x41302)),x41303)),f333(f333(f6(x41301,a875),x41302),x41303)) % 183.90/184.43 [4131]E(f333(a107,f333(f333(f9(x41311,a1),f333(f333(f8(a875,a1,x41311),f103(a1)),x41312)),x41313)),f333(f333(f9(x41311,a875),x41312),x41313)) % 183.90/184.43 [4208]E(f333(f157(f876(x42081),x42081,f333(f173(x42081),x42082),f333(f16(f882(f876(x42081),f876(x42081)),x42081),f333(f333(f7(f876(x42081),f876(x42081),f876(x42081)),f135(x42081)),x42082))),x42083),f333(f173(x42081),f333(f333(f135(x42081),x42083),x42082))) % 183.90/184.43 [4239]P1(f333(f333(f247(f882(f882(x42391,a870),a870)),f333(f333(f113(f882(f882(x42391,a870),a870)),f333(f310(x42391),x42392)),f333(f310(x42391),x42393))),f333(f310(x42391),f333(f333(f113(f882(x42391,a870)),x42392),x42393)))) % 183.90/184.43 [4332]E(f333(f253(x43321),f333(f333(f18(x43321,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43321),a331),f333(f333(f7(x43321,f882(x43321,a870),a870),f335(x43321)),x43322))),f333(f333(f8(a870,a870,x43321),a328),f333(f333(f7(x43321,f882(x43321,a870),a870),f335(x43321)),x43323)))),f333(f333(f22(f882(x43321,a870)),x43322),x43323)) % 183.90/184.43 [4354]E(f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,a875,a870),f248(a875)),f333(f197(f876(x43541)),x43542)))),f333(f333(f8(x43541,a870,a875),x43543),f333(f166(x43541),x43542))))),f333(f197(f876(x43541)),f333(f137(x43541,x43543),x43542))) % 183.90/184.43 [4356]E(f333(f197(f876(x43561)),f178(x43561,x43562,x43563)),f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,a875,a870),f248(a875)),f333(f197(f876(x43561)),x43562)))),f333(f333(f7(a875,f882(a875,a870),a870),f335(a875)),x43563))))) % 183.90/184.43 [4453]E(f333(f333(f104(f882(f881(f876(x44531),f876(x44531)),a870)),f333(f312(f881(f881(x44531,f876(x44531)),f881(x44531,f876(x44531))),f881(f876(x44531),f876(x44531)),f273(f881(x44531,f876(x44531)),f876(x44531),f881(x44531,f876(x44531)),f876(x44531),f333(f272(x44531,f876(x44531),f876(x44531)),f152(x44531)),f333(f272(x44531,f876(x44531),f876(x44531)),f152(x44531)))),f326(x44531,f876(x44531),x44532,f333(f144(x44531,x44532),x44533)))),f333(f253(f881(f876(x44531),f876(x44531))),f333(f272(f876(x44531),f876(x44531),a870),f333(f333(f7(f876(x44531),f882(f876(x44531),a870),f882(f876(x44531),a870)),f333(f333(f8(f882(a870,a870),f882(f882(f876(x44531),a870),f882(f876(x44531),a870)),f876(x44531)),f8(a870,a870,f876(x44531))),f333(f333(f8(a870,f882(a870,a870),f876(x44531)),a331),f333(f333(f7(f876(x44531),a875,a870),f333(f333(f8(a875,f882(a875,a870),f876(x44531)),a330),f197(f876(x44531)))),f333(a115,x44533))))),f333(f333(f7(f876(x44531),a875,a870),f333(f333(f8(a875,f882(a875,a870),f876(x44531)),a330),f197(f876(x44531)))),f333(a115,x44533)))))),f333(f144(x44531,x44532),f333(a115,x44533))) % 183.90/184.43 [3935]E(f44(a875,f333(a115,f333(f333(f79(a875),f333(f333(f80(a875),x39351),x39352)),x39353)),x39352),f44(a875,f333(a115,x39353),x39352)) % 183.90/184.43 [4196]E(f333(f253(x41961),f333(f333(f18(x41961,a870,a870),f333(f333(f8(a870,f882(a870,a870),x41961),a331),x41962)),x41963)),f333(f333(f104(f882(x41961,a870)),f333(f253(x41961),x41962)),f333(f253(x41961),x41963))) % 183.90/184.43 [4197]E(f333(f253(x41971),f333(f333(f18(x41971,a870,a870),f333(f333(f8(a870,f882(a870,a870),x41971),a332),x41972)),x41973)),f333(f333(f113(f882(x41971,a870)),f333(f253(x41971),x41972)),f333(f253(x41971),x41973))) % 183.90/184.43 [4199]E(f333(f333(f135(x41991),f333(f333(f139(x41991),f44(a875,x41992,f333(f197(f876(x41991)),x41993))),x41993)),f333(f333(f177(x41991),f44(a875,x41992,f333(f197(f876(x41991)),x41993))),x41993)),f333(f333(f333(f191(f876(x41991),f876(x41991)),x41992),f169(x41991)),x41993)) % 183.90/184.43 [4205]E(f333(f253(x42051),f333(f333(f18(x42051,a870,a870),f333(f333(f8(a870,f882(a870,a870),x42051),a336),x42052)),x42053)),f333(f333(f113(f882(x42051,a870)),f333(f78(f882(x42051,a870)),f333(f253(x42051),x42052))),f333(f253(x42051),x42053))) % 183.90/184.43 [4221]E(f333(f333(f79(a875),f333(f197(f876(x42211)),f333(f137(x42211,x42212),x42213))),f333(f197(f876(x42211)),f333(f137(x42211,f333(f333(f8(a870,a870,x42211),a328),x42212)),x42213))),f333(f197(f876(x42211)),x42213)) % 183.90/184.43 [4246]P1(f333(f333(f247(f882(x42461,a870)),f333(f333(f113(f882(x42461,a870)),f40(f882(x42461,a870),x42462)),f40(f882(x42461,a870),x42463))),f40(f882(x42461,a870),f333(f333(f104(f882(f882(x42461,a870),a870)),x42462),x42463)))) % 183.90/184.43 [4260]E(f333(f174(x42601),f333(f137(x42601,f333(f333(f8(a870,a870,x42601),a328),f333(f333(f7(x42601,x42601,a870),a330),x42602))),x42603)),f333(f333(f22(f882(x42601,a870)),f333(f174(x42601),x42603)),f333(f333(f311(x42601),x42602),f196(f882(x42601,a870))))) % 183.90/184.43 [4269]P1(f333(f333(f247(f882(f881(x42691,x42691),a870)),f333(f333(f113(f882(f881(x42691,x42691),a870)),f309(x42691,x42692)),f309(x42691,x42693))),f309(x42691,f333(f333(f113(f882(f881(x42691,x42691),a870)),x42692),x42693)))) % 183.90/184.43 [4294]E(f333(f333(f80(a875),f333(a115,f333(a115,f2(a875)))),f333(f333(f6(a875,a875),f333(f333(f8(a875,a875,a875),f333(f79(a875),x42941)),f333(f333(f7(a875,a875,a875),f80(a875)),x42942))),f333(f254(a875),x42943))),f333(f333(f80(a875),x42943),f333(f333(f79(a875),x42941),f333(f333(f79(a875),x42941),f333(f333(f80(a875),f333(f333(f22(a875),x42943),f77(a875))),x42942))))) % 183.90/184.43 [4304]E(f333(f253(x43041),f333(f333(f18(x43041,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43041),a331),f333(f333(f7(x43041,f882(x43041,a870),a870),f335(x43041)),f333(f174(x43041),x43042)))),x43043)),f333(f174(x43041),f333(f137(x43041,x43043),x43042))) % 183.90/184.43 [4452]E(f333(f253(x44521),f333(f333(f8(f882(a875,a870),a870,x44521),f86(a875)),f333(f333(f7(x44521,f882(a875,a870),f882(a875,a870)),f333(f333(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),x44521),f18(a875,a870,a870)),f333(f333(f8(f882(a875,a870),f882(a875,f882(a870,a870)),x44521),f333(f8(a870,f882(a870,a870),a875),a331)),f333(f333(f7(x44521,f882(a875,x44521),f882(a875,a870)),f333(f333(f8(f882(x44521,a870),f882(f882(a875,x44521),f882(a875,a870)),x44521),f8(x44521,a870,a875)),a330)),f333(f166(x44521),x44522))))),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,a875,a870),f248(a875)),f333(f197(f876(x44521)),x44522)))),f333(f333(f7(a875,f882(a875,a870),a870),f335(a875)),x44523))))),f333(f174(x44521),f178(x44521,x44522,x44523))) % 183.90/184.43 [4344]E(f333(f253(x43441),f333(f333(f18(x43441,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43441),a336),f333(f333(f8(a870,a870,x43441),a328),f333(f333(f7(x43441,x43441,a870),a330),x43442)))),x43443)),f333(f333(f311(x43441),x43442),f333(f253(x43441),x43443))) % 183.90/184.43 [4376]E(f333(f333(f155(f881(x43761,a875),x43761),f267(x43761,a875)),f333(f137(f881(x43761,a875),f333(f333(f7(f881(x43761,a875),f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),f881(x43761,a875)),f335(a875)),f271(x43761,a875))),x43762)),f333(f333(f184(x43761,a875),x43763),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(x43761)),x43763)))))),f178(x43761,x43763,x43762)) % 183.90/184.43 [4406]E(f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f6(a875,a1),f333(f333(f8(a1,a1,a875),f333(f79(a1),x44061)),f333(f333(f7(a875,a1,a1),f333(f333(f8(a1,f882(a1,a1),a875),f80(a1)),f103(a1))),x44062))),f333(f254(a875),x44063))),f333(f333(f80(a1),f333(f103(a1),x44063)),f333(f333(f79(a1),x44061),f333(f333(f79(a1),x44061),f333(f333(f80(a1),f333(f103(a1),f333(f333(f22(a875),x44063),f77(a875)))),x44062))))) % 183.90/184.43 [4446]E(f333(f253(f881(x44461,x44462)),f333(f272(x44461,x44462,a870),f333(f333(f7(x44461,f882(f881(x44462,x44461),a870),f882(x44462,a870)),f333(f333(f8(f882(x44462,f882(f882(f881(x44462,x44461),a870),a870)),f882(f882(f881(x44462,x44461),a870),f882(x44462,a870)),x44461),f7(x44462,f882(f881(x44462,x44461),a870),a870)),f333(f333(f8(f882(x44462,f881(x44462,x44461)),f882(x44462,f882(f882(f881(x44462,x44461),a870),a870)),x44461),f333(f8(f881(x44462,x44461),f882(f882(f881(x44462,x44461),a870),a870),x44462),f335(f881(x44462,x44461)))),f333(f7(x44462,x44461,f881(x44462,x44461)),f268(x44462,x44461))))),x44463))),f333(f288(x44462,x44461),x44463)) % 183.90/184.43 [4468]E(f333(f253(f876(x44681)),f333(f333(f8(f882(x44681,a870),a870,f876(x44681)),f86(x44681)),f333(f333(f8(f882(x44681,f882(f876(x44681),a870)),f882(x44681,a870),f876(x44681)),f333(f8(f882(f876(x44681),a870),a870,x44681),f86(f876(x44681)))),f333(f333(f7(f876(x44681),f882(x44681,f882(f876(x44681),a870)),f882(x44681,f882(f876(x44681),a870))),f333(f333(f8(f882(x44681,f882(f882(f876(x44681),a870),f882(f876(x44681),a870))),f882(f882(x44681,f882(f876(x44681),a870)),f882(x44681,f882(f876(x44681),a870))),f876(x44681)),f18(x44681,f882(f876(x44681),a870),f882(f876(x44681),a870))),f333(f333(f8(f882(x44681,f882(f876(x44681),f882(a870,a870))),f882(x44681,f882(f882(f876(x44681),a870),f882(f876(x44681),a870))),f876(x44681)),f333(f8(f882(f876(x44681),f882(a870,a870)),f882(f882(f876(x44681),a870),f882(f876(x44681),a870)),x44681),f18(f876(x44681),a870,a870))),f333(f333(f8(f882(x44681,f882(f876(x44681),a870)),f882(x44681,f882(f876(x44681),f882(a870,a870))),f876(x44681)),f333(f8(f882(f876(x44681),a870),f882(f876(x44681),f882(a870,a870)),x44681),f333(f8(a870,f882(a870,a870),f876(x44681)),a331))),f333(f333(f7(f876(x44681),f882(x44681,f882(f876(x44681),f876(x44681))),f882(x44681,f882(f876(x44681),a870))),f333(f333(f8(f882(f882(f876(x44681),f876(x44681)),f882(f876(x44681),a870)),f882(f882(x44681,f882(f876(x44681),f876(x44681))),f882(x44681,f882(f876(x44681),a870))),f876(x44681)),f8(f882(f876(x44681),f876(x44681)),f882(f876(x44681),a870),x44681)),f333(f333(f8(f882(f876(x44681),a870),f882(f882(f876(x44681),f876(x44681)),f882(f876(x44681),a870)),f876(x44681)),f8(f876(x44681),a870,f876(x44681))),a330))),f152(x44681)))))),f333(f333(f7(x44681,f882(f876(x44681),a870),f882(f876(x44681),a870)),f333(f333(f8(f882(a870,a870),f882(f882(f876(x44681),a870),f882(f876(x44681),a870)),x44681),f8(a870,a870,f876(x44681))),f333(f333(f8(a870,f882(a870,a870),x44681),a331),f333(f333(f7(x44681,f882(x44681,a870),a870),f335(x44681)),x44682)))),f333(f333(f7(f876(x44681),f882(f876(x44681),a870),a870),f335(f876(x44681))),x44683)))))),f176(x44681,x44682,x44683)) % 183.90/184.43 [4465]E(f333(f333(f85(a1,f881(a1,a1)),f333(f333(f22(a1),x44651),x44652)),f333(f333(f7(a1,f881(a1,a1),f881(a1,a1)),f333(f333(f18(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f333(f333(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f99(f881(a1,a1))),f333(f247(a1),f2(a1)))),f333(f268(a1,a1),f333(f333(f79(a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x44653)),f77(a1))))),f333(f333(f268(a1,a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x44653)),x44651))),f333(f43(x44652),f333(f333(f268(a1,a1),x44653),x44651))) % 183.90/184.43 [4496]~E(f31(x44961,x44962),f32(x44963,x44964)) % 183.90/184.43 [4513]~E(f333(a25,x45131),f29(x45132,x45133,x45134)) % 183.90/184.43 [4514]~E(f333(a25,x45141),f28(x45142,x45143,x45144)) % 183.90/184.43 [4515]~E(f29(x45151,x45152,x45153),f333(a25,x45154)) % 183.90/184.43 [4516]~E(f28(x45161,x45162,x45163),f333(a25,x45164)) % 183.90/184.43 [3475]E(f333(f333(f333(f71(x34751,x34752),x34753),x34754),f333(x34753,x34754)),x34753) % 183.90/184.43 [3483]E(f119(x34831,f333(x34832,x34833),f333(x34834,x34833)),f333(f215(x34831,x34832,x34834),x34833)) % 183.90/184.43 [3536]E(f333(f333(f259(x35361,x35362,x35363),x35364),f2(a875)),x35362) % 183.90/184.43 [3577]E(f193(x35771,x35772,x35773,f333(a115,x35774)),f333(x35773,x35774)) % 183.90/184.43 [3618]E(f172(x36181,x36182,f172(x36181,x36183,x36184)),f172(x36181,x36183,f172(x36181,x36182,x36184))) % 183.90/184.43 [3619]E(f119(x36191,f128(x36191,x36192,x36193),x36194),f128(x36191,x36192,f119(x36191,x36193,x36194))) % 183.90/184.43 [3756]E(f333(f157(x37561,x37562,x37563,x37564),f116(x37562)),x37563) % 183.90/184.43 [3757]E(f333(f242(x37571,x37572,x37573,x37574),f209(x37572)),x37573) % 183.90/184.43 [3758]E(f333(f143(x37581,x37582,x37583,x37584),f116(x37582)),x37584) % 183.90/184.43 [3865]E(f333(f333(f135(x38651),f171(x38651,x38652,x38653)),f171(x38651,x38654,x38653)),f333(f333(f135(x38651),f171(x38651,x38654,x38653)),f171(x38651,x38652,x38653))) % 183.90/184.43 [3878]E(f333(f242(f879(x38781),x38782,f209(x38781),f333(f16(f879(x38781),x38782),f209(x38781))),f333(x38783,x38784)),f209(x38781)) % 183.90/184.43 [3923]E(f333(f333(f113(f882(x39231,a870)),f186(x39231,x39232,x39233)),f186(x39231,x39232,x39234)),f186(x39231,x39232,f187(x39231,x39232,x39234,x39233))) % 183.90/184.43 [3955]E(f333(f333(f274(x39551,x39552,x39553,f881(x39552,x39553)),x39554),f268(x39552,x39553)),x39554) % 183.90/184.43 [3964]E(f189(x39641,x39642,x39643,x39644,f116(x39642)),x39643) % 183.90/184.43 [3965]E(f243(x39651,x39652,x39653,x39654,f209(x39652)),x39653) % 183.90/184.43 [3966]E(f189(x39661,x39662,x39663,f116(x39661),x39664),x39663) % 183.90/184.43 [4253]P42(x42531,x42532,x42533,x42534,f196(f882(x42531,a870)),x42534) % 183.90/184.43 [3276]E(f333(f333(f16(x32761,x32762),x32763),x32764),x32763) % 183.90/184.43 [3392]E(f333(f333(f210(x33921,x33922),x33923),f333(f240(x33921),x33924)),f333(f240(x33922),f333(x33923,x33924))) % 183.90/184.43 [3567]E(f172(x35671,x35672,f333(f137(x35671,x35673),x35674)),f333(f137(x35671,x35673),f172(x35671,x35672,x35674))) % 183.90/184.43 [3602]E(f333(f333(f64(x36021,x36022,x36023),x36024),f196(f882(x36021,a870))),x36024) % 183.90/184.43 [3625]E(f333(f333(f166(x36251),f333(f333(f152(x36251),x36252),x36253)),f333(a115,x36254)),f333(f333(f166(x36251),x36253),x36254)) % 183.90/184.43 [3670]P27(x36701,f2(a875),f333(f333(f333(f91(x36701),x36702),f333(a25,x36703)),x36704)) % 183.90/184.43 [3695]E(f333(f333(x36951,x36952),f333(f192(x36953,x36954,x36951),x36952)),f333(f192(x36953,x36954,x36951),f333(a115,x36952))) % 183.90/184.43 [3794]E(f333(f333(f160(x37941,f333(f333(f152(x37941),x37942),x37943)),f2(a875)),x37944),f333(f333(f152(x37941),x37944),x37943)) % 183.90/184.43 [3805]E(f333(f333(f41(f882(x38051,a870),f882(x38052,a870)),x38053),f312(x38051,x38052,x38054)),f333(f312(x38051,x38052,x38054),f39(f882(x38051,a870),x38053))) % 183.90/184.43 [3806]E(f333(f333(f41(f882(x38061,a870),f882(x38062,a870)),x38063),f313(x38062,x38061,x38064)),f333(f313(x38062,x38061,x38064),f39(f882(x38061,a870),x38063))) % 183.90/184.43 [3905]E(f186(x39051,x39052,f190(x39051,x39052,x39053,x39054)),f333(f333(f104(f882(x39051,a870)),f186(x39051,x39052,x39053)),x39054)) % 183.90/184.43 [3909]E(f333(f130(x39091,x39092),f128(x39091,x39093,x39094)),f333(f333(f79(a875),f333(f333(f79(a875),f333(x39092,x39093)),f333(f130(x39091,x39092),x39094))),f333(a115,f2(a875)))) % 183.90/184.43 [3929]E(f333(f143(x39291,x39292,f333(f7(x39292,x39291,x39291),x39293),x39294),f333(f170(x39292),f116(x39292))),x39294) % 183.90/184.43 [3977]E(f75(x39771,x39772,x39773,x39774,f196(f882(x39771,a870))),x39773) % 183.90/184.43 [4023]E(f333(f333(f333(f333(f71(x40231,f879(x40232)),f333(f16(f879(x40232),x40231),f209(x40232))),x40233),f209(x40232)),x40234),f209(x40232)) % 183.90/184.43 [4179]E(f333(f272(x41791,x41792,x41793),f333(f333(f8(f882(x41792,f881(x41791,x41792)),f882(x41792,x41793),x41791),f333(f8(f881(x41791,x41792),x41793,x41792),x41794)),f268(x41791,x41792))),x41794) % 183.90/184.43 [3473]E(f333(f271(x34731,x34732),f333(f333(f268(x34731,x34732),x34733),x34734)),x34734) % 183.90/184.43 [3474]E(f333(f267(x34741,x34742),f333(f333(f268(x34741,x34742),x34743),x34744)),x34743) % 183.90/184.43 [3509]E(f333(f197(f876(x35091)),f333(f333(f160(x35091,x35092),x35093),x35094)),f333(f197(f876(x35091)),x35092)) % 183.90/184.43 [3510]E(f333(f197(f876(x35101)),f333(f333(f155(x35102,x35101),x35103),x35104)),f333(f197(f876(x35102)),x35104)) % 183.90/184.43 [3530]E(f333(f333(f139(x35301),f333(a115,x35302)),f333(f333(f152(x35301),x35303),x35304)),f333(f333(f139(x35301),x35302),x35304)) % 183.90/184.43 [3597]E(f333(f333(f177(x35971),x35972),f171(x35971,x35973,x35974)),f171(x35971,f333(f333(f245(a875),x35972),x35973),x35974)) % 183.90/184.43 [3598]E(f333(f333(f139(x35981),x35982),f171(x35981,x35983,x35984)),f171(x35981,f333(f333(f22(a875),x35983),x35982),x35984)) % 183.90/184.43 [3604]E(f333(f333(f311(x36041),x36042),f333(f333(f311(x36041),x36043),x36044)),f333(f333(f311(x36041),x36043),f333(f333(f311(x36041),x36042),x36044))) % 183.90/184.43 [3607]E(f333(f333(f155(x36071,x36072),x36073),f117(x36071,x36074)),f117(x36072,f333(f333(f155(x36071,x36072),x36073),x36074))) % 183.90/184.43 [3623]E(f333(f170(x36231),f333(f333(f155(x36232,x36231),x36233),x36234)),f333(f333(f155(x36232,x36231),x36233),f333(f170(x36232),x36234))) % 183.90/184.43 [3624]E(f333(f333(f155(x36241,x36242),x36243),f333(f173(x36241),x36244)),f333(f173(x36242),f333(f333(f155(x36241,x36242),x36243),x36244))) % 183.90/184.43 [3637]E(f333(f333(f177(x36371),f333(a115,x36372)),f333(f333(f152(x36371),x36373),x36374)),f333(f333(f152(x36371),x36373),f333(f333(f177(x36371),x36372),x36374))) % 183.90/184.43 [3641]E(f333(f174(x36411),f333(f333(f155(x36412,x36411),x36413),x36414)),f333(f312(x36412,x36411,x36413),f333(f174(x36412),x36414))) % 183.90/184.43 [3656]E(f333(f333(f155(x36561,x36562),f333(f16(x36562,x36561),x36563)),x36564),f171(x36562,f333(f197(f876(x36561)),x36564),x36563)) % 183.90/184.43 [3694]E(f17(x36941,x36942,x36943,f333(a3,f333(a115,f333(a19,x36944)))),f333(x36943,x36944)) % 183.90/184.43 [3697]E(f333(f333(f135(x36971),f333(f137(x36971,x36972),x36973)),f333(f137(x36971,x36972),x36974)),f333(f137(x36971,x36972),f333(f333(f135(x36971),x36973),x36974))) % 183.90/184.43 [3710]E(f153(x37101,f333(f333(f155(x37102,x37101),x37103),f153(x37102,x37104))),f153(x37101,f333(f333(f155(x37102,x37101),x37103),x37104))) % 183.90/184.43 [3726]E(f333(f288(x37261,x37261),f333(f333(f289(x37262,x37261),x37263),x37264)),f333(f333(f289(x37262,x37261),f333(f288(x37262,x37262),x37263)),x37264)) % 183.90/184.43 [3737]E(f333(f333(f290(x37371,x37372,x37373),x37374),f196(f882(f881(x37372,x37373),a870))),f196(f882(f881(x37371,x37373),a870))) % 183.90/184.43 [3738]E(f333(f333(f177(x37381),f333(f333(f22(a875),x37382),x37383)),f333(f333(f139(x37381),x37383),x37384)),f333(f333(f139(x37381),x37383),f333(f333(f177(x37381),x37382),x37384))) % 183.90/184.43 [3759]E(f333(f333(f135(x37591),f171(x37591,x37592,x37593)),f171(x37591,x37594,x37593)),f171(x37591,f333(f333(f79(a875),x37592),x37594),x37593)) % 183.90/184.43 [3786]E(f40(f882(x37861,a870),f333(f312(x37862,f882(x37861,a870),x37863),x37864)),f333(f333(f42(x37862,f882(x37861,a870)),x37864),x37863)) % 183.90/184.43 [3787]E(f39(f882(x37871,a870),f333(f312(x37872,f882(x37871,a870),x37873),x37874)),f333(f333(f41(x37872,f882(x37871,a870)),x37874),x37873)) % 183.90/184.43 [3788]E(f333(f197(f876(f881(x37881,x37882))),f333(f333(f184(x37881,x37882),x37883),x37884)),f333(f333(f245(a875),f333(f197(f876(x37881)),x37883)),f333(f197(f876(x37882)),x37884))) % 183.90/184.43 [3790]E(f333(f313(x37901,x37902,x37903),f333(f78(f882(x37902,a870)),x37904)),f333(f78(f882(x37901,a870)),f333(f313(x37901,x37902,x37903),x37904))) % 183.90/184.43 [3820]E(f333(f190(x38201,x38202,x38203,f196(f882(x38201,a870))),x38204),f209(x38202)) % 183.90/184.43 [3841]E(f333(f313(x38411,x38412,x38413),f333(f253(x38412),x38414)),f333(f253(x38411),f333(f333(f8(x38412,a870,x38411),x38414),x38413))) % 183.90/184.43 [3859]E(f333(f333(f166(x38591),f333(f333(f135(x38591),x38592),f333(f333(f152(x38591),x38593),x38594))),f333(f197(f876(x38591)),x38592)),x38593) % 183.90/184.43 [3864]E(f333(f190(x38641,x38642,f333(f16(f879(x38642),x38641),f209(x38642)),x38643),x38644),f209(x38642)) % 183.90/184.43 [3886]E(f333(f312(x38861,x38862,x38863),f333(f313(x38861,x38862,x38863),x38864)),f333(f333(f104(f882(x38862,a870)),x38864),f333(f312(x38861,x38862,x38863),f256(f882(x38861,a870))))) % 183.90/184.43 [3904]P1(f333(f333(f335(x39041),f333(x39042,x39043)),f333(f312(x39044,x39041,x39042),f256(f882(x39044,a870))))) % 183.90/184.43 [3916]E(f333(f333(f135(x39161),f171(x39161,x39162,x39163)),f333(f333(f152(x39161),x39163),x39164)),f333(f333(f152(x39161),x39163),f333(f333(f135(x39161),f171(x39161,x39162,x39163)),x39164))) % 183.90/184.43 [3918]E(f333(f333(f270(x39181,x39182),f333(f174(x39181),x39183)),f333(f16(f882(x39182,a870),x39181),f333(f174(x39182),x39184))),f333(f174(f881(x39181,x39182)),f59(x39181,x39182,x39183,x39184))) % 183.90/184.43 [3932]E(f156(x39321,x39322,f333(f333(f152(x39321),x39323),x39324)),f333(f333(f79(a875),f333(f333(f79(a875),f333(x39322,x39323)),f156(x39321,x39322,x39324))),f333(a115,f2(a875)))) % 183.90/184.43 [3946]E(f193(f876(x39461),f333(f333(f152(x39461),x39462),x39463),f333(f333(f7(a875,f876(x39461),f876(x39461)),f139(x39461)),x39463),x39464),f333(f333(f139(x39461),x39464),f333(f333(f152(x39461),x39462),x39463))) % 183.90/184.43 [3947]P25(x39471,f881(x39472,x39471),f337(x39473,x39474,x39472,x39471),f333(f333(f41(x39472,f882(x39471,a870)),x39474),x39473)) % 183.90/184.43 [3956]E(f333(f333(f22(f882(x39561,a870)),f333(f333(f22(f882(x39561,a870)),x39562),x39563)),f333(f333(f311(x39561),x39564),f196(f882(x39561,a870)))),f333(f333(f22(f882(x39561,a870)),x39562),f333(f333(f311(x39561),x39564),x39563))) % 183.90/184.43 [3968]E(f333(f333(f191(f882(x39681,x39682),f882(x39681,x39682)),x39683),f72(x39682,x39682,x39681,x39684)),f72(x39682,x39682,x39681,f333(f333(f191(x39682,x39682),x39683),x39684))) % 183.90/184.43 [4046]E(f333(f333(f333(f191(f876(x40461),f876(x40461)),x40462),f169(x40461)),f333(f333(f333(f191(f876(x40461),f876(x40461)),x40463),f169(x40461)),x40464)),f333(f333(f333(f191(f876(x40461),f876(x40461)),f333(f333(f79(a875),x40462),x40463)),f169(x40461)),x40464)) % 183.90/184.43 [4133]P1(f333(f333(f247(f882(x41331,a870)),f333(f174(x41331),f333(f333(f160(x41331,x41332),x41333),x41334))),f333(f333(f311(x41331),x41334),f333(f174(x41331),x41332)))) % 183.90/184.43 [4169]E(f333(f333(f41(f882(x41691,a870),f882(f881(x41691,x41692),a870)),x41693),f333(f333(f7(f882(x41691,a870),f882(x41691,f882(x41692,a870)),f882(f881(x41691,x41692),a870)),f270(x41691,x41692)),x41694)),f333(f333(f270(x41691,x41692),f39(f882(x41691,a870),x41693)),x41694)) % 183.90/184.43 [4207]E(f221(x42071,x42072,x42073,f333(f72(x42072,f882(a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(x42072))))),x42071,f220(x42072)),x42074)),f222(x42071,x42072,x42074,x42073)) % 183.90/184.43 [4224]E(f217(x42241,x42242,x42243,f333(f72(x42242,f882(a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(f879(x42242)))))),x42241,f216(x42242)),x42244)),f218(x42241,x42242,x42244,x42243)) % 183.90/184.43 [4229]P1(f333(f66(x42291,x42292,x42293,x42294,f196(f882(x42291,a870))),x42294)) % 183.90/184.43 [4271]E(f333(f333(f41(x42711,f882(x42712,a870)),x42713),f333(f333(f7(x42711,f882(x42712,a870),f882(x42712,a870)),f333(f333(f8(x42712,f882(f882(x42712,a870),f882(x42712,a870)),x42711),f311(x42712)),x42714)),f196(f882(x42712,a870)))),f333(f312(x42711,x42712,x42714),x42713)) % 183.90/184.43 [4278]P1(f333(f333(f247(f882(x42781,a870)),f333(f264(x42782,x42781),f333(f333(f104(f882(f881(x42782,x42781),a870)),x42783),x42784))),f333(f333(f104(f882(x42781,a870)),f333(f264(x42782,x42781),x42783)),f333(f264(x42782,x42781),x42784)))) % 183.90/184.43 [4279]P1(f333(f333(f247(f882(x42791,a870)),f333(f266(x42791,x42792),f333(f333(f104(f882(f881(x42791,x42792),a870)),x42793),x42794))),f333(f333(f104(f882(x42791,a870)),f333(f266(x42791,x42792),x42793)),f333(f266(x42791,x42792),x42794)))) % 183.90/184.43 [4341]P1(f333(f333(f247(f882(f881(x43411,x43412),a870)),f333(f312(x43412,f881(x43411,x43412),f337(x43413,x43414,x43411,x43412)),f333(f333(f41(x43411,f882(x43412,a870)),x43414),x43413))),f333(f333(f270(x43411,x43412),x43414),x43413))) % 183.90/184.43 [4342]E(f333(f121(x43421,f881(x43421,x43422),x43423),f333(f333(f8(f882(x43422,f877(f881(x43421,x43422))),f877(f881(x43421,x43422)),x43421),f121(x43422,f881(x43421,x43422),x43424)),f333(f333(f8(f882(x43422,f881(x43421,x43422)),f882(x43422,f877(f881(x43421,x43422))),x43421),f333(f8(f881(x43421,x43422),f877(f881(x43421,x43422)),x43422),f127(f881(x43421,x43422)))),f268(x43421,x43422)))),f132(x43421,x43422,x43423,x43424)) % 183.90/184.43 [4382]E(f84(f881(x43821,x43822),f333(f272(x43821,x43822,a870),f333(f333(f7(x43821,f882(x43822,a870),f882(x43822,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x43822,a870),f882(x43822,a870)),x43821),f8(a870,a870,x43822)),f333(f333(f8(a870,f882(a870,a870),x43821),a331),f333(a330,x43823)))),f333(a330,x43824)))),f333(f333(f268(x43821,x43822),x43823),x43824)) % 183.90/184.43 [4383]E(f89(f881(x43831,x43832),f333(f272(x43831,x43832,a870),f333(f333(f7(x43831,f882(x43832,a870),f882(x43832,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x43832,a870),f882(x43832,a870)),x43831),f8(a870,a870,x43832)),f333(f333(f8(a870,f882(a870,a870),x43831),a331),f333(a330,x43833)))),f333(a330,x43834)))),f333(f333(f268(x43831,x43832),x43833),x43834)) % 183.90/184.43 [4454]E(f333(f333(f272(f876(x44541),f876(x44541),f881(f876(x44541),f876(x44541))),f333(f333(f18(f876(x44541),f882(f876(x44541),f881(f876(x44541),f876(x44541))),f882(f876(x44541),f881(f876(x44541),f876(x44541)))),f333(f333(f8(f882(f876(x44541),f882(f881(f876(x44541),f876(x44541)),f881(f876(x44541),f876(x44541)))),f882(f882(f876(x44541),f881(f876(x44541),f876(x44541))),f882(f876(x44541),f881(f876(x44541),f876(x44541)))),f876(x44541)),f18(f876(x44541),f881(f876(x44541),f876(x44541)),f881(f876(x44541),f876(x44541)))),f333(f333(f8(f882(f876(x44541),f881(f876(x44541),f876(x44541))),f882(f876(x44541),f882(f881(f876(x44541),f876(x44541)),f881(f876(x44541),f876(x44541)))),f876(x44541)),f333(f8(f881(f876(x44541),f876(x44541)),f882(f881(f876(x44541),f876(x44541)),f881(f876(x44541),f876(x44541))),f876(x44541)),f333(f99(f881(f876(x44541),f876(x44541))),f333(x44542,x44543)))),f333(f333(f8(f876(x44541),f882(f876(x44541),f881(f876(x44541),f876(x44541))),f876(x44541)),f268(f876(x44541),f876(x44541))),f333(f152(x44541),x44543))))),f333(f333(f7(f876(x44541),f882(f876(x44541),f876(x44541)),f882(f876(x44541),f881(f876(x44541),f876(x44541)))),f333(f333(f8(f882(f876(x44541),f881(f876(x44541),f876(x44541))),f882(f882(f876(x44541),f876(x44541)),f882(f876(x44541),f881(f876(x44541),f876(x44541)))),f876(x44541)),f8(f876(x44541),f881(f876(x44541),f876(x44541)),f876(x44541))),f268(f876(x44541),f876(x44541)))),f333(f152(x44541),x44543)))),f168(x44541,x44542,x44544)),f168(x44541,x44542,f333(f333(f152(x44541),x44543),x44544))) % 183.90/184.43 [4460]E(f333(f143(f882(x44601,f879(x44602)),f881(x44601,x44602),f333(f7(f881(x44601,x44602),f882(x44601,f879(x44602)),f882(x44601,f879(x44602))),f333(f272(x44601,x44602,f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602)))),f333(f333(f7(x44601,f882(x44602,f879(x44602)),f882(x44602,f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602))))),f333(f333(f8(f882(f879(x44602),f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602)))),f882(f882(x44602,f879(x44602)),f882(x44602,f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602))))),x44601),f8(f879(x44602),f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602))),x44602)),f333(f333(f8(f882(f882(x44601,f879(x44602)),f882(f879(x44602),f882(x44601,f879(x44602)))),f882(f879(x44602),f882(f882(x44601,f879(x44602)),f882(x44601,f879(x44602)))),x44601),f7(f882(x44601,f879(x44602)),f879(x44602),f882(x44601,f879(x44602)))),f333(f7(f882(x44601,f879(x44602)),x44601,f882(f879(x44602),f882(x44601,f879(x44602)))),f71(x44601,f879(x44602)))))),f240(x44602)))),x44603),f333(f170(f881(x44601,x44602)),x44604)),f187(x44601,x44602,x44603,f333(f180(x44601,x44602),x44604))) % 183.90/184.43 [3549]E(f333(f197(f874(x35491)),f333(f333(f333(f91(x35491),x35492),x35493),x35494)),f2(a875)) % 183.90/184.43 [3673]E(f333(f333(f177(x36731),x36732),f333(f333(f177(x36731),x36733),x36734)),f333(f333(f177(x36731),f333(f333(f245(a875),x36732),x36733)),x36734)) % 183.90/184.43 [3674]E(f333(f333(f139(x36741),x36742),f333(f333(f139(x36741),x36743),x36744)),f333(f333(f139(x36741),f333(f333(f79(a875),x36742),x36743)),x36744)) % 183.90/184.43 [3686]E(f333(f333(f135(x36861),f333(f333(f152(x36861),x36862),x36863)),x36864),f333(f333(f152(x36861),x36862),f333(f333(f135(x36861),x36863),x36864))) % 183.90/184.43 [3687]E(f333(f333(f135(x36871),f333(f333(f135(x36871),x36872),x36873)),x36874),f333(f333(f135(x36871),x36872),f333(f333(f135(x36871),x36873),x36874))) % 183.90/184.43 [3770]E(f333(f333(f166(x37701),f333(f333(f152(x37701),x37702),x37703)),x37704),f193(x37701,x37702,f333(f166(x37701),x37703),x37704)) % 183.90/184.43 [3779]E(f333(f333(f191(x37791,x37791),x37792),f333(f333(f191(x37791,x37791),x37793),x37794)),f333(f333(f191(x37791,x37791),f333(f333(f80(a875),x37793),x37792)),x37794)) % 183.90/184.43 [3808]E(f333(f333(f113(f882(x38081,a870)),x38082),f333(f333(f311(x38081),x38083),x38084)),f333(f333(f311(x38081),x38083),f333(f333(f113(f882(x38081,a870)),x38082),x38084))) % 183.90/184.43 [3823]E(f333(f333(f333(f191(x38231,x38231),x38232),x38233),f333(x38233,x38234)),f333(x38233,f333(f333(f333(f191(x38231,x38231),x38232),x38233),x38234))) % 183.90/184.43 [3831]E(f333(f333(f290(x38311,x38312,x38313),f196(f882(f881(x38311,x38312),a870))),x38314),f196(f882(f881(x38311,x38313),a870))) % 183.90/184.43 [3847]E(f333(f333(f113(f882(x38471,a870)),f333(f333(f311(x38471),x38472),x38473)),x38474),f333(f333(f311(x38471),x38472),f333(f333(f113(f882(x38471,a870)),x38473),x38474))) % 183.90/184.43 [3867]E(f187(x38671,x38672,f333(f180(x38671,x38672),x38673),f333(f180(x38671,x38672),x38674)),f333(f180(x38671,x38672),f333(f333(f135(f881(x38671,x38672)),x38674),x38673))) % 183.90/184.43 [3868]E(f333(f37(f881(x38681,x38682)),f333(f333(f270(x38681,x38682),x38683),f333(f16(f882(x38682,a870),x38681),x38684))),f333(f333(f80(a875),f333(f37(x38681),x38683)),f333(f37(x38682),x38684))) % 183.90/184.43 [3875]E(f333(f333(f104(f882(x38751,a870)),f333(f333(f311(x38751),x38752),x38753)),f333(f333(f311(x38751),x38752),x38754)),f333(f333(f311(x38751),x38752),f333(f333(f104(f882(x38751,a870)),x38753),x38754))) % 183.90/184.43 [3890]E(f333(f333(f113(f882(x38901,a870)),x38902),f333(f333(f113(f882(x38901,a870)),x38903),x38904)),f333(f333(f113(f882(x38901,a870)),x38903),f333(f333(f113(f882(x38901,a870)),x38902),x38904))) % 183.90/184.43 [3891]E(f333(f333(f104(f882(x38911,a870)),x38912),f333(f333(f104(f882(x38911,a870)),x38913),x38914)),f333(f333(f104(f882(x38911,a870)),x38913),f333(f333(f104(f882(x38911,a870)),x38912),x38914))) % 183.90/184.43 [3900]E(f64(x39001,x39002,f333(f333(f8(x39002,f882(x39002,x39002),x39001),x39003),x39004)),f333(f65(x39002,x39001,x39003),x39004)) % 183.90/184.43 [3910]E(f182(x39101,f333(f333(f155(f876(x39102),f876(x39101)),f333(f155(x39102,x39101),x39103)),x39104)),f333(f333(f155(f876(x39102),f876(x39101)),f333(f155(x39102,x39101),x39103)),f182(x39102,x39104))) % 183.90/184.43 [3928]E(f333(f143(f876(x39281),f876(x39281),f135(x39281),f116(x39281)),f333(f333(f155(x39282,f876(x39281)),x39283),x39284)),f165(x39282,x39281,x39283,x39284)) % 183.90/184.43 [3931]E(f190(x39311,x39312,x39313,f333(f78(f882(x39311,a870)),f333(f333(f311(x39311),x39314),f196(f882(x39311,a870))))),f333(f333(f333(f71(x39311,f879(x39312)),x39313),x39314),f209(x39312))) % 183.90/184.43 [3973]E(f333(f333(f333(f71(x39731,f879(x39732)),f333(f180(x39731,x39732),x39733)),f333(f267(x39731,x39732),x39734)),f333(f240(x39732),f333(f271(x39731,x39732),x39734))),f333(f180(x39731,x39732),f333(f333(f152(f881(x39731,x39732)),x39734),x39733))) % 183.90/184.43 [3990]E(f333(f72(x39901,x39901,x39901,f333(f333(f191(x39901,x39901),x39902),x39903)),f333(f333(f191(x39901,x39901),x39904),x39903)),f333(f333(f191(x39901,x39901),f333(f333(f79(a875),x39902),x39904)),x39903)) % 183.90/184.43 [4015]E(f333(f333(f104(f882(x40151,a870)),f333(f333(f113(f882(x40151,a870)),x40152),x40153)),f333(f333(f113(f882(x40151,a870)),x40152),x40154)),f333(f333(f113(f882(x40151,a870)),x40152),f333(f333(f104(f882(x40151,a870)),x40153),x40154))) % 183.90/184.43 [4016]E(f333(f333(f104(f882(x40161,a870)),f333(f333(f22(f882(x40161,a870)),x40162),x40163)),f333(f333(f22(f882(x40161,a870)),x40162),x40164)),f333(f333(f22(f882(x40161,a870)),x40162),f333(f333(f113(f882(x40161,a870)),x40163),x40164))) % 183.90/184.43 [4017]E(f333(f333(f113(f882(x40171,a870)),f333(f333(f22(f882(x40171,a870)),x40172),x40173)),f333(f333(f22(f882(x40171,a870)),x40172),x40174)),f333(f333(f22(f882(x40171,a870)),x40172),f333(f333(f104(f882(x40171,a870)),x40173),x40174))) % 183.90/184.43 [4018]E(f333(f333(f113(f882(x40181,a870)),f333(f333(f104(f882(x40181,a870)),x40182),x40183)),f333(f333(f104(f882(x40181,a870)),x40182),x40184)),f333(f333(f104(f882(x40181,a870)),x40182),f333(f333(f113(f882(x40181,a870)),x40183),x40184))) % 183.90/184.43 [4019]E(f333(f333(f22(f882(x40191,a870)),f333(f333(f104(f882(x40191,a870)),x40192),x40193)),f333(f333(f104(f882(x40191,a870)),x40192),x40194)),f333(f333(f104(f882(x40191,a870)),x40192),f333(f333(f22(f882(x40191,a870)),x40193),x40194))) % 183.90/184.43 [4025]E(f333(f37(f881(x40251,x40252)),f333(f333(f270(x40251,x40252),f333(f333(f311(x40251),x40253),f196(f882(x40251,a870)))),f333(f16(f882(x40252,a870),x40251),x40254))),f333(f37(x40252),x40254)) % 183.90/184.43 [4062]E(f333(f333(f42(x40621,f882(x40622,a870)),x40623),f333(f333(f8(f882(x40622,a870),f882(x40622,a870),x40621),f78(f882(x40622,a870))),x40624)),f333(f78(f882(x40622,a870)),f333(f333(f41(x40621,f882(x40622,a870)),x40623),x40624))) % 183.90/184.43 [4063]E(f333(f333(f41(x40631,f882(x40632,a870)),x40633),f333(f333(f8(f882(x40632,a870),f882(x40632,a870),x40631),f78(f882(x40632,a870))),x40634)),f333(f78(f882(x40632,a870)),f333(f333(f42(x40631,f882(x40632,a870)),x40633),x40634))) % 183.90/184.43 [4077]E(f333(f333(f290(x40771,x40771,x40771),f333(f333(f191(f881(x40771,x40771),a870),x40772),x40773)),f333(f333(f191(f881(x40771,x40771),a870),x40774),x40773)),f333(f333(f191(f881(x40771,x40771),a870),f333(f333(f79(a875),x40772),x40774)),x40773)) % 183.90/184.43 [4108]E(f333(f333(f42(x41081,f882(f882(x41082,a870),a870)),x41083),f333(f333(f8(f882(x41082,a870),f882(f882(x41082,a870),a870),x41081),f310(x41082)),x41084)),f333(f310(x41082),f333(f333(f42(x41081,f882(x41082,a870)),x41083),x41084))) % 183.90/184.43 [4137]E(f333(f333(f41(f882(x41371,a870),f882(x41372,a870)),x41373),f333(f333(f7(f882(x41371,a870),f882(x41371,f882(x41372,a870)),f882(x41372,a870)),f41(x41371,f882(x41372,a870))),x41374)),f333(f333(f41(x41371,f882(x41372,a870)),f39(f882(x41371,a870),x41373)),x41374)) % 183.90/184.43 [4138]E(f333(f333(f42(f882(x41381,a870),f882(x41382,a870)),x41383),f333(f333(f7(f882(x41381,a870),f882(x41381,f882(x41382,a870)),f882(x41382,a870)),f42(x41381,f882(x41382,a870))),x41384)),f333(f333(f42(x41381,f882(x41382,a870)),f39(f882(x41381,a870),x41383)),x41384)) % 183.90/184.43 [4143]E(f333(f333(f155(x41431,x41432),x41433),f333(f143(f876(x41431),f876(x41431),f135(x41431),f116(x41431)),x41434)),f333(f143(f876(x41432),f876(x41432),f135(x41432),f116(x41432)),f333(f333(f155(f876(x41431),f876(x41432)),f333(f155(x41431,x41432),x41433)),x41434))) % 183.90/184.43 [4147]E(f193(f876(x41471),f116(x41471),f333(f333(f8(f876(x41471),f876(x41471),a875),f333(f152(x41471),x41472)),f333(f333(f7(a875,f876(x41471),f876(x41471)),f177(x41471)),x41473)),x41474),f333(f333(f177(x41471),x41474),f333(f333(f152(x41471),x41472),x41473))) % 183.90/184.43 [4189]P1(f333(f333(f247(f882(x41891,a870)),f333(f312(x41892,x41891,x41893),f333(f313(x41892,x41891,x41893),x41894))),x41894)) % 183.90/184.43 [4192]E(f333(f312(f881(x41921,x41922),f881(x41922,x41921),f333(f272(x41921,x41922,f881(x41922,x41921)),f333(f7(x41922,x41921,f881(x41922,x41921)),f268(x41922,x41921)))),f333(f333(f270(x41921,x41922),x41923),f333(f16(f882(x41922,a870),x41921),x41924))),f333(f333(f270(x41922,x41921),x41924),f333(f16(f882(x41921,a870),x41922),x41923))) % 183.90/184.43 [4201]E(f333(f333(f41(x42011,f882(x42012,a870)),x42013),f333(f333(f8(f882(x42011,a870),f882(x42012,a870),x42011),f313(x42012,x42011,x42014)),f333(f333(f7(x42011,f882(x42011,a870),f882(x42011,a870)),f311(x42011)),f196(f882(x42011,a870))))),f333(f313(x42012,x42011,x42014),x42013)) % 183.90/184.43 [4202]E(f333(f333(f41(x42021,f882(x42022,a870)),x42023),f333(f333(f8(f882(x42021,a870),f882(x42022,a870),x42021),f287(x42021,x42022,x42024)),f333(f333(f7(x42021,f882(x42021,a870),f882(x42021,a870)),f311(x42021)),f196(f882(x42021,a870))))),f333(f287(x42021,x42022,x42024),x42023)) % 183.90/184.43 [4293]E(f333(f333(f113(f882(x42931,a870)),f333(f333(f113(f882(x42931,a870)),f333(f333(f104(f882(x42931,a870)),x42932),x42933)),f333(f333(f104(f882(x42931,a870)),x42933),x42934))),f333(f333(f104(f882(x42931,a870)),x42934),x42932)),f333(f333(f104(f882(x42931,a870)),f333(f333(f104(f882(x42931,a870)),f333(f333(f113(f882(x42931,a870)),x42932),x42933)),f333(f333(f113(f882(x42931,a870)),x42933),x42934))),f333(f333(f113(f882(x42931,a870)),x42934),x42932))) % 183.90/184.43 [4355]E(f333(f143(f876(x43551),f876(x43551),f135(x43551),f116(x43551)),f333(f333(f155(x43552,f876(x43551)),f333(f333(f7(x43552,f876(x43551),f876(x43551)),f333(f333(f8(x43551,f882(f876(x43551),f876(x43551)),x43552),f152(x43551)),x43553)),f116(x43551))),x43554)),f333(f333(f155(x43552,x43551),x43553),x43554)) % 183.90/184.43 [4366]E(f333(f333(f85(a1,x43661),f333(f106(a1),f333(f333(f79(a1),x43662),a100))),f333(f333(f18(a1,x43661,x43661),f333(f333(f7(a1,x43661,f882(x43661,x43661)),f333(f333(f8(a870,f882(x43661,f882(x43661,x43661)),a1),f99(x43661)),a201)),x43663)),f333(f333(f8(a875,x43661,a1),x43664),a107))),f193(x43661,x43663,x43664,f333(f106(a875),x43662))) % 183.90/184.43 [4568]~P1(f333(f333(f196(f882(x45681,f882(x45682,a870))),x45683),x45684)) % 183.90/184.43 [3834]E(f333(f333(f166(x38341),f333(f333(f135(x38341),x38342),x38343)),f333(f333(f79(a875),f333(f197(f876(x38341)),x38342)),x38344)),f333(f333(f166(x38341),x38343),x38344)) % 183.90/184.43 [3840]E(f333(f333(f139(x38401),x38402),f333(f333(f177(x38401),f333(f333(f79(a875),x38403),x38402)),x38404)),f333(f333(f177(x38401),x38403),f333(f333(f139(x38401),x38402),x38404))) % 183.90/184.43 [3944]E(f333(f333(f113(f882(x39441,a870)),f333(f264(x39442,x39441),x39443)),f333(f264(x39442,x39441),x39444)),f333(f264(x39442,x39441),f333(f333(f113(f882(f881(x39442,x39441),a870)),x39443),x39444))) % 183.90/184.43 [3945]E(f333(f333(f113(f882(x39451,a870)),f333(f266(x39451,x39452),x39453)),f333(f266(x39451,x39452),x39454)),f333(f266(x39451,x39452),f333(f333(f113(f882(f881(x39451,x39452),a870)),x39453),x39454))) % 183.90/184.43 [3950]E(f333(f333(f113(f882(x39501,a870)),f333(f333(f113(f882(x39501,a870)),x39502),x39503)),x39504),f333(f333(f113(f882(x39501,a870)),x39502),f333(f333(f113(f882(x39501,a870)),x39503),x39504))) % 183.90/184.43 [3951]E(f333(f333(f22(f882(x39511,a870)),f333(f333(f104(f882(x39511,a870)),x39512),x39513)),x39514),f333(f333(f104(f882(x39511,a870)),x39512),f333(f333(f22(f882(x39511,a870)),x39513),x39514))) % 183.90/184.43 [3952]E(f333(f333(f104(f882(x39521,a870)),f333(f333(f104(f882(x39521,a870)),x39522),x39523)),x39524),f333(f333(f104(f882(x39521,a870)),x39522),f333(f333(f104(f882(x39521,a870)),x39523),x39524))) % 183.90/184.43 [3992]E(f333(f333(f113(f882(f881(x39921,x39922),a870)),f333(f288(x39922,x39921),x39923)),f333(f288(x39922,x39921),x39924)),f333(f288(x39922,x39921),f333(f333(f113(f882(f881(x39922,x39921),a870)),x39923),x39924))) % 183.90/184.43 [3993]E(f333(f333(f104(f882(f881(x39931,x39932),a870)),f333(f288(x39932,x39931),x39933)),f333(f288(x39932,x39931),x39934)),f333(f288(x39932,x39931),f333(f333(f104(f882(f881(x39932,x39931),a870)),x39933),x39934))) % 183.90/184.43 [4007]E(f333(f333(f113(f882(x40071,f882(x40072,a870))),f257(x40072,x40071,x40073)),f257(x40072,x40071,x40074)),f257(x40072,x40071,f333(f333(f113(f882(x40072,f882(x40071,a870))),x40073),x40074))) % 183.90/184.43 [4008]E(f333(f333(f104(f882(x40081,f882(x40082,a870))),f257(x40082,x40081,x40083)),f257(x40082,x40081,x40084)),f257(x40082,x40081,f333(f333(f104(f882(x40082,f882(x40081,a870))),x40083),x40084))) % 183.90/184.43 [4066]E(f333(f333(f104(f882(x40661,a870)),f333(f333(f113(f882(x40661,a870)),x40662),x40663)),f333(f333(f113(f882(x40661,a870)),x40664),x40663)),f333(f333(f113(f882(x40661,a870)),f333(f333(f104(f882(x40661,a870)),x40662),x40664)),x40663)) % 183.90/184.43 [4067]E(f333(f333(f113(f882(x40671,a870)),f333(f333(f22(f882(x40671,a870)),x40672),x40673)),f333(f333(f22(f882(x40671,a870)),x40674),x40673)),f333(f333(f22(f882(x40671,a870)),f333(f333(f113(f882(x40671,a870)),x40672),x40674)),x40673)) % 183.90/184.43 [4068]E(f333(f333(f113(f882(x40681,a870)),f333(f333(f104(f882(x40681,a870)),x40682),x40683)),f333(f333(f104(f882(x40681,a870)),x40684),x40683)),f333(f333(f104(f882(x40681,a870)),f333(f333(f113(f882(x40681,a870)),x40682),x40684)),x40683)) % 183.90/184.43 [4069]E(f333(f333(f22(f882(x40691,a870)),f333(f333(f104(f882(x40691,a870)),x40692),x40693)),f333(f333(f104(f882(x40691,a870)),x40694),x40693)),f333(f333(f104(f882(x40691,a870)),f333(f333(f22(f882(x40691,a870)),x40692),x40694)),x40693)) % 183.90/184.43 [4070]E(f333(f333(f22(f882(x40701,a870)),f333(f333(f104(f882(x40701,a870)),x40702),x40703)),f333(f333(f104(f882(x40701,a870)),x40704),x40703)),f333(f333(f22(f882(x40701,a870)),f333(f333(f104(f882(x40701,a870)),x40702),x40703)),x40704)) % 183.90/184.43 [4080]E(f333(f333(f22(f882(x40801,a870)),f333(f333(f22(f882(x40801,a870)),x40802),f333(f333(f311(x40801),x40803),f196(f882(x40801,a870))))),x40804),f333(f333(f22(f882(x40801,a870)),x40802),f333(f333(f311(x40801),x40803),x40804))) % 183.90/184.43 [4134]E(f333(f333(f113(f882(x41341,a870)),f333(f333(f311(x41341),x41342),f333(f333(f311(x41341),x41343),f196(f882(x41341,a870))))),f333(f286(x41341),x41344)),f333(f286(x41341),f333(f333(f311(f881(x41341,x41341)),f333(f333(f268(x41341,x41341),x41342),x41343)),x41344))) % 183.90/184.43 [4164]E(f333(f333(f41(a875,f882(x41641,a870)),f333(f302(a875),x41642)),f333(f333(f8(a875,f882(x41641,a870),a875),x41643),f333(f333(f7(a875,a875,a875),f79(a875)),x41644))),f333(f333(f41(a875,f882(x41641,a870)),f304(a875,x41644,f333(f333(f79(a875),x41642),x41644))),x41643)) % 183.90/184.43 [4165]E(f176(x41651,f333(f287(x41651,x41651,x41652),f333(f333(f311(x41651),x41653),f196(f882(x41651,a870)))),f333(f287(f876(x41651),f876(x41651),f159(x41651,x41652)),f333(f333(f311(f876(x41651)),x41654),f196(f882(f876(x41651),a870))))),f333(f287(f876(x41651),f876(x41651),f159(x41651,x41652)),f333(f333(f311(f876(x41651)),f333(f333(f152(x41651),x41653),x41654)),f196(f882(f876(x41651),a870))))) % 183.90/184.43 [4227]E(f333(f180(x42271,x42272),f333(f333(f155(x42271,f881(x42271,x42272)),f333(f333(f18(x42271,x42272,f881(x42271,x42272)),f268(x42271,x42272)),x42273)),x42274)),f190(x42271,x42272,f333(f72(x42272,f879(x42272),x42271,f240(x42272)),x42273),f333(f174(x42271),x42274))) % 183.90/184.43 [4232]E(f333(f253(x42321),f333(f333(f7(x42321,f882(x42322,a870),a870),f333(f333(f8(x42322,f882(f882(x42322,a870),a870),x42321),f335(x42322)),x42323)),x42324)),f333(f313(x42321,x42322,x42323),x42324)) % 183.90/184.43 [4326]E(f333(f253(x43261),f333(f333(f7(x43261,f882(f881(x43262,x43261),a870),a870),f333(f333(f8(f881(x43262,x43261),f882(f882(f881(x43262,x43261),a870),a870),x43261),f335(f881(x43262,x43261))),f333(f268(x43262,x43261),x43263))),x43264)),f333(f287(x43262,x43261,x43264),f333(f333(f311(x43262),x43263),f196(f882(x43262,a870))))) % 183.90/184.43 [4340]E(f333(f333(f155(f881(x43401,a875),x43401),f267(x43401,a875)),f333(f137(f881(x43401,a875),f333(f333(f8(a875,a870,f881(x43401,a875)),x43402),f333(f333(f8(a875,a875,f881(x43401,a875)),a115),f271(x43401,a875)))),f333(f333(f184(x43401,a875),x43403),x43404))),f333(f333(f155(f881(x43401,a875),x43401),f267(x43401,a875)),f333(f137(f881(x43401,a875),f333(f333(f8(a875,a870,f881(x43401,a875)),x43402),f271(x43401,a875))),f333(f333(f184(x43401,a875),x43403),f333(f333(f155(a875,a875),a115),x43404))))) % 183.90/184.43 [4348]P1(f333(f333(f247(f882(f882(x43481,a870),a870)),f333(f333(f41(x43482,f882(f882(x43481,a870),a870)),x43483),f333(f333(f8(f882(x43481,a870),f882(f882(x43481,a870),a870),x43482),f310(x43481)),x43484))),f333(f310(x43481),f333(f333(f41(x43482,f882(x43481,a870)),x43483),x43484)))) % 183.90/184.43 [4390]E(f333(f333(f85(a1,x43901),f333(f106(a1),f333(f333(f79(a1),x43902),a100))),f333(f333(f18(a1,x43901,x43901),f333(f333(f7(a1,x43901,f882(x43901,x43901)),f333(f333(f8(a870,f882(x43901,f882(x43901,x43901)),a1),f99(x43901)),a201)),x43903)),f333(f333(f18(a1,x43901,x43901),f333(f333(f8(a875,f882(x43901,x43901),a1),x43904),a107)),f333(f333(f8(a875,x43901,a1),f192(x43901,x43903,x43904)),a107)))),f333(f192(x43901,x43903,x43904),f333(f106(a875),x43902))) % 183.90/184.43 [4393]E(f333(f333(f155(x43931,x43932),f333(f72(f879(x43932),x43932,x43931,f244(x43932)),x43933)),f333(f137(x43931,f333(f333(f8(a870,a870,x43931),a328),f333(f333(f7(x43931,f879(x43932),a870),f333(f333(f8(f879(x43932),f882(f879(x43932),a870),x43931),a330),x43933)),f209(x43932)))),x43934)),f164(x43931,x43932,x43933,x43934)) % 183.90/184.43 [4416]E(f333(f253(f881(x44161,x44162)),f333(f272(x44161,x44162,a870),f333(f333(f7(x44161,f882(x44162,a870),f882(x44162,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x44162,a870),f882(x44162,a870)),x44161),f8(a870,a870,x44162)),f333(f333(f8(a870,f882(a870,a870),x44161),a331),f333(f333(f7(x44161,f882(x44161,a870),a870),f335(x44161)),x44163)))),f333(f333(f7(x44162,f882(x44162,a870),a870),f335(x44162)),x44164)))),f234(x44161,x44162,x44163,x44164)) % 183.90/184.43 [4449]E(f333(f333(f41(x44491,f882(f881(x44491,x44492),a870)),x44493),f333(f333(f18(x44491,f882(x44492,f882(f881(x44491,x44492),a870)),f882(f881(x44491,x44492),a870)),f333(f333(f8(f882(x44492,a870),f882(f882(x44492,f882(f881(x44491,x44492),a870)),f882(f881(x44491,x44492),a870)),x44491),f41(x44492,f882(f881(x44491,x44492),a870))),x44494)),f333(f333(f7(x44491,f882(f881(x44491,x44492),a870),f882(x44492,f882(f881(x44491,x44492),a870))),f333(f333(f8(f882(x44492,f882(f882(f881(x44491,x44492),a870),f882(f881(x44491,x44492),a870))),f882(f882(f881(x44491,x44492),a870),f882(x44492,f882(f881(x44491,x44492),a870))),x44491),f7(x44492,f882(f881(x44491,x44492),a870),f882(f881(x44491,x44492),a870))),f333(f333(f8(f882(x44492,f881(x44491,x44492)),f882(x44492,f882(f882(f881(x44491,x44492),a870),f882(f881(x44491,x44492),a870))),x44491),f333(f8(f881(x44491,x44492),f882(f882(f881(x44491,x44492),a870),f882(f881(x44491,x44492),a870)),x44492),f311(f881(x44491,x44492)))),f268(x44491,x44492)))),f196(f882(f881(x44491,x44492),a870))))),f333(f333(f270(x44491,x44492),x44493),x44494)) % 183.90/184.43 [4002]E(f333(f333(f135(x40021),f333(f333(f177(x40021),x40022),x40023)),f333(f333(f177(x40021),f333(f333(f22(a875),x40022),f333(f197(f876(x40021)),x40023))),x40024)),f333(f333(f177(x40021),x40022),f333(f333(f135(x40021),x40023),x40024))) % 183.90/184.43 [4003]E(f333(f333(f135(x40031),f333(f333(f139(x40031),x40032),x40033)),f333(f333(f139(x40031),f333(f333(f22(a875),x40032),f333(f197(f876(x40031)),x40033))),x40034)),f333(f333(f139(x40031),x40032),f333(f333(f135(x40031),x40033),x40034))) % 183.90/184.43 [4055]E(f333(f333(f79(a875),f333(f333(f80(a875),x40551),x40552)),f333(f333(f79(a875),f333(f333(f80(a875),x40553),x40552)),x40554)),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f79(a875),x40551),x40553)),x40552)),x40554)) % 183.90/184.43 [4257]P1(f333(f333(f247(f882(x42571,a870)),f333(f333(f22(f882(x42571,a870)),f333(f264(x42572,x42571),x42573)),f333(f264(x42572,x42571),x42574))),f333(f264(x42572,x42571),f333(f333(f22(f882(f881(x42572,x42571),a870)),x42573),x42574)))) % 183.90/184.43 [4258]P1(f333(f333(f247(f882(x42581,a870)),f333(f333(f22(f882(x42581,a870)),f333(f266(x42581,x42582),x42583)),f333(f266(x42581,x42582),x42584))),f333(f266(x42581,x42582),f333(f333(f22(f882(f881(x42581,x42582),a870)),x42583),x42584)))) % 183.90/184.43 [4368]E(f333(f333(f79(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x43681),x43682)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x43683),x43684)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),f333(f333(f79(a875),x43681),x43683)),f333(f333(f79(a875),x43682),x43684))),f196(f882(f881(a875,a875),a870)))))) % 183.90/184.43 [4411]E(f333(f333(f80(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x44111),x44112)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x44113),x44114)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),f333(f333(f79(a875),f333(f333(f80(a875),x44111),x44113)),f333(f333(f80(a875),x44112),x44114))),f333(f333(f79(a875),f333(f333(f80(a875),x44111),x44114)),f333(f333(f80(a875),x44112),x44113)))),f196(f882(f881(a875,a875),a870)))))) % 183.90/184.43 [4431]E(f333(f253(x44311),f333(f333(f8(f882(x44312,a870),a870,x44311),f87(x44312)),f333(f333(f8(f882(x44312,a870),f882(x44312,a870),x44311),f333(f18(x44312,a870,a870),f333(f333(f8(a870,f882(a870,a870),x44312),a336),f333(f333(f7(x44312,f882(x44312,a870),a870),f335(x44312)),x44313)))),f333(f333(f7(x44311,f882(x44312,f882(x44311,a870)),f882(x44312,a870)),f333(f333(f8(f882(f882(x44311,a870),a870),f882(f882(x44312,f882(x44311,a870)),f882(x44312,a870)),x44311),f8(f882(x44311,a870),a870,x44312)),f335(x44311))),x44314)))),f333(f333(f42(x44312,f882(x44311,a870)),x44313),x44314)) % 183.90/184.43 [4464]E(f333(f333(f290(x44641,x44641,x44641),f333(f333(f311(f881(x44641,x44641)),f333(f333(f268(x44641,x44641),x44642),x44643)),x44644)),f309(x44641,f333(f333(f311(f881(x44641,x44641)),f333(f333(f268(x44641,x44641),x44642),x44643)),x44644))),f333(f333(f113(f882(f881(x44641,x44641),a870)),f333(f333(f290(x44641,x44641,x44641),x44644),f309(x44641,x44644))),f333(f253(f881(x44641,x44641)),f333(f272(x44641,x44641,a870),f333(f333(f7(x44641,f882(x44641,a870),f882(x44641,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x44641,a870),f882(x44641,a870)),x44641),f8(a870,a870,x44641)),f333(f333(f8(a870,f882(a870,a870),x44641),a331),f333(f333(f7(x44641,f882(f881(x44641,x44641),a870),a870),f333(f333(f8(f881(x44641,x44641),f882(f882(f881(x44641,x44641),a870),a870),x44641),f335(f881(x44641,x44641))),f333(f333(f7(x44641,x44641,f881(x44641,x44641)),f268(x44641,x44641)),x44642))),f309(x44641,x44644))))),f333(f333(f7(x44641,f882(f881(x44641,x44641),a870),a870),f333(f333(f8(f881(x44641,x44641),f882(f882(f881(x44641,x44641),a870),a870),x44641),f335(f881(x44641,x44641))),f333(f268(x44641,x44641),x44643))),f309(x44641,x44644))))))) % 183.90/184.43 [4259]E(f333(f137(x42591,f333(f333(f18(x42591,a870,a870),f333(f333(f8(a870,f882(a870,a870),x42591),a331),x42592)),x42593)),x42594),f333(f137(x42591,x42593),f333(f137(x42591,x42592),x42594))) % 183.90/184.43 [4362]E(f333(f333(f135(x43621),f333(f333(f333(f99(f876(x43621)),f333(f333(f335(a875),f2(a875)),x43622)),f333(f333(f152(x43621),x43623),f116(x43621))),f116(x43621))),f178(x43621,x43624,f333(f253(a875),f333(f333(f7(a875,f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),a875),f335(a875)),a115)),x43622)))),f178(x43621,f333(f333(f152(x43621),x43623),x43624),x43622)) % 183.90/184.43 [4458]E(f333(f253(f881(x44581,x44582)),f333(f333(f8(f882(a875,a870),a870,f881(x44581,x44582)),f86(a875)),f333(f333(f7(f881(x44581,x44582),f882(a875,a870),f882(a875,a870)),f333(f333(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),f881(x44581,x44582)),f18(a875,a870,a870)),f333(f333(f8(f882(a875,a870),f882(a875,f882(a870,a870)),f881(x44581,x44582)),f333(f8(a870,f882(a870,a870),a875),a331)),f333(f333(f7(f881(x44581,x44582),f882(a875,f881(x44581,x44582)),f882(a875,a870)),f333(f333(f8(f882(f881(x44581,x44582),a870),f882(f882(a875,f881(x44581,x44582)),f882(a875,a870)),f881(x44581,x44582)),f8(f881(x44581,x44582),a870,a875)),a330)),f333(f333(f18(a875,x44582,f881(x44581,x44582)),f333(f333(f8(x44581,f882(x44582,f881(x44581,x44582)),a875),f268(x44581,x44582)),f333(f166(x44581),x44583))),f333(f166(x44582),x44584)))))),f333(f333(f7(a875,a875,a870),f248(a875)),f333(f333(f245(a875),f333(f197(f876(x44581)),x44583)),f333(f197(f876(x44582)),x44584)))))),f333(f174(f881(x44581,x44582)),f333(f333(f184(x44581,x44582),x44583),x44584))) % 183.90/184.43 [4381]E(f333(f253(f881(x43811,x43812)),f333(f272(x43811,x43812,a870),f333(f333(f7(x43811,f882(x43812,a870),f882(x43812,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x43812,a870),f882(x43812,a870)),x43811),f8(a870,a870,x43812)),f333(f333(f8(a870,f882(a870,a870),x43811),a331),x43813))),x43814))),f333(f333(f270(x43811,x43812),f333(f253(x43811),x43813)),f333(f16(f882(x43812,a870),x43811),f333(f253(x43812),x43814)))) % 183.90/184.43 [4384]E(f333(f253(f881(x43841,x43842)),f333(f272(x43841,x43842,a870),f333(f333(f18(x43841,f882(x43842,a870),f882(x43842,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x43842,a870),f882(x43842,a870)),x43841),f8(a870,a870,x43842)),f333(f333(f8(a870,f882(a870,a870),x43841),a331),x43843))),x43844))),f333(f333(f270(x43841,x43842),f333(f253(x43841),x43843)),f333(f333(f8(f882(x43842,a870),f882(x43842,a870),x43841),f253(x43842)),x43844))) % 183.90/184.43 [4400]E(f333(f253(x44001),f333(f333(f8(f882(x44002,a870),a870,x44001),f87(x44002)),f333(f333(f8(f882(x44002,a870),f882(x44002,a870),x44001),f333(f18(x44002,a870,a870),f333(f333(f8(a870,f882(a870,a870),x44002),a336),f333(f333(f7(x44002,f882(x44002,a870),a870),f335(x44002)),x44003)))),x44004))),f333(f333(f42(x44002,f882(x44001,a870)),x44003),f333(f333(f8(f882(x44001,a870),f882(x44001,a870),x44002),f253(x44001)),f333(f7(x44001,x44002,a870),x44004)))) % 183.90/184.43 [4444]E(f333(f333(f155(f881(x44441,a875),x44441),f267(x44441,a875)),f333(f137(f881(x44441,a875),f333(f333(f7(f881(x44441,a875),f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),f881(x44441,a875)),f335(a875)),f271(x44441,a875))),x44442)),f333(f333(f184(x44441,a875),x44443),f140(a875,f333(f303(a875,x44444),f333(f333(f79(a875),x44444),f333(f197(f876(x44441)),x44443))))))),f333(f333(f155(f881(x44441,a875),x44441),f267(x44441,a875)),f333(f137(f881(x44441,a875),f333(f333(f7(f881(x44441,a875),f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),f881(x44441,a875)),f335(a875)),f333(f333(f7(f881(x44441,a875),a875,a875),f333(f333(f8(a875,f882(a875,a875),f881(x44441,a875)),f79(a875)),f271(x44441,a875))),x44444))),x44442)),f333(f333(f184(x44441,a875),x44443),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(x44441)),x44443))))))) % 183.90/184.43 [4445]E(f333(a115,f333(f333(f246(a875),f333(f197(f876(x44451)),x44452)),f333(f143(a875,f876(x44453),f333(f7(f876(x44453),a875,a875),f333(f333(f8(a875,f882(a875,a875),f876(x44453)),f246(a875)),f333(f333(f7(f876(x44453),a875,a875),f333(f333(f8(a875,f882(a875,a875),f876(x44453)),f22(a875)),f197(f876(x44453)))),f333(a115,f2(a875))))),f2(a875)),f333(f170(f876(x44453)),f333(f137(f876(x44453),f333(f333(f8(a870,a870,f876(x44453)),a328),f333(f333(f7(f876(x44453),f876(x44453),a870),a330),f116(x44453)))),x44454))))),f333(f333(f246(a875),f333(a115,f333(f197(f876(x44451)),x44452))),f333(f143(a875,f876(x44453),f333(f7(f876(x44453),a875,a875),f333(f333(f8(a875,f882(a875,a875),f876(x44453)),f246(a875)),f197(f876(x44453)))),f2(a875)),f333(f170(f876(x44453)),x44454)))) % 183.90/184.43 [4399]E(f333(f333(f135(x43991),f178(x43991,x43992,x43993)),f178(x43991,x43994,f333(f253(a875),f333(f333(f7(a875,f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),a875),f335(a875)),f333(f333(f7(a875,a875,a875),f79(a875)),f333(f197(f876(x43991)),x43992)))),x43993)))),f178(x43991,f333(f333(f135(x43991),x43992),x43994),x43993)) % 183.90/184.43 [4451]E(f333(f333(f152(f876(x44511)),f333(f333(f152(x44511),x44512),f333(f143(f876(x44511),f876(x44511),f135(x44511),f116(x44511)),f333(f333(f155(f876(x44511),f876(x44511)),f157(f876(x44511),x44511,f116(x44511),f333(f333(f8(f876(x44511),f882(f876(x44511),f876(x44511)),x44511),f16(f876(x44511),f876(x44511))),f333(f333(f7(x44511,f876(x44511),f876(x44511)),f152(x44511)),f116(x44511))))),x44513)))),f182(x44511,f333(f333(f152(f876(x44511)),x44514),f333(f143(f876(f876(x44511)),f876(f876(x44511)),f135(f876(x44511)),f116(f876(x44511))),f333(f333(f155(f876(x44511),f876(f876(x44511))),f157(f876(f876(x44511)),x44511,f116(f876(x44511)),f333(f16(f882(f876(x44511),f876(f876(x44511))),x44511),f333(f333(f7(f876(x44511),f876(f876(x44511)),f876(f876(x44511))),f152(f876(x44511))),f116(f876(x44511)))))),x44513))))),f182(x44511,f333(f333(f152(f876(x44511)),f333(f333(f152(x44511),x44512),x44514)),x44513))) % 183.90/184.43 [4459]E(f333(f253(f881(x44591,x44591)),f333(f272(x44591,x44591,a870),f333(f333(f7(x44591,f882(f881(x44592,x44592),a870),f882(x44591,a870)),f333(f333(f8(f882(x44591,f882(f882(f881(x44592,x44592),a870),a870)),f882(f882(f881(x44592,x44592),a870),f882(x44591,a870)),x44591),f7(x44591,f882(f881(x44592,x44592),a870),a870)),f333(f333(f8(f882(x44591,f881(x44592,x44592)),f882(x44591,f882(f882(f881(x44592,x44592),a870),a870)),x44591),f333(f8(f881(x44592,x44592),f882(f882(f881(x44592,x44592),a870),a870),x44591),f335(f881(x44592,x44592)))),f333(f333(f7(x44591,f882(x44591,x44592),f882(x44591,f881(x44592,x44592))),f333(f333(f8(f882(x44592,f881(x44592,x44592)),f882(f882(x44591,x44592),f882(x44591,f881(x44592,x44592))),x44591),f8(x44592,f881(x44592,x44592),x44591)),f333(f333(f8(x44592,f882(x44592,f881(x44592,x44592)),x44591),f268(x44592,x44592)),x44593))),x44593)))),x44594))),f333(f333(f289(x44592,x44591),x44594),x44593)) % 183.90/184.43 [4517]~E(f32(x45171,x45172),f29(x45173,x45174,x45175)) % 183.90/184.43 [4518]~E(f32(x45181,x45182),f28(x45183,x45184,x45185)) % 183.90/184.43 [4519]~E(f31(x45191,x45192),f29(x45193,x45194,x45195)) % 183.90/184.43 [4520]~E(f31(x45201,x45202),f28(x45203,x45204,x45205)) % 183.90/184.43 [4521]~E(f29(x45211,x45212,x45213),f32(x45214,x45215)) % 183.90/184.43 [4522]~E(f29(x45221,x45222,x45223),f31(x45224,x45225)) % 183.90/184.43 [4523]~E(f28(x45231,x45232,x45233),f32(x45234,x45235)) % 183.90/184.43 [4524]~E(f28(x45241,x45242,x45243),f31(x45244,x45245)) % 183.90/184.43 [3568]E(f333(f333(f155(x35681,x35682),x35683),f171(x35681,x35684,x35685)),f171(x35682,x35684,f333(x35683,x35685))) % 183.90/184.43 [3942]E(f333(f187(x39421,x39422,x39423,x39424),x39425),f333(f242(f879(x39422),x39422,f333(x39423,x39425),f240(x39422)),f333(x39424,x39425))) % 183.90/184.43 [4030]E(f187(x40301,x40302,f187(x40301,x40302,x40303,x40304),x40305),f187(x40301,x40302,x40303,f187(x40301,x40302,x40304,x40305))) % 183.90/184.43 [4206]E(f269(x42061,x42062,x42063,f257(x42062,x42061,x42064),f257(x42063,x42062,x42065)),f257(x42063,x42061,f269(x42063,x42062,x42061,x42065,x42064))) % 183.90/184.43 [4213]E(f333(f333(f113(f882(x42131,a870)),f333(f174(x42131),f333(f333(f177(x42131),f333(f197(f876(x42132)),x42133)),x42134))),f186(x42131,x42132,x42135)),f186(x42131,x42132,f189(x42131,x42132,x42135,x42134,x42133))) % 183.90/184.43 [3764]E(f333(f333(f272(x37641,x37642,x37643),x37644),x37645),f333(f333(x37644,f333(f267(x37641,x37642),x37645)),f333(f271(x37641,x37642),x37645))) % 183.90/184.43 [3791]E(f333(f242(x37911,x37912,x37913,x37914),f333(f240(x37912),x37915)),f333(x37914,x37915)) % 183.90/184.43 [3800]E(f333(f333(f333(f65(x38001,x38002,x38003),x38004),x38005),f196(f882(x38002,a870))),x38005) % 183.90/184.43 [3974]E(f243(x39741,x39742,x39743,x39744,f333(f240(x39742),x39745)),f333(x39744,x39745)) % 183.90/184.43 [4086]E(f333(f72(f879(x40861),f879(x40862),f879(x40863),f333(f210(x40861,x40862),x40864)),f333(f210(x40863,x40861),x40865)),f333(f210(x40863,x40862),f333(f72(x40861,x40862,x40863,x40864),x40865))) % 183.90/184.43 [4088]E(f333(f72(f876(x40881),f876(x40882),f876(x40883),f333(f155(x40881,x40882),x40884)),f333(f155(x40883,x40881),x40885)),f333(f155(x40883,x40882),f333(f72(x40881,x40882,x40883,x40884),x40885))) % 183.90/184.43 [4144]E(f333(f242(x41441,f881(x41442,f877(x41442)),x41443,f333(f272(x41442,f877(x41442),x41441),x41444)),f333(f136(x41442),x41445)),f131(x41441,x41442,x41443,x41444,x41445)) % 183.90/184.43 [4168]E(f84(x41681,f66(x41682,x41681,x41683,x41684,x41685)),f333(f333(f64(x41682,x41681,x41683),x41684),x41685)) % 183.90/184.43 [4204]E(f333(f333(f79(a875),f333(f333(f79(a875),f333(x42041,f333(f267(x42042,x42043),x42044))),f333(x42045,f333(f271(x42042,x42043),x42044)))),f333(a115,f2(a875))),f276(x42042,x42043,x42041,x42045,x42044)) % 183.90/184.43 [4395]E(f164(x43951,x43952,f333(f333(f7(x43951,f879(x43952),f879(x43952)),f333(f333(f18(x43951,f879(x43952),f882(f879(x43952),f879(x43952))),f333(f333(f8(a870,f882(f879(x43952),f882(f879(x43952),f879(x43952))),x43951),f99(f879(x43952))),x43953)),f333(f333(f8(x43952,f879(x43952),x43951),f240(x43952)),x43954))),f209(x43952)),x43955),f333(f333(f155(x43951,x43952),x43954),f333(f137(x43951,x43953),x43955))) % 183.90/184.43 [4560]~E(f333(f333(f333(f71(x45601,f879(x45602)),x45603),x45604),f333(f240(x45602),x45605)),f333(f16(f879(x45602),x45601),f209(x45602))) % 183.90/184.43 [3698]E(f333(f333(f177(x36981),x36982),f333(f333(f155(x36983,x36981),x36984),x36985)),f333(f333(f155(x36983,x36981),x36984),f333(f333(f177(x36983),x36982),x36985))) % 183.90/184.43 [3699]E(f333(f333(f139(x36991),x36992),f333(f333(f155(x36993,x36991),x36994),x36995)),f333(f333(f155(x36993,x36991),x36994),f333(f333(f139(x36993),x36992),x36995))) % 183.90/184.43 [3732]E(f333(f333(f155(x37321,x37322),x37323),f333(f333(f152(x37321),x37324),x37325)),f333(f333(f152(x37322),f333(x37323,x37324)),f333(f333(f155(x37321,x37322),x37323),x37325))) % 183.90/184.43 [3795]E(f333(f312(x37951,x37952,x37953),f333(f333(f311(x37951),x37954),x37955)),f333(f333(f311(x37952),f333(x37953,x37954)),f333(f312(x37951,x37952,x37953),x37955))) % 183.90/184.43 [3824]E(f175(x38241,f333(f333(f152(x38241),x38242),x38243),f333(f333(f152(x38241),x38244),x38245)),f333(f333(f152(x38241),x38242),f333(f333(f152(x38241),x38244),f175(x38241,x38243,x38245)))) % 183.90/184.43 [3861]E(f333(f333(f184(x38611,x38612),f333(f333(f177(x38611),x38613),x38614)),f333(f333(f177(x38612),x38613),x38615)),f333(f333(f177(f881(x38611,x38612)),x38613),f333(f333(f184(x38611,x38612),x38614),x38615))) % 183.90/184.43 [3862]E(f333(f333(f184(x38621,x38622),f333(f333(f139(x38621),x38623),x38624)),f333(f333(f139(x38622),x38623),x38625)),f333(f333(f139(f881(x38621,x38622)),x38623),f333(f333(f184(x38621,x38622),x38624),x38625))) % 183.90/184.43 [3874]E(f333(f333(f160(x38741,f333(f333(f152(x38741),x38742),x38743)),f333(a115,x38744)),x38745),f333(f333(f152(x38741),x38742),f333(f333(f160(x38741,x38743),x38744),x38745))) % 183.90/184.43 [3877]E(f333(f242(f879(x38771),x38772,f209(x38771),x38773),f333(f333(f16(f879(x38772),x38774),f209(x38772)),x38775)),f209(x38771)) % 183.90/184.43 [3879]E(f333(f333(f135(x38791),f333(f333(f155(x38792,x38791),x38793),x38794)),f333(f333(f155(x38792,x38791),x38793),x38795)),f333(f333(f155(x38792,x38791),x38793),f333(f333(f135(x38792),x38794),x38795))) % 183.90/184.43 [3883]E(f333(f333(x38831,x38832),f333(f333(f259(x38833,x38834,x38831),x38832),x38835)),f333(f333(f259(x38833,x38834,x38831),x38832),f333(a115,x38835))) % 183.90/184.43 [3913]E(f165(x39131,x39132,x39133,f333(f333(f152(x39131),x39134),x39135)),f333(f333(f135(x39132),f333(x39133,x39134)),f165(x39131,x39132,x39133,x39135))) % 183.90/184.43 [3926]E(f333(f333(f290(x39261,x39262,x39263),f333(f288(x39262,x39261),x39264)),f333(f288(x39263,x39262),x39265)),f333(f288(x39263,x39261),f333(f333(f290(x39263,x39262,x39261),x39265),x39264))) % 183.90/184.43 [3960]E(f333(f333(f333(f191(f876(x39601),f876(x39601)),x39602),f169(x39601)),f333(f333(f155(x39603,x39601),x39604),x39605)),f333(f333(f155(x39603,x39601),x39604),f333(f333(f333(f191(f876(x39603),f876(x39603)),x39602),f169(x39603)),x39605))) % 183.90/184.43 [3961]E(f333(f333(f274(x39611,x39612,x39611,x39613),f333(f268(x39612,x39611),x39614)),x39615),f333(x39615,x39614)) % 183.90/184.43 [3988]E(f156(x39881,x39882,f333(f333(f155(x39883,x39881),x39884),x39885)),f156(x39883,f333(f72(x39881,a875,x39883,x39882),x39884),x39885)) % 183.90/184.43 [4053]E(f333(f333(f72(f879(x40531),f879(x40532),x40533,f333(f210(x40531,x40532),x40534)),f333(f16(f879(x40531),x40533),f209(x40531))),x40535),f209(x40532)) % 183.90/184.43 [4054]E(f179(f881(x40541,x40542),f333(f72(x40542,a870,f881(x40541,x40542),x40543),f271(x40541,x40542)),f333(f333(f184(x40541,x40542),x40544),x40545)),f333(f333(f184(x40541,x40542),x40544),f179(x40542,x40543,x40545))) % 183.90/184.43 [4060]E(f333(f312(x40601,x40602,f333(f333(f8(x40603,x40602,x40601),x40604),x40605)),f256(f882(x40601,a870))),f333(f312(x40603,x40602,x40604),f333(f312(x40601,x40603,x40605),f256(f882(x40601,a870))))) % 183.90/184.43 [4073]E(f179(f881(x40731,x40732),f333(f72(x40731,a870,f881(x40731,x40732),x40733),f267(x40731,x40732)),f333(f333(f184(x40731,x40732),x40734),x40735)),f333(f333(f184(x40731,x40732),f179(x40731,x40733,x40734)),x40735)) % 183.90/184.43 [4092]E(f333(f333(f113(f882(x40921,a870)),f333(f313(x40921,x40922,x40923),f333(f333(f311(x40922),x40924),f196(f882(x40922,a870))))),f333(f313(x40921,x40922,x40923),x40925)),f333(f313(x40921,x40922,x40923),f333(f333(f311(x40922),x40924),x40925))) % 183.90/184.43 [4152]E(f333(f333(f135(f881(x41521,x41522)),f333(f333(f155(x41522,f881(x41521,x41522)),f333(f268(x41521,x41522),x41523)),x41524)),f59(x41521,x41522,x41525,x41524)),f59(x41521,x41522,f333(f333(f152(x41521),x41523),x41525),x41524)) % 183.90/184.43 [4153]E(f333(f333(f155(x41531,x41532),x41533),f179(x41531,f333(f72(x41532,a870,x41531,x41534),x41533),x41535)),f179(x41532,x41534,f333(f333(f155(x41531,x41532),x41533),x41535))) % 183.90/184.43 [4159]E(f333(f143(x41591,x41592,f333(f7(x41592,x41591,x41591),f333(f7(x41591,x41592,x41591),x41593)),x41594),f333(f170(x41592),f333(f170(x41592),x41595))),f333(f143(x41591,x41592,x41593,x41594),x41595)) % 183.90/184.43 [4160]E(f333(f333(f333(f71(x41601,f879(x41602)),f190(x41601,x41602,x41603,x41604)),x41605),f333(x41603,x41605)),f190(x41601,x41602,x41603,f333(f333(f311(x41601),x41605),x41604))) % 183.90/184.43 [4230]E(f333(f242(f876(x42301),x42301,f164(x42302,x42301,x42303,x42304),f333(f333(f7(x42301,f876(x42301),f876(x42301)),f152(x42301)),f164(x42302,x42301,x42303,x42304))),f333(x42303,x42305)),f164(x42302,x42301,x42303,f333(f333(f152(x42302),x42305),x42304))) % 183.90/184.43 [4267]P1(f333(f333(f247(f882(x42671,a870)),f333(f312(x42672,x42671,x42673),f333(f333(f104(f882(x42672,a870)),x42674),x42675))),f333(f333(f104(f882(x42671,a870)),f333(f312(x42672,x42671,x42673),x42674)),f333(f312(x42672,x42671,x42673),x42675)))) % 183.90/184.43 [4268]P1(f333(f333(f247(f882(x42681,a870)),f333(f287(x42682,x42681,x42683),f333(f333(f104(f882(x42682,a870)),x42684),x42685))),f333(f333(f104(f882(x42681,a870)),f333(f287(x42682,x42681,x42683),x42684)),f333(f287(x42682,x42681,x42683),x42685)))) % 183.90/184.43 [4369]E(f333(f271(x43691,x43692),f333(f273(x43693,x43691,x43692,x43692,x43694,f33(x43692)),x43695)),f333(f271(x43693,x43692),x43695)) % 183.90/184.43 [4370]E(f333(f267(x43701,x43702),f333(f273(x43701,x43701,x43703,x43702,f33(x43701),x43704),x43705)),f333(f267(x43701,x43703),x43705)) % 183.90/184.43 [4455]E(f333(f143(f882(x44551,f879(x44552)),f881(x44551,x44552),f333(f333(f8(f882(x44551,f882(x44552,f882(x44551,f879(x44552)))),f882(f881(x44551,x44552),f882(x44551,f879(x44552))),f882(x44551,f879(x44552))),f272(x44551,x44552,f882(x44551,f879(x44552)))),f333(f333(f7(f882(x44551,f879(x44552)),f882(x44552,f879(x44552)),f882(x44551,f882(x44552,f882(x44551,f879(x44552))))),f333(f333(f8(f882(x44551,f882(f882(x44552,f879(x44552)),f882(x44552,f882(x44551,f879(x44552))))),f882(f882(x44552,f879(x44552)),f882(x44551,f882(x44552,f882(x44551,f879(x44552))))),f882(x44551,f879(x44552))),f7(x44551,f882(x44552,f879(x44552)),f882(x44552,f882(x44551,f879(x44552))))),f333(f333(f8(f882(x44551,f882(f879(x44552),f882(x44551,f879(x44552)))),f882(x44551,f882(f882(x44552,f879(x44552)),f882(x44552,f882(x44551,f879(x44552))))),f882(x44551,f879(x44552))),f333(f8(f882(f879(x44552),f882(x44551,f879(x44552))),f882(f882(x44552,f879(x44552)),f882(x44552,f882(x44551,f879(x44552)))),x44551),f8(f879(x44552),f882(x44551,f879(x44552)),x44552))),f71(x44551,f879(x44552))))),f240(x44552))),x44553),f333(f333(f184(x44551,x44552),x44554),x44555)),f189(x44551,x44552,x44553,x44554,x44555)) % 183.90/184.43 [4457]P24(x44571,x44572,f333(f333(f311(f874(x44571)),f333(f333(f333(f91(x44571),f333(f333(f7(x44571,f882(a872,a870),f882(a872,a870)),f333(f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x44571),f18(a872,a870,a870)),f333(f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x44571),f333(f8(a870,f882(a870,a870),a872),a331)),x44573))),f333(f333(f8(a870,a870,a872),a328),x44574))),f31(x44574,x44575)),x44573)),f196(f882(f874(x44571),a870)))) % 183.90/184.43 [3537]E(f333(f333(f333(f333(f216(x35371),x35372),x35373),x35374),x35375),f200(x35371,x35372)) % 183.90/184.43 [3538]E(f333(f333(f333(f333(f220(x35381),x35382),x35383),x35384),x35385),f211(x35381,x35382)) % 183.90/184.43 [3584]E(f96(x35841,x35842,f333(f333(f333(f91(x35841),x35843),x35844),x35845)),f2(a875)) % 183.90/184.43 [3682]E(f333(f333(f333(f333(f71(x36821,x36822),x36823),x36824),x36825),x36824),x36825) % 183.90/184.43 [3914]E(f333(f333(f41(x39141,f882(x39142,a870)),f333(f333(f311(x39141),x39143),x39144)),x39145),f333(f333(f113(f882(x39142,a870)),f333(x39145,x39143)),f333(f333(f41(x39141,f882(x39142,a870)),x39144),x39145))) % 183.90/184.43 [3915]E(f333(f333(f42(x39151,f882(x39152,a870)),f333(f333(f311(x39151),x39153),x39154)),x39155),f333(f333(f104(f882(x39152,a870)),f333(x39155,x39153)),f333(f333(f42(x39151,f882(x39152,a870)),x39154),x39155))) % 183.90/184.43 [3967]E(f333(f121(x39671,x39672,f333(x39673,x39674)),f333(f333(f7(x39671,a102,f877(x39672)),x39675),x39674)),f333(f207(x39671,x39672,x39673,x39675),x39674)) % 183.90/184.43 [3981]E(f333(f333(f113(f882(x39811,a870)),f333(f312(x39812,x39811,x39813),x39814)),f333(f312(x39812,x39811,x39813),x39815)),f333(f312(x39812,x39811,x39813),f333(f333(f113(f882(x39812,a870)),x39814),x39815))) % 183.90/184.43 [3982]E(f333(f333(f113(f882(x39821,a870)),f333(f313(x39821,x39822,x39823),x39824)),f333(f313(x39821,x39822,x39823),x39825)),f333(f313(x39821,x39822,x39823),f333(f333(f113(f882(x39822,a870)),x39824),x39825))) % 183.90/184.43 [3983]E(f333(f333(f22(f882(x39831,a870)),f333(f313(x39831,x39832,x39833),x39834)),f333(f313(x39831,x39832,x39833),x39835)),f333(f313(x39831,x39832,x39833),f333(f333(f22(f882(x39832,a870)),x39834),x39835))) % 183.90/184.43 [3984]E(f333(f333(f104(f882(x39841,a870)),f333(f313(x39841,x39842,x39843),x39844)),f333(f313(x39841,x39842,x39843),x39845)),f333(f313(x39841,x39842,x39843),f333(f333(f104(f882(x39842,a870)),x39844),x39845))) % 183.90/184.43 [3985]E(f333(f333(f113(f882(x39851,a870)),f333(f287(x39852,x39851,x39853),x39854)),f333(f287(x39852,x39851,x39853),x39855)),f333(f287(x39852,x39851,x39853),f333(f333(f113(f882(x39852,a870)),x39854),x39855))) % 183.90/184.43 [3987]E(f190(x39871,x39872,f190(x39871,x39872,x39873,x39874),x39875),f190(x39871,x39872,x39873,f333(f333(f104(f882(x39871,a870)),x39874),x39875))) % 183.90/184.43 [4049]E(f333(f333(f160(x40491,f333(f333(f135(x40491),x40492),f333(f333(f152(x40491),x40493),x40494))),f333(f197(f876(x40491)),x40492)),x40495),f333(f333(f135(x40491),x40492),f333(f333(f152(x40491),x40495),x40494))) % 183.90/184.43 [4057]E(f333(f333(f42(x40571,f882(x40572,a870)),x40573),f333(f333(f8(f882(x40572,a870),f882(x40572,a870),x40571),f333(f311(x40572),x40574)),x40575)),f333(f333(f311(x40572),x40574),f333(f333(f42(x40571,f882(x40572,a870)),x40573),x40575))) % 183.90/184.43 [4126]E(f190(x41261,x41262,f333(f333(f333(f71(x41261,f879(x41262)),x41263),x41264),f333(f240(x41262),x41265)),f333(f78(f882(x41261,a870)),f333(f333(f311(x41261),x41264),f196(f882(x41261,a870))))),f190(x41261,x41262,x41263,f333(f78(f882(x41261,a870)),f333(f333(f311(x41261),x41264),f196(f882(x41261,a870)))))) % 183.90/184.43 [4217]E(f333(f333(f155(x42171,x42172),x42173),f333(f137(x42171,f333(f72(x42172,a870,x42171,x42174),x42173)),x42175)),f333(f137(x42172,x42174),f333(f333(f155(x42171,x42172),x42173),x42175))) % 183.90/184.43 [4223]E(f333(f197(f876(x42231)),f333(f137(x42231,x42232),f333(f333(f155(x42233,x42231),x42234),x42235))),f333(f197(f876(x42233)),f333(f137(x42233,f333(f72(x42231,a870,x42233,x42232),x42234)),x42235))) % 183.90/184.43 [4361]E(f333(f333(f113(f882(x43611,a870)),f333(f333(f22(f882(x43611,a870)),f186(x43611,x43612,x43613)),f333(f253(x43611),f333(f333(f7(x43611,f882(x43611,a870),a870),f335(x43611)),f333(f333(f22(f882(x43611,a870)),x43614),f186(x43611,x43612,x43615)))))),f333(f253(x43611),f333(f333(f7(x43611,f882(x43611,a870),a870),f335(x43611)),f333(f333(f104(f882(x43611,a870)),x43614),f186(x43611,x43612,x43615))))),f186(x43611,x43612,f75(x43611,f879(x43612),x43613,x43615,x43614))) % 183.90/184.43 [4436]E(f333(f157(f876(f881(x44361,x44362)),x44362,f116(f881(x44361,x44362)),f333(f333(f7(x44362,f882(f876(x44362),f876(f881(x44361,x44362))),f882(f876(x44362),f876(f881(x44361,x44362)))),f333(f333(f8(f882(f876(f881(x44361,x44362)),f876(f881(x44361,x44362))),f882(f882(f876(x44362),f876(f881(x44361,x44362))),f882(f876(x44362),f876(f881(x44361,x44362)))),x44362),f8(f876(f881(x44361,x44362)),f876(f881(x44361,x44362)),f876(x44362))),f333(f333(f8(f881(x44361,x44362),f882(f876(f881(x44361,x44362)),f876(f881(x44361,x44362))),x44362),f152(f881(x44361,x44362))),f333(f268(x44361,x44362),x44363)))),f333(f184(x44361,x44362),x44364))),x44365),f333(f333(f184(x44361,x44362),f333(f333(f152(x44361),x44363),x44364)),x44365)) % 183.90/184.43 [3908]E(f333(f333(f160(x39081,f333(f333(f160(x39081,x39082),x39083),x39084)),x39083),x39085),f333(f333(f160(x39081,x39082),x39083),x39085)) % 183.90/184.43 [3962]E(f333(f264(x39621,x39622),f333(f333(f311(f881(x39621,x39622)),f333(f333(f268(x39621,x39622),x39623),x39624)),x39625)),f333(f333(f311(x39622),x39624),f333(f264(x39621,x39622),x39625))) % 183.90/184.43 [3963]E(f333(f266(x39631,x39632),f333(f333(f311(f881(x39631,x39632)),f333(f333(f268(x39631,x39632),x39633),x39634)),x39635)),f333(f333(f311(x39631),x39633),f333(f266(x39631,x39632),x39635))) % 183.90/184.43 [4012]E(f123(x40121,x40122,f333(x40123,x40124),f333(f333(f7(x40121,a102,f877(f879(x40122))),x40125),x40124)),f333(f205(x40121,x40122,x40123,x40125),x40124)) % 183.90/184.43 [4042]E(f333(f333(f113(f882(f881(x40421,x40422),a870)),f333(f333(f270(x40421,x40422),x40423),x40424)),f333(f333(f270(x40421,x40422),x40425),x40424)),f333(f333(f270(x40421,x40422),f333(f333(f113(f882(x40421,a870)),x40423),x40425)),x40424)) % 183.90/184.43 [4043]E(f333(f333(f22(f882(f881(x40431,x40432),a870)),f333(f333(f270(x40431,x40432),x40433),x40434)),f333(f333(f270(x40431,x40432),x40435),x40434)),f333(f333(f270(x40431,x40432),f333(f333(f22(f882(x40431,a870)),x40433),x40435)),x40434)) % 183.90/184.43 [4044]E(f333(f333(f104(f882(f881(x40441,x40442),a870)),f333(f333(f270(x40441,x40442),x40443),x40444)),f333(f333(f270(x40441,x40442),x40445),x40444)),f333(f333(f270(x40441,x40442),f333(f333(f104(f882(x40441,a870)),x40443),x40445)),x40444)) % 183.90/184.43 [4104]E(f333(f333(f113(f882(x41041,a870)),f333(f333(f41(x41042,f882(x41041,a870)),x41043),x41044)),f333(f333(f41(x41042,f882(x41041,a870)),x41045),x41044)),f333(f333(f41(x41042,f882(x41041,a870)),f333(f333(f113(f882(x41042,a870)),x41043),x41045)),x41044)) % 183.90/184.43 [4105]E(f333(f333(f104(f882(x41051,a870)),f333(f333(f42(x41052,f882(x41051,a870)),x41053),x41054)),f333(f333(f42(x41052,f882(x41051,a870)),x41055),x41054)),f333(f333(f42(x41052,f882(x41051,a870)),f333(f333(f113(f882(x41052,a870)),x41053),x41055)),x41054)) % 183.90/184.43 [4119]E(f333(f333(f41(x41191,f882(x41192,a870)),x41193),f333(f333(f8(f882(x41192,a870),f882(x41192,a870),x41191),f333(f22(f882(x41192,a870)),x41194)),x41195)),f333(f333(f22(f882(x41192,a870)),x41194),f333(f333(f42(x41191,f882(x41192,a870)),x41193),x41195))) % 183.90/184.43 [4120]E(f333(f333(f41(x41201,f882(x41202,a870)),x41203),f333(f333(f8(f882(x41202,a870),f882(x41202,a870),x41201),f333(f104(f882(x41202,a870)),x41204)),x41205)),f333(f333(f104(f882(x41202,a870)),x41204),f333(f333(f41(x41201,f882(x41202,a870)),x41203),x41205))) % 183.90/184.43 [4121]E(f333(f333(f42(x41211,f882(x41212,a870)),x41213),f333(f333(f8(f882(x41212,a870),f882(x41212,a870),x41211),f333(f113(f882(x41212,a870)),x41214)),x41215)),f333(f333(f113(f882(x41212,a870)),x41214),f333(f333(f42(x41211,f882(x41212,a870)),x41213),x41215))) % 183.90/184.43 [4158]E(f187(x41581,x41582,x41583,f333(f180(x41581,x41582),f333(f170(f881(x41581,x41582)),f333(f333(f184(x41581,x41582),x41584),x41585)))),f189(x41581,x41582,x41583,x41584,x41585)) % 183.90/184.43 [4180]E(f193(f876(x41801),f333(f333(f152(x41801),x41802),x41803),f333(f333(f8(f876(x41801),f876(x41801),a875),f333(f152(x41801),x41804)),f333(f333(f7(a875,x41801,f876(x41801)),f160(x41801,x41803)),x41802)),x41805),f333(f333(f160(x41801,f333(f333(f152(x41801),x41804),x41803)),x41805),x41802)) % 183.90/184.43 [4184]E(f333(f333(f41(x41841,f882(f881(x41842,x41843),a870)),x41844),f333(f333(f8(f882(f881(x41843,x41842),a870),f882(f881(x41842,x41843),a870),x41841),f288(x41843,x41842)),x41845)),f333(f288(x41843,x41842),f333(f333(f41(x41841,f882(f881(x41843,x41842),a870)),x41844),x41845))) % 183.90/184.43 [4185]E(f333(f333(f42(x41851,f882(f881(x41852,x41853),a870)),x41854),f333(f333(f8(f882(f881(x41853,x41852),a870),f882(f881(x41852,x41853),a870),x41851),f288(x41853,x41852)),x41855)),f333(f288(x41853,x41852),f333(f333(f42(x41851,f882(f881(x41853,x41852),a870)),x41854),x41855))) % 183.90/184.43 [4241]E(f186(x42411,x42412,f333(f333(f18(x42411,f879(x42413),f879(x42412)),f333(f333(f8(f882(x42413,x42412),f882(f879(x42413),f879(x42412)),x42411),f210(x42413,x42412)),x42414)),x42415)),f186(x42411,x42413,x42415)) % 183.90/184.43 [4292]P1(f333(f333(f247(f882(x42921,a870)),f333(f333(f22(f882(x42921,a870)),f333(f312(x42922,x42921,x42923),x42924)),f333(f312(x42922,x42921,x42923),x42925))),f333(f312(x42922,x42921,x42923),f333(f333(f22(f882(x42922,a870)),x42924),x42925)))) % 183.90/184.43 [4440]E(f333(f157(f876(f881(x44401,x44402)),x44401,f116(f881(x44401,x44402)),f333(f333(f7(x44401,f882(f876(x44401),f876(f881(x44401,x44402))),f882(f876(x44401),f876(f881(x44401,x44402)))),f333(f333(f8(f882(f876(f881(x44401,x44402)),f876(f881(x44401,x44402))),f882(f882(f876(x44401),f876(f881(x44401,x44402))),f882(f876(x44401),f876(f881(x44401,x44402)))),x44401),f8(f876(f881(x44401,x44402)),f876(f881(x44401,x44402)),f876(x44401))),f333(f333(f8(f881(x44401,x44402),f882(f876(f881(x44401,x44402)),f876(f881(x44401,x44402))),x44401),f152(f881(x44401,x44402))),f333(f333(f7(x44401,x44402,f881(x44401,x44402)),f268(x44401,x44402)),x44403)))),f333(f333(f7(f876(x44401),f876(x44402),f876(f881(x44401,x44402))),f184(x44401,x44402)),x44404))),x44405),f333(f333(f184(x44401,x44402),x44405),f333(f333(f152(x44402),x44403),x44404))) % 183.90/184.43 [4146]E(f333(f333(f113(f882(x41461,a870)),f333(f287(x41462,x41461,x41463),x41464)),f333(f287(x41462,x41461,x41465),x41464)),f333(f287(x41462,x41461,f333(f333(f113(f882(f881(x41462,x41461),a870)),x41463),x41465)),x41464)) % 183.90/184.43 [4187]E(f333(f333(f135(f881(x41871,x41872)),f333(f333(f184(x41871,x41872),x41873),f333(f333(f177(x41872),f333(f197(f876(x41871)),x41873)),x41874))),f333(f333(f184(x41871,x41872),x41875),f333(f333(f139(x41872),f333(f197(f876(x41871)),x41873)),x41874))),f333(f333(f184(x41871,x41872),f333(f333(f135(x41871),x41873),x41875)),x41874)) % 183.90/184.43 [4295]E(f333(f333(f270(x42951,x42952),x42953),f333(f333(f18(x42951,f882(x42952,a870),f882(x42952,a870)),f333(f333(f8(f882(x42952,a870),f882(f882(x42952,a870),f882(x42952,a870)),x42951),f113(f882(x42952,a870))),x42954)),x42955)),f333(f333(f113(f882(f881(x42951,x42952),a870)),f333(f333(f270(x42951,x42952),x42953),x42954)),f333(f333(f270(x42951,x42952),x42953),x42955))) % 183.90/184.43 [4296]E(f333(f333(f270(x42961,x42962),x42963),f333(f333(f18(x42961,f882(x42962,a870),f882(x42962,a870)),f333(f333(f8(f882(x42962,a870),f882(f882(x42962,a870),f882(x42962,a870)),x42961),f22(f882(x42962,a870))),x42964)),x42965)),f333(f333(f22(f882(f881(x42961,x42962),a870)),f333(f333(f270(x42961,x42962),x42963),x42964)),f333(f333(f270(x42961,x42962),x42963),x42965))) % 183.90/184.43 [4297]E(f333(f333(f270(x42971,x42972),x42973),f333(f333(f18(x42971,f882(x42972,a870),f882(x42972,a870)),f333(f333(f8(f882(x42972,a870),f882(f882(x42972,a870),f882(x42972,a870)),x42971),f104(f882(x42972,a870))),x42974)),x42975)),f333(f333(f104(f882(f881(x42971,x42972),a870)),f333(f333(f270(x42971,x42972),x42973),x42974)),f333(f333(f270(x42971,x42972),x42973),x42975))) % 183.90/184.43 [4301]E(f333(f333(f41(x43011,f882(x43012,a870)),x43013),f333(f333(f7(x43011,f882(x43012,a870),f882(x43012,a870)),f333(f333(f8(f882(x43012,a870),f882(f882(x43012,a870),f882(x43012,a870)),x43011),f22(f882(x43012,a870))),x43014)),x43015)),f333(f333(f22(f882(x43012,a870)),f333(f333(f41(x43011,f882(x43012,a870)),x43013),x43014)),x43015)) % 183.90/184.43 [4302]E(f333(f333(f41(x43021,f882(x43022,a870)),x43023),f333(f333(f7(x43021,f882(x43022,a870),f882(x43022,a870)),f333(f333(f8(f882(x43022,a870),f882(f882(x43022,a870),f882(x43022,a870)),x43021),f104(f882(x43022,a870))),x43024)),x43025)),f333(f333(f104(f882(x43022,a870)),f333(f333(f41(x43021,f882(x43022,a870)),x43023),x43024)),x43025)) % 183.90/184.43 [4303]E(f333(f333(f42(x43031,f882(x43032,a870)),x43033),f333(f333(f7(x43031,f882(x43032,a870),f882(x43032,a870)),f333(f333(f8(f882(x43032,a870),f882(f882(x43032,a870),f882(x43032,a870)),x43031),f113(f882(x43032,a870))),x43034)),x43035)),f333(f333(f113(f882(x43032,a870)),f333(f333(f42(x43031,f882(x43032,a870)),x43033),x43034)),x43035)) % 183.90/184.43 [4307]E(f333(f333(f41(x43071,f882(x43072,a870)),x43073),f333(f333(f18(x43071,f882(x43072,a870),f882(x43072,a870)),f333(f333(f8(f882(x43072,a870),f882(f882(x43072,a870),f882(x43072,a870)),x43071),f113(f882(x43072,a870))),x43074)),x43075)),f333(f333(f113(f882(x43072,a870)),f333(f333(f41(x43071,f882(x43072,a870)),x43073),x43074)),f333(f333(f41(x43071,f882(x43072,a870)),x43073),x43075))) % 183.90/184.43 [4308]E(f333(f333(f42(x43081,f882(x43082,a870)),x43083),f333(f333(f18(x43081,f882(x43082,a870),f882(x43082,a870)),f333(f333(f8(f882(x43082,a870),f882(f882(x43082,a870),f882(x43082,a870)),x43081),f104(f882(x43082,a870))),x43084)),x43085)),f333(f333(f104(f882(x43082,a870)),f333(f333(f42(x43081,f882(x43082,a870)),x43083),x43084)),f333(f333(f42(x43081,f882(x43082,a870)),x43083),x43085))) % 183.90/184.43 [4322]E(f333(f333(f41(x43221,f882(x43222,a870)),x43223),f333(f333(f18(x43221,f882(x43222,a870),f882(x43222,a870)),f333(f333(f8(f882(x43222,a870),f882(f882(x43222,a870),f882(x43222,a870)),x43221),f113(f882(x43222,a870))),x43224)),x43225)),f333(f333(f113(f882(x43222,a870)),f39(f882(x43222,a870),f333(f312(x43221,f882(x43222,a870),x43224),x43223))),f39(f882(x43222,a870),f333(f312(x43221,f882(x43222,a870),x43225),x43223)))) % 183.90/184.43 [4323]E(f333(f333(f42(x43231,f882(x43232,a870)),x43233),f333(f333(f18(x43231,f882(x43232,a870),f882(x43232,a870)),f333(f333(f8(f882(x43232,a870),f882(f882(x43232,a870),f882(x43232,a870)),x43231),f104(f882(x43232,a870))),x43234)),x43235)),f333(f333(f104(f882(x43232,a870)),f40(f882(x43232,a870),f333(f312(x43231,f882(x43232,a870),x43234),x43233))),f40(f882(x43232,a870),f333(f312(x43231,f882(x43232,a870),x43235),x43233)))) % 183.90/184.43 [4357]E(f333(f333(f139(x43571),f333(f197(f876(x43571)),f179(x43571,x43572,f333(f333(f155(x43573,x43571),x43574),x43575)))),f333(f333(f155(x43573,x43571),x43574),x43575)),f333(f333(f155(x43573,x43571),x43574),f333(f333(f139(x43573),f333(f197(f876(x43573)),f179(x43573,f333(f72(x43571,a870,x43573,x43572),x43574),x43575))),x43575))) % 183.90/184.43 [4231]E(f333(f333(f135(f881(x42311,x42312)),f333(f333(f184(x42311,x42312),f333(f333(f177(x42311),f333(f197(f876(x42312)),x42313)),x42314)),x42313)),f333(f333(f184(x42311,x42312),f333(f333(f139(x42311),f333(f197(f876(x42312)),x42313)),x42314)),x42315)),f333(f333(f184(x42311,x42312),x42314),f333(f333(f135(x42312),x42313),x42315))) % 183.90/184.43 [4349]E(f84(x43491,f333(f333(f18(x43491,a870,a870),f333(f333(f8(a870,f882(a870,a870),x43491),a331),f333(f333(f7(x43491,f882(x43491,a870),a870),f335(x43491)),x43492))),f333(f333(f7(x43491,x43493,a870),f333(f333(f8(x43493,f882(x43493,a870),x43491),a330),x43494)),x43495))),f333(f76(x43491,x43493,x43492,x43494),x43495)) % 183.90/184.43 [4401]E(f333(f333(f85(a1,x44011),f333(f106(a1),f333(f333(f79(a1),x44012),a100))),f333(f333(f18(a1,x44011,x44011),f333(f333(f7(a1,x44011,f882(x44011,x44011)),f333(f333(f8(a870,f882(x44011,f882(x44011,x44011)),a1),f99(x44011)),a201)),f193(x44011,x44013,x44014,x44015))),f333(f333(f8(a875,x44011,a1),x44014),f333(f333(f7(a1,a875,a875),f333(f333(f8(a875,f882(a875,a875),a1),f79(a875)),a107)),x44015)))),f193(x44011,x44013,x44014,f333(f333(f79(a875),f333(f106(a875),x44012)),x44015))) % 183.90/184.43 [4437]E(f333(f180(x44371,x44372),f333(f333(f155(f881(x44371,x44373),f881(x44371,x44372)),f333(f272(x44371,x44373,f881(x44371,x44372)),f333(f333(f7(x44371,f882(x44373,x44372),f882(x44373,f881(x44371,x44372))),f333(f333(f8(f882(x44372,f881(x44371,x44372)),f882(f882(x44373,x44372),f882(x44373,f881(x44371,x44372))),x44371),f8(x44372,f881(x44371,x44372),x44373)),f268(x44371,x44372))),x44374))),x44375)),f333(f72(f879(x44373),f879(x44372),x44371,f333(f210(x44373,x44372),x44374)),f333(f180(x44371,x44373),x44375))) % 183.90/184.43 [4394]E(f186(x43941,x43942,f333(f333(f18(x43941,f879(x43942),f879(x43942)),f333(f333(f18(x43941,f879(x43942),f882(f879(x43942),f879(x43942))),f333(f333(f8(a870,f882(f879(x43942),f882(f879(x43942),f879(x43942))),x43941),f99(f879(x43942))),x43943)),x43944)),x43945)),f333(f333(f113(f882(x43941,a870)),f333(f333(f104(f882(x43941,a870)),f186(x43941,x43942,x43944)),f333(f253(x43941),x43943))),f333(f333(f104(f882(x43941,a870)),f186(x43941,x43942,x43945)),f333(f253(x43941),f333(f333(f8(a870,a870,x43941),a328),x43943))))) % 183.90/184.43 [4435]E(f333(f333(f85(a1,x44351),f333(f106(a1),f333(f333(f79(a1),x44352),a100))),f333(f333(f18(a1,x44351,x44351),f333(f333(f7(a1,x44351,f882(x44351,x44351)),f333(f333(f8(a870,f882(x44351,f882(x44351,x44351)),a1),f99(x44351)),a201)),f333(f192(x44351,x44353,x44354),x44355))),f333(f333(f18(a1,x44351,x44351),f333(f333(f8(a875,f882(x44351,x44351),a1),x44354),f333(f333(f7(a1,a875,a875),f333(f333(f8(a875,f882(a875,a875),a1),f79(a875)),a107)),x44355))),f333(f333(f8(a875,x44351,a1),f192(x44351,x44353,x44354)),f333(f333(f7(a1,a875,a875),f333(f333(f8(a875,f882(a875,a875),a1),f79(a875)),a107)),x44355))))),f333(f192(x44351,x44353,x44354),f333(f333(f79(a875),f333(f106(a875),x44352)),x44355))) % 183.90/184.43 [4469]E(f333(f253(f881(x44691,x44692)),f333(f272(x44691,x44692,a870),f333(f333(f8(f882(x44692,f882(x44693,a870)),f882(x44692,a870),x44691),f333(f8(f882(x44693,a870),a870,x44692),f86(x44693))),f333(f333(f7(x44691,f882(x44692,f882(x44693,a870)),f882(x44692,f882(x44693,a870))),f333(f333(f8(f882(f882(x44693,a870),f882(x44693,a870)),f882(f882(x44692,f882(x44693,a870)),f882(x44692,f882(x44693,a870))),x44691),f8(f882(x44693,a870),f882(x44693,a870),x44692)),f333(f333(f8(f882(x44693,f882(a870,a870)),f882(f882(x44693,a870),f882(x44693,a870)),x44691),f18(x44693,a870,a870)),f333(f333(f8(f882(x44693,a870),f882(x44693,f882(a870,a870)),x44691),f333(f8(a870,f882(a870,a870),x44693),a331)),f333(f333(f7(x44691,f882(f881(x44691,x44693),a870),f882(x44693,a870)),f333(f333(f8(f882(x44693,f882(f882(f881(x44691,x44693),a870),a870)),f882(f882(f881(x44691,x44693),a870),f882(x44693,a870)),x44691),f7(x44693,f882(f881(x44691,x44693),a870),a870)),f333(f333(f8(f882(x44693,f881(x44691,x44693)),f882(x44693,f882(f882(f881(x44691,x44693),a870),a870)),x44691),f333(f8(f881(x44691,x44693),f882(f882(f881(x44691,x44693),a870),a870),x44693),f335(f881(x44691,x44693)))),f268(x44691,x44693)))),x44694))))),f333(f333(f7(x44692,f882(f881(x44693,x44692),a870),f882(x44693,a870)),f333(f333(f8(f882(x44693,f882(f882(f881(x44693,x44692),a870),a870)),f882(f882(f881(x44693,x44692),a870),f882(x44693,a870)),x44692),f7(x44693,f882(f881(x44693,x44692),a870),a870)),f333(f333(f8(f882(x44693,f881(x44693,x44692)),f882(x44693,f882(f882(f881(x44693,x44692),a870),a870)),x44692),f333(f8(f881(x44693,x44692),f882(f882(f881(x44693,x44692),a870),a870),x44693),f335(f881(x44693,x44692)))),f333(f7(x44693,x44692,f881(x44693,x44692)),f268(x44693,x44692))))),x44695))))),f333(f333(f290(x44691,x44693,x44692),x44694),x44695)) % 183.90/184.43 [4545]~E(f28(x45451,x45452,x45453),f29(x45454,x45455,x45456)) % 183.90/184.43 [3997]E(f131(x39971,x39972,x39973,x39974,f128(x39972,x39975,x39976)),f333(f333(x39974,x39975),x39976)) % 183.90/184.43 [4215]E(f189(x42151,x42152,f187(x42151,x42152,x42153,x42154),x42155,x42156),f187(x42151,x42152,x42153,f189(x42151,x42152,x42154,x42155,x42156))) % 183.90/184.43 [4338]E(f333(f72(f881(x43381,x43382),x43382,f881(x43383,x43384),f271(x43381,x43382)),f273(x43383,x43381,x43384,x43382,x43385,x43386)),f333(f72(x43384,x43382,f881(x43383,x43384),x43386),f271(x43383,x43384))) % 183.90/184.43 [4339]E(f333(f72(f881(x43391,x43392),x43391,f881(x43393,x43394),f267(x43391,x43392)),f273(x43393,x43391,x43394,x43392,x43395,x43396)),f333(f72(x43393,x43391,f881(x43393,x43394),x43395),f267(x43393,x43394))) % 183.90/184.43 [3937]E(f333(f333(f72(x39371,x39372,x39373,x39374),x39375),x39376),f333(x39374,f333(x39375,x39376))) % 183.90/184.43 [3730]E(f333(f333(f272(x37301,x37302,x37303),x37304),f333(f333(f268(x37301,x37302),x37305),x37306)),f333(f333(x37304,x37305),x37306)) % 183.90/184.43 [3792]E(f333(f333(f333(f8(x37921,x37922,x37923),x37924),x37925),x37926),f333(x37924,f333(x37925,x37926))) % 183.90/184.43 [3793]E(f333(f333(f333(f7(x37931,x37932,x37933),x37934),x37935),x37936),f333(f333(x37934,x37936),x37935)) % 183.90/184.43 [3810]E(f333(f333(f333(f18(x38101,x38102,x38103),x38104),x38105),x38106),f333(f333(x38104,x38106),f333(x38105,x38106))) % 183.90/184.43 [3832]E(f333(f157(x38321,x38322,x38323,x38324),f333(f333(f152(x38322),x38325),x38326)),f333(f333(x38324,x38325),x38326)) % 183.90/184.43 [3873]E(f171(f881(x38731,x38732),f333(f333(f245(a875),x38733),x38734),f333(f333(f268(x38731,x38732),x38735),x38736)),f333(f333(f184(x38731,x38732),f171(x38731,x38733,x38735)),f171(x38732,x38734,x38736))) % 183.90/184.43 [3941]E(f333(f333(f152(f881(x39411,x39412)),f333(f333(f268(x39411,x39412),x39413),x39414)),f333(f333(f184(x39411,x39412),x39415),x39416)),f333(f333(f184(x39411,x39412),f333(f333(f152(x39411),x39413),x39415)),f333(f333(f152(x39412),x39414),x39416))) % 183.90/184.43 [3943]E(f333(f333(f155(x39431,x39432),x39433),f333(f333(f160(x39431,x39434),x39435),x39436)),f333(f333(f160(x39432,f333(f333(f155(x39431,x39432),x39433),x39434)),x39435),f333(x39433,x39436))) % 183.90/184.43 [3986]E(f333(f143(x39861,x39862,x39863,x39864),f333(f333(f152(x39862),x39865),x39866)),f333(f143(x39861,x39862,x39863,f333(f333(x39863,x39864),x39865)),x39866)) % 183.90/184.43 [4013]E(f275(x40131,x40132,x40133,x40134,f333(f333(f268(x40131,x40132),x40135),x40136)),f333(f333(x40134,x40135),x40136)) % 183.90/184.43 [4097]E(f333(f333(f41(x40971,f882(x40972,a870)),x40973),f333(f72(x40974,f882(x40972,a870),x40971,x40975),x40976)),f333(f333(f41(x40974,f882(x40972,a870)),f333(f312(x40971,x40974,x40976),x40973)),x40975)) % 183.90/184.43 [4149]E(f333(f333(f155(x41491,x41492),x41493),f333(f333(f155(x41494,x41491),x41495),x41496)),f333(f333(f155(x41494,x41492),f333(f72(x41491,x41492,x41494,x41493),x41495)),x41496)) % 183.90/184.43 [4151]E(f333(f333(f210(x41511,x41512),x41513),f333(f333(f210(x41514,x41511),x41515),x41516)),f333(f333(f210(x41514,x41512),f333(f72(x41511,x41512,x41514,x41513),x41515)),x41516)) % 183.90/184.43 [4156]E(f333(f312(x41561,x41562,f333(f72(x41563,x41562,x41561,x41564),x41565)),x41566),f333(f312(x41563,x41562,x41564),f333(f312(x41561,x41563,x41565),x41566))) % 183.90/184.43 [4157]E(f333(f313(x41571,x41572,f333(f72(x41573,x41572,x41571,x41574),x41575)),x41576),f333(f313(x41571,x41573,x41575),f333(f313(x41573,x41572,x41574),x41576))) % 183.90/184.43 [4186]E(f187(x41861,x41862,x41863,f333(f333(f333(f71(x41861,f879(x41862)),x41864),x41865),f333(f240(x41862),x41866))),f333(f333(f333(f71(x41861,f879(x41862)),f187(x41861,x41862,x41863,x41864)),x41865),f333(f240(x41862),x41866))) % 183.90/184.43 [4188]E(f333(f143(x41881,x41882,x41883,f333(f143(x41881,x41882,x41883,x41884),x41885)),x41886),f333(f143(x41881,x41882,x41883,x41884),f333(f333(f135(x41882),x41885),x41886))) % 183.90/184.43 [4328]E(f333(f273(x43281,x43281,x43282,x43283,f33(x43281),x43284),f333(f333(f268(x43281,x43282),x43285),x43286)),f333(f333(f268(x43281,x43283),x43285),f333(x43284,x43286))) % 183.90/184.43 [4329]E(f333(f273(x43291,x43292,x43293,x43293,x43294,f33(x43293)),f333(f333(f268(x43291,x43293),x43295),x43296)),f333(f333(f268(x43292,x43293),f333(x43294,x43295)),x43296)) % 183.90/184.43 [4419]E(f333(f333(f155(f881(x44191,x44192),f881(x44191,x44193)),f333(f272(x44191,x44192,f881(x44191,x44193)),f333(f333(f7(x44191,f882(x44192,x44193),f882(x44192,f881(x44191,x44193))),f333(f333(f8(f882(x44193,f881(x44191,x44193)),f882(f882(x44192,x44193),f882(x44192,f881(x44191,x44193))),x44191),f8(x44193,f881(x44191,x44193),x44192)),f268(x44191,x44193))),x44194))),f333(f333(f184(x44191,x44192),x44195),x44196)),f333(f333(f184(x44191,x44193),x44195),f333(f333(f155(x44192,x44193),x44194),x44196))) % 183.90/184.43 [3797]E(f97(x37971,x37972,x37973,f333(f333(f333(f91(x37971),x37974),x37975),x37976)),f333(f333(f333(x37973,x37974),x37975),x37976)) % 183.90/184.43 [3798]E(f98(x37981,x37982,x37983,f333(f333(f333(f91(x37981),x37984),x37985),x37986)),f333(f333(f333(x37983,x37984),x37985),x37986)) % 183.90/184.43 [3996]E(f333(f333(f72(x39961,x39962,x39963,f333(f16(x39962,x39961),x39964)),x39965),x39966),x39964) % 183.90/184.43 [4032]E(f333(f312(x40321,x40322,x40323),f333(f312(x40324,x40321,x40325),x40326)),f333(f312(x40324,x40322,f333(f333(f8(x40321,x40322,x40324),x40323),x40325)),x40326)) % 183.90/184.43 [4038]E(f333(f333(f41(x40381,f882(x40382,a870)),f333(f312(x40383,x40381,x40384),x40385)),x40386),f333(f333(f41(x40383,f882(x40382,a870)),x40385),f333(f333(f8(x40381,f882(x40382,a870),x40383),x40386),x40384))) % 183.90/184.43 [4039]E(f333(f333(f42(x40391,f882(x40392,a870)),f333(f312(x40393,x40391,x40394),x40395)),x40396),f333(f333(f42(x40393,f882(x40392,a870)),x40395),f333(f333(f8(x40391,f882(x40392,a870),x40393),x40396),x40394))) % 183.90/184.43 [4040]E(f333(f333(f41(x40401,f882(x40402,a870)),x40403),f333(f333(f8(x40404,f882(x40402,a870),x40401),x40405),x40406)),f333(f333(f41(x40404,f882(x40402,a870)),f333(f312(x40401,x40404,x40406),x40403)),x40405)) % 183.90/184.43 [4041]E(f333(f333(f42(x40411,f882(x40412,a870)),x40413),f333(f333(f8(x40414,f882(x40412,a870),x40411),x40415),x40416)),f333(f333(f42(x40414,f882(x40412,a870)),f333(f312(x40411,x40414,x40416),x40413)),x40415)) % 183.90/184.43 [4099]E(f333(f333(f41(x40991,f882(x40992,a870)),x40993),f333(f333(f8(f882(x40994,a870),f882(x40992,a870),x40991),f312(x40994,x40992,x40995)),x40996)),f333(f312(x40994,x40992,x40995),f333(f333(f41(x40991,f882(x40994,a870)),x40993),x40996))) % 183.90/184.43 [4100]E(f333(f333(f41(x41001,f882(x41002,a870)),x41003),f333(f333(f8(f882(x41004,a870),f882(x41002,a870),x41001),f313(x41002,x41004,x41005)),x41006)),f333(f313(x41002,x41004,x41005),f333(f333(f41(x41001,f882(x41004,a870)),x41003),x41006))) % 183.90/184.43 [4101]E(f333(f333(f42(x41011,f882(x41012,a870)),x41013),f333(f333(f8(f882(x41014,a870),f882(x41012,a870),x41011),f313(x41012,x41014,x41015)),x41016)),f333(f313(x41012,x41014,x41015),f333(f333(f42(x41011,f882(x41014,a870)),x41013),x41016))) % 183.90/184.43 [4102]E(f333(f333(f41(x41021,f882(x41022,a870)),x41023),f333(f333(f8(f882(x41024,a870),f882(x41022,a870),x41021),f287(x41024,x41022,x41025)),x41026)),f333(f287(x41024,x41022,x41025),f333(f333(f41(x41021,f882(x41024,a870)),x41023),x41026))) % 183.90/184.43 [4194]E(f333(f143(x41941,x41942,f333(f7(x41942,x41941,x41941),x41943),x41944),f333(f170(x41942),f333(f333(f152(x41942),x41945),x41946))),f333(f333(x41943,x41945),f333(f143(x41941,x41942,f333(f7(x41942,x41941,x41941),x41943),x41944),f333(f170(x41942),x41946)))) % 183.90/184.43 [4254]E(f333(f333(f18(f881(x42541,x42542),x42542,x42543),f333(f333(f8(x42544,f882(x42542,x42543),f881(x42541,x42542)),x42545),f333(f333(f8(x42541,x42544,f881(x42541,x42542)),x42546),f267(x42541,x42542)))),f271(x42541,x42542)),f333(f272(x42541,x42542,x42543),f333(f333(f8(x42544,f882(x42542,x42543),x42541),x42545),x42546))) % 183.90/184.43 [4261]E(f333(f143(x42611,x42612,f333(f7(x42612,x42611,x42611),x42613),f333(f143(x42611,x42612,f333(f7(x42612,x42611,x42611),x42613),x42614),f333(f170(x42612),x42615))),f333(f170(x42612),x42616)),f333(f143(x42611,x42612,f333(f7(x42612,x42611,x42611),x42613),x42614),f333(f170(x42612),f333(f333(f135(x42612),x42616),x42615)))) % 183.90/184.43 [4263]E(f333(f333(f155(f881(x42631,x42632),f881(x42633,x42632)),f333(f272(x42631,x42632,f881(x42633,x42632)),f333(f333(f8(x42633,f882(x42632,f881(x42633,x42632)),x42631),f268(x42633,x42632)),x42634))),f333(f333(f184(x42631,x42632),x42635),x42636)),f333(f333(f184(x42633,x42632),f333(f333(f155(x42631,x42633),x42634),x42635)),x42636)) % 183.90/184.43 [4311]P1(f333(f333(f247(f882(x43111,a870)),f333(f287(x43112,x43111,x43113),f333(f333(f42(x43114,f882(x43112,a870)),x43115),x43116))),f333(f333(f42(x43114,f882(x43111,a870)),x43115),f333(f333(f8(f882(x43112,a870),f882(x43111,a870),x43114),f287(x43112,x43111,x43113)),x43116)))) % 183.90/184.43 [4112]E(f333(f333(f184(x41121,x41122),f333(f333(f160(x41121,x41123),x41124),f333(f267(x41121,x41122),x41125))),f333(f333(f160(x41122,x41126),x41124),f333(f271(x41121,x41122),x41125))),f333(f333(f160(f881(x41121,x41122),f333(f333(f184(x41121,x41122),x41123),x41126)),x41124),x41125)) % 183.90/184.43 [4175]E(f333(f333(f113(f882(f881(x41751,x41752),a870)),f333(f333(f290(x41751,x41753,x41752),x41754),x41755)),f333(f333(f290(x41751,x41753,x41752),x41754),x41756)),f333(f333(f290(x41751,x41753,x41752),x41754),f333(f333(f113(f882(f881(x41753,x41752),a870)),x41755),x41756))) % 183.90/184.43 [4274]E(f333(f333(f311(f881(x42741,x42742)),f333(f333(f268(x42741,x42742),x42743),x42744)),f333(f333(f113(f882(f881(x42741,x42742),a870)),f333(f333(f270(x42741,x42742),x42745),f333(f16(f882(x42742,a870),x42741),f333(f333(f311(x42742),x42744),x42746)))),f333(f333(f270(x42741,x42742),f333(f333(f311(x42741),x42743),x42745)),f333(f16(f882(x42742,a870),x42741),x42746)))),f333(f333(f270(x42741,x42742),f333(f333(f311(x42741),x42743),x42745)),f333(f16(f882(x42742,a870),x42741),f333(f333(f311(x42742),x42744),x42746)))) % 183.90/184.43 [4352]E(f333(f333(f104(f882(x43521,a870)),f333(f313(x43521,x43522,f333(f72(f881(x43522,x43523),x43522,x43521,f267(x43522,x43523)),x43524)),x43525)),f333(f313(x43521,x43523,f333(f72(f881(x43522,x43523),x43523,x43521,f271(x43522,x43523)),x43524)),x43526)),f333(f313(x43521,f881(x43522,x43523),x43524),f333(f333(f270(x43522,x43523),x43525),f333(f16(f882(x43523,a870),x43522),x43526)))) % 183.90/184.43 [4096]E(f333(f333(f333(f71(x40961,x40962),f333(f333(f333(f71(x40961,x40962),x40963),x40964),x40965)),x40964),x40966),f333(f333(f333(f71(x40961,x40962),x40963),x40964),x40966)) % 183.90/184.43 [4200]E(f333(f333(f113(f882(f881(x42001,x42002),a870)),f333(f333(f290(x42001,x42003,x42002),x42004),x42005)),f333(f333(f290(x42001,x42003,x42002),x42006),x42005)),f333(f333(f290(x42001,x42003,x42002),f333(f333(f113(f882(f881(x42001,x42003),a870)),x42004),x42006)),x42005)) % 183.90/184.43 [4336]E(f333(f333(f41(x43361,f882(x43362,a870)),x43363),f333(f333(f7(x43361,f882(x43364,f882(x43362,a870)),f882(x43362,a870)),f333(f333(f8(f882(x43364,a870),f882(f882(x43364,f882(x43362,a870)),f882(x43362,a870)),x43361),f41(x43364,f882(x43362,a870))),x43365)),x43366)),f333(f333(f41(x43364,f882(x43362,a870)),f333(f333(f41(x43361,f882(x43364,a870)),x43363),x43365)),x43366)) % 183.90/184.43 [4337]E(f333(f333(f42(x43371,f882(x43372,a870)),x43373),f333(f333(f7(x43371,f882(x43374,f882(x43372,a870)),f882(x43372,a870)),f333(f333(f8(f882(x43374,a870),f882(f882(x43374,f882(x43372,a870)),f882(x43372,a870)),x43371),f42(x43374,f882(x43372,a870))),x43375)),x43376)),f333(f333(f42(x43374,f882(x43372,a870)),f333(f333(f41(x43371,f882(x43374,a870)),x43373),x43375)),x43376)) % 183.90/184.43 [4389]E(f333(f272(x43891,x43892,f881(x43893,x43894)),f333(f333(f7(x43891,f882(x43892,x43894),f882(x43892,f881(x43893,x43894))),f333(f333(f8(f882(x43894,f881(x43893,x43894)),f882(f882(x43892,x43894),f882(x43892,f881(x43893,x43894))),x43891),f8(x43894,f881(x43893,x43894),x43892)),f333(f333(f8(x43893,f882(x43894,f881(x43893,x43894)),x43891),f268(x43893,x43894)),x43895))),x43896)),f273(x43891,x43893,x43892,x43894,x43895,x43896)) % 183.90/184.43 [4310]E(f333(f333(f333(f71(x43101,f879(x43102)),f190(x43101,x43102,x43103,f333(f333(f22(f882(x43101,a870)),x43104),f333(f333(f311(x43101),x43105),f196(f882(x43101,a870)))))),x43105),x43106),f333(f333(f333(f71(x43101,f879(x43102)),f190(x43101,x43102,x43103,x43104)),x43105),x43106)) % 183.90/184.43 [4414]E(f333(f312(x44141,x44142,f333(f333(f18(x44141,x44142,x44142),f333(f333(f18(x44141,x44142,f882(x44142,x44142)),f333(f333(f8(a870,f882(x44142,f882(x44142,x44142)),x44141),f99(x44142)),x44143)),x44144)),x44145)),x44146),f333(f333(f113(f882(x44142,a870)),f333(f312(x44141,x44142,x44144),f333(f333(f104(f882(x44141,a870)),x44146),f333(f253(x44141),x44143)))),f333(f312(x44141,x44142,x44145),f333(f333(f104(f882(x44141,a870)),x44146),f333(f253(x44141),f333(f333(f8(a870,a870,x44141),a328),x44143)))))) % 183.90/184.43 [4425]E(f333(f312(x44251,f881(x44252,x44253),f333(f333(f18(x44251,x44253,f881(x44252,x44253)),f333(f333(f8(x44252,f882(x44253,f881(x44252,x44253)),x44251),f268(x44252,x44253)),x44254)),x44255)),x44256),f333(f333(f270(x44252,x44253),f333(f312(x44251,x44252,x44254),x44256)),f333(f333(f8(f882(x44251,a870),f882(x44253,a870),x44252),f312(x44251,x44253,x44255)),f333(f333(f7(x44252,f882(x44251,a870),f882(x44251,a870)),f333(f333(f8(f882(x44251,a870),f882(f882(x44251,a870),f882(x44251,a870)),x44252),f104(f882(x44251,a870))),f333(f333(f8(f882(x44252,a870),f882(x44251,a870),x44252),f313(x44251,x44252,x44254)),f333(f333(f7(x44252,f882(x44252,a870),f882(x44252,a870)),f311(x44252)),f196(f882(x44252,a870)))))),x44256)))) % 183.90/184.43 [4371]E(f333(f271(x43711,x43712),f333(f273(x43713,x43711,x43714,x43712,x43715,x43716),x43717)),f333(x43716,f333(f271(x43713,x43714),x43717))) % 183.90/184.43 [4372]E(f333(f267(x43721,x43722),f333(f273(x43723,x43721,x43724,x43722,x43725,x43726),x43727)),f333(x43725,f333(f267(x43723,x43724),x43727))) % 183.90/184.43 [4074]E(f333(f333(f184(x40741,x40742),f333(f333(f160(x40741,x40743),x40744),x40745)),f333(f333(f160(x40742,x40746),x40744),x40747)),f333(f333(f160(f881(x40741,x40742),f333(f333(f184(x40741,x40742),x40743),x40746)),x40744),f333(f333(f268(x40741,x40742),x40745),x40747))) % 183.90/184.43 [4142]E(f333(f333(f333(f274(x41421,x41422,x41423,x41424),x41425),x41426),x41427),f333(f333(f272(x41422,x41423,x41424),x41426),f333(x41425,x41427))) % 183.90/184.43 [4155]E(f333(f333(f333(f274(x41551,x41552,x41553,x41554),x41555),x41556),x41557),f333(f333(x41556,f333(f267(x41552,x41553),f333(x41555,x41557))),f333(f271(x41552,x41553),f333(x41555,x41557)))) % 183.90/184.43 [4190]E(f189(x41901,x41902,f333(f333(f333(f71(x41901,f879(x41902)),x41903),x41904),f333(f240(x41902),x41905)),x41906,x41907),f189(x41901,x41902,x41903,f333(f333(f152(x41901),x41904),x41906),f333(f333(f152(x41902),x41905),x41907))) % 183.90/184.43 [4209]E(f333(f72(x42091,x42092,x42093,x42094),f333(f72(x42095,x42091,x42093,x42096),x42097)),f333(f72(x42095,x42092,x42093,f333(f72(x42091,x42092,x42095,x42094),x42096)),x42097)) % 183.90/184.43 [4270]E(f333(f72(f879(x42701),f879(x42702),x42703,f333(f210(x42701,x42702),x42704)),f333(f333(f333(f71(x42703,f879(x42701)),x42705),x42706),f333(f240(x42701),x42707))),f333(f333(f333(f71(x42703,f879(x42702)),f333(f72(f879(x42701),f879(x42702),x42703,f333(f210(x42701,x42702),x42704)),x42705)),x42706),f333(f240(x42702),f333(x42704,x42707)))) % 183.90/184.43 [4396]E(f333(f273(x43961,x43962,x43963,x43963,x43964,f33(x43963)),f333(f273(x43961,x43961,x43965,x43963,f33(x43961),x43966),x43967)),f333(f333(f268(x43962,x43963),f333(x43964,f333(f267(x43961,x43965),x43967))),f333(x43966,f333(f271(x43961,x43965),x43967)))) % 183.90/184.43 [4397]E(f333(f273(x43971,x43971,x43972,x43973,f33(x43971),x43974),f333(f273(x43975,x43971,x43972,x43972,x43976,f33(x43972)),x43977)),f333(f333(f268(x43971,x43973),f333(x43976,f333(f267(x43975,x43972),x43977))),f333(x43974,f333(f271(x43975,x43972),x43977)))) % 183.90/184.43 [4412]E(f333(f273(x44121,x44122,x44123,x44123,x44124,f33(x44123)),f333(f273(x44125,x44121,x44123,x44123,x44126,f33(x44123)),x44127)),f333(f273(x44125,x44122,x44123,x44123,f333(f72(x44121,x44122,x44125,x44124),x44126),f33(x44123)),x44127)) % 183.90/184.43 [4413]E(f333(f273(x44131,x44131,x44132,x44133,f33(x44131),x44134),f333(f273(x44131,x44131,x44135,x44132,f33(x44131),x44136),x44137)),f333(f273(x44131,x44131,x44135,x44133,f33(x44131),f333(f72(x44132,x44133,x44135,x44134),x44136)),x44137)) % 183.90/184.43 [4422]E(f333(f273(x44221,x44222,x44223,x44223,x44224,f33(x44223)),f333(f273(x44221,x44221,x44225,x44223,f33(x44221),x44226),x44227)),f333(f273(x44222,x44222,x44225,x44223,f33(x44222),x44226),f333(f273(x44221,x44222,x44225,x44225,x44224,f33(x44225)),x44227))) % 183.90/184.43 [4109]E(f333(f333(f290(x41091,x41092,x41093),f333(f333(f290(x41091,x41094,x41092),x41095),x41096)),x41097),f333(f333(f290(x41091,x41094,x41093),x41095),f333(f333(f290(x41094,x41092,x41093),x41096),x41097))) % 183.90/184.43 [4181]E(f333(f333(f272(x41811,x41812,x41813),f333(f72(x41814,f882(x41812,x41813),x41811,x41815),x41816)),x41817),f333(f333(x41815,f333(x41816,f333(f267(x41811,x41812),x41817))),f333(f271(x41811,x41812),x41817))) % 183.90/184.43 [4234]E(f333(f72(x42341,x42342,x42343,x42344),f333(f333(f333(f71(x42343,x42341),x42345),x42346),x42347)),f333(f333(f333(f71(x42343,x42342),f333(f72(x42341,x42342,x42343,x42344),x42345)),x42346),f333(x42344,x42347))) % 183.90/184.43 [4266]E(f333(f143(x42661,x42662,f333(f7(x42662,x42661,x42661),x42663),x42664),f333(f170(x42662),f333(f333(f155(x42665,x42662),x42666),x42667))),f333(f143(x42661,x42665,f333(f7(x42665,x42661,x42661),f333(f72(x42662,f882(x42661,x42661),x42665,x42663),x42666)),x42664),f333(f170(x42665),x42667))) % 183.90/184.43 [4210]E(f333(f333(f41(x42101,f882(f881(x42102,x42103),a870)),x42104),f333(f333(f8(f882(f881(x42105,x42103),a870),f882(f881(x42102,x42103),a870),x42101),f333(f290(x42102,x42105,x42103),x42106)),x42107)),f333(f333(f290(x42102,x42105,x42103),x42106),f333(f333(f41(x42101,f882(f881(x42105,x42103),a870)),x42104),x42107))) % 183.90/184.43 [4358]E(f333(f333(f41(x43581,f882(f881(x43582,x43583),a870)),x43584),f333(f333(f7(x43581,f882(f881(x43585,x43583),a870),f882(f881(x43582,x43583),a870)),f333(f333(f8(f882(f881(x43582,x43585),a870),f882(f882(f881(x43585,x43583),a870),f882(f881(x43582,x43583),a870)),x43581),f290(x43582,x43585,x43583)),x43586)),x43587)),f333(f333(f290(x43582,x43585,x43583),f333(f333(f41(x43581,f882(f881(x43582,x43585),a870)),x43584),x43586)),x43587)) % 183.90/184.43 [4359]E(f333(f143(x43591,x43592,f333(f333(f7(x43591,f882(x43592,x43593),f882(x43592,x43591)),f333(f333(f8(f882(x43593,x43591),f882(f882(x43592,x43593),f882(x43592,x43591)),x43591),f8(x43593,x43591,x43592)),x43594)),x43595),x43596),x43597),f333(f143(x43591,x43593,x43594,x43596),f333(f333(f155(x43592,x43593),x43595),x43597))) % 183.90/184.43 [4423]E(f333(f333(f42(x44231,f882(x44232,a870)),x44233),f333(f333(f8(f882(x44234,f882(x44232,a870)),f882(x44232,a870),x44231),f333(f42(x44234,f882(x44232,a870)),x44235)),f333(f333(f7(x44231,f882(x44234,f882(x44232,a870)),f882(x44234,f882(x44232,a870))),f333(f333(f8(f882(f882(x44232,a870),f882(x44232,a870)),f882(f882(x44234,f882(x44232,a870)),f882(x44234,f882(x44232,a870))),x44231),f8(f882(x44232,a870),f882(x44232,a870),x44234)),f333(f333(f8(f882(x44232,a870),f882(f882(x44232,a870),f882(x44232,a870)),x44231),f113(f882(x44232,a870))),x44236))),x44237))),f333(f333(f113(f882(x44232,a870)),f333(f333(f42(x44231,f882(x44232,a870)),x44233),x44236)),f333(f333(f42(x44234,f882(x44232,a870)),x44235),x44237))) % 183.90/184.43 [4424]E(f333(f333(f41(x44241,f882(x44242,a870)),x44243),f333(f333(f8(f882(x44244,f882(x44242,a870)),f882(x44242,a870),x44241),f333(f41(x44244,f882(x44242,a870)),x44245)),f333(f333(f7(x44241,f882(x44244,f882(x44242,a870)),f882(x44244,f882(x44242,a870))),f333(f333(f8(f882(f882(x44242,a870),f882(x44242,a870)),f882(f882(x44244,f882(x44242,a870)),f882(x44244,f882(x44242,a870))),x44241),f8(f882(x44242,a870),f882(x44242,a870),x44244)),f333(f333(f8(f882(x44242,a870),f882(f882(x44242,a870),f882(x44242,a870)),x44241),f104(f882(x44242,a870))),x44246))),x44247))),f333(f333(f104(f882(x44242,a870)),f333(f333(f41(x44241,f882(x44242,a870)),x44243),x44246)),f333(f333(f41(x44244,f882(x44242,a870)),x44245),x44247))) % 183.90/184.43 [4417]E(f207(x44171,x44172,f333(f333(f333(x44173,x44174),x44175),x44176),f333(f333(f7(x44171,f881(a102,a102),f882(a102,f877(x44172))),f333(f333(f7(x44171,a102,f882(f881(a102,a102),f882(a102,f877(x44172)))),f333(f333(f7(x44171,a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(x44172))))),x44177),x44174)),x44175)),x44176)),f333(f333(f333(f221(x44171,x44172,x44173,x44177),x44174),x44175),x44176)) % 183.90/184.43 [4430]E(f208(x44301,x44302,f333(f333(f333(x44303,x44304),x44305),x44306),f333(f333(f7(x44301,f881(a102,a102),f882(a102,f877(x44302))),f333(f333(f7(x44301,a102,f882(f881(a102,a102),f882(a102,f877(x44302)))),f333(f333(f7(x44301,a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(x44302))))),x44307),x44304)),x44305)),x44306)),f223(x44301,x44302,x44303,x44307,x44304,x44305,x44306)) % 183.90/184.43 [4421]E(f205(x44211,x44212,f333(f333(f333(x44213,x44214),x44215),x44216),f333(f333(f7(x44211,f881(a102,a102),f882(a102,f877(f879(x44212)))),f333(f333(f7(x44211,a102,f882(f881(a102,a102),f882(a102,f877(f879(x44212))))),f333(f333(f7(x44211,a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(f879(x44212)))))),x44217),x44214)),x44215)),x44216)),f333(f333(f333(f217(x44211,x44212,x44213,x44217),x44214),x44215),x44216)) % 183.90/184.43 [4432]E(f206(x44321,x44322,f333(f333(f333(x44323,x44324),x44325),x44326),f333(f333(f7(x44321,f881(a102,a102),f882(a102,f877(f879(x44322)))),f333(f333(f7(x44321,a102,f882(f881(a102,a102),f882(a102,f877(f879(x44322))))),f333(f333(f7(x44321,a102,f882(a102,f882(f881(a102,a102),f882(a102,f877(f879(x44322)))))),x44327),x44324)),x44325)),x44326)),f219(x44321,x44322,x44323,x44327,x44324,x44325,x44326)) % 183.90/184.43 [4330]E(f333(f273(x43301,x43302,x43303,x43304,x43305,x43306),f333(f333(f268(x43301,x43303),x43307),x43308)),f333(f333(f268(x43302,x43304),f333(x43305,x43307)),f333(x43306,x43308))) % 183.90/184.43 [4434]E(f333(f333(f155(f881(x44341,x44342),f881(x44343,x44344)),f333(f272(x44341,x44342,f881(x44343,x44344)),f333(f333(f7(x44341,f882(x44342,x44344),f882(x44342,f881(x44343,x44344))),f333(f333(f8(f882(x44344,f881(x44343,x44344)),f882(f882(x44342,x44344),f882(x44342,f881(x44343,x44344))),x44341),f8(x44344,f881(x44343,x44344),x44342)),f333(f333(f8(x44343,f882(x44344,f881(x44343,x44344)),x44341),f268(x44343,x44344)),x44345))),x44346))),f333(f333(f184(x44341,x44342),x44347),x44348)),f333(f333(f184(x44343,x44344),f333(f333(f155(x44341,x44343),x44345),x44347)),f333(f333(f155(x44342,x44344),x44346),x44348))) % 183.90/184.43 [4438]E(f333(f333(f155(f881(x44381,x44382),x44383),f333(f272(x44381,x44382,x44383),f333(f333(f8(f882(x44382,f881(x44381,x44384)),f882(x44382,x44383),x44381),f333(f8(f881(x44381,x44384),x44383,x44382),x44385)),f333(f333(f7(x44381,f882(x44382,x44384),f882(x44382,f881(x44381,x44384))),f333(f333(f8(f882(x44384,f881(x44381,x44384)),f882(f882(x44382,x44384),f882(x44382,f881(x44381,x44384))),x44381),f8(x44384,f881(x44381,x44384),x44382)),f268(x44381,x44384))),x44386)))),f333(f333(f184(x44381,x44382),x44387),x44388)),f333(f333(f155(f881(x44381,x44384),x44383),x44385),f333(f333(f184(x44381,x44384),x44387),f333(f333(f155(x44382,x44384),x44386),x44388)))) % 183.90/184.43 [4363]E(f333(f333(f155(f881(x43631,x43632),x43633),f333(f272(x43631,x43632,x43633),f333(f333(f8(f882(x43632,f881(x43634,x43632)),f882(x43632,x43633),x43631),f333(f8(f881(x43634,x43632),x43633,x43632),x43635)),f333(f333(f8(x43634,f882(x43632,f881(x43634,x43632)),x43631),f268(x43634,x43632)),x43636)))),f333(f333(f184(x43631,x43632),x43637),x43638)),f333(f333(f155(f881(x43634,x43632),x43633),x43635),f333(f333(f184(x43634,x43632),f333(f333(f155(x43631,x43634),x43636),x43637)),x43638))) % 183.90/184.43 [4321]E(f333(f333(f272(x43211,x43212,x43213),f333(f333(f8(f882(x43212,f881(x43214,x43215)),f882(x43212,x43213),x43211),f333(f8(f881(x43214,x43215),x43213,x43212),f333(f272(x43214,x43215,x43213),x43216))),x43217)),x43218),f333(f333(f272(x43214,x43215,x43213),x43216),f333(f333(f272(x43211,x43212,f881(x43214,x43215)),x43217),x43218))) % 183.90/184.43 [4439]E(f333(f333(f41(f881(x44391,x44392),f882(f881(x44393,x44394),a870)),f333(f333(f270(x44391,x44392),x44395),f333(f16(f882(x44392,a870),x44391),x44396))),f333(f272(x44391,x44392,f882(f881(x44393,x44394),a870)),f333(f333(f7(x44391,f882(x44392,f882(x44393,f882(x44394,a870))),f882(x44392,f882(f881(x44393,x44394),a870))),f333(f333(f8(f882(f882(x44393,f882(x44394,a870)),f882(f881(x44393,x44394),a870)),f882(f882(x44392,f882(x44393,f882(x44394,a870))),f882(x44392,f882(f881(x44393,x44394),a870))),x44391),f8(f882(x44393,f882(x44394,a870)),f882(f881(x44393,x44394),a870),x44392)),f333(f333(f8(f882(x44393,a870),f882(f882(x44393,f882(x44394,a870)),f882(f881(x44393,x44394),a870)),x44391),f270(x44393,x44394)),x44397))),f333(f333(f8(f882(x44394,a870),f882(x44393,f882(x44394,a870)),x44392),f16(f882(x44394,a870),x44393)),x44398)))),f333(f333(f270(x44393,x44394),f333(f333(f41(x44391,f882(x44393,a870)),x44395),x44397)),f333(f16(f882(x44394,a870),x44393),f333(f333(f41(x44392,f882(x44394,a870)),x44396),x44398)))) % 183.90/184.43 [4377]E(f333(f333(f274(x43771,x43772,x43773,x43774),f333(f333(f274(x43771,x43775,x43776,f881(x43772,x43773)),x43777),x43778)),x43779),f333(f333(f274(x43771,x43775,x43776,x43774),x43777),f333(f333(f7(x43775,f882(x43772,f882(x43773,x43774)),f882(x43776,x43774)),f333(f333(f8(f882(x43776,f881(x43772,x43773)),f882(f882(x43772,f882(x43773,x43774)),f882(x43776,x43774)),x43775),f274(x43776,x43772,x43773,x43774)),x43778)),x43779))) % 183.90/184.43 [4409]E(f333(f72(f881(x44091,x44092),f881(x44093,x44094),f881(x44095,x44096),f273(x44091,x44093,x44092,x44094,x44097,x44098)),f273(x44095,x44091,x44096,x44092,x44099,x440910)),f273(x44095,x44093,x44096,x44094,f333(f72(x44091,x44093,x44095,x44097),x44099),f333(f72(x44092,x44094,x44096,x44098),x440910))) % 183.90/184.43 [4415]E(f333(f273(x44151,x44152,x44153,x44154,x44155,x44156),f333(f273(x44157,x44151,x44158,x44153,x44159,x441510),x441511)),f333(f273(x44157,x44152,x44158,x44154,f333(f72(x44151,x44152,x44157,x44155),x44159),f333(f72(x44153,x44154,x44158,x44156),x441510)),x441511)) % 183.90/184.43 [4581]~P92(x45811)+E(f90(x45811),a330) % 183.90/184.43 [4582]~P3(x45821)+P3(f879(x45821)) % 183.90/184.43 [4583]~P57(x45831)+P57(f879(x45831)) % 183.90/184.43 [4584]~P101(x45841)+P101(f876(x45841)) % 183.90/184.43 [4587]~P140(x45871)+~E(f77(x45871),f2(x45871)) % 183.90/184.43 [4589]~E(x45891,f2(a102))+E(f333(a20,x45891),f2(a1)) % 183.90/184.43 [4590]~E(x45901,f2(a1))+E(f81(a1,x45901),f2(a1)) % 183.90/184.43 [4596]~P141(x45961)+P30(x45961,f2(x45961)) % 183.90/184.43 [4598]~P106(x45981)+P14(x45981,f116(x45981)) % 183.90/184.43 [4607]P1(x46071)+P1(f333(a328,x46071)) % 183.90/184.43 [4650]~P141(x46501)+~P30(x46501,f77(x46501)) % 183.90/184.43 [4697]~P1(x46971)+~P1(f333(a328,x46971)) % 183.90/184.43 [4720]E(f333(a107,x47201),f2(a875))+~P1(f333(a201,x47201)) % 183.90/184.43 [4786]~P98(x47861)+P15(x47861,x47861,f113(x47861)) % 183.90/184.43 [4787]~P99(x47871)+P15(x47871,x47871,f104(x47871)) % 183.90/184.43 [4788]~P94(x47881)+P15(x47881,x47881,f80(x47881)) % 183.90/184.43 [4789]~P106(x47891)+P15(x47891,x47891,f245(x47891)) % 183.90/184.43 [4790]~P106(x47901)+P15(x47901,x47901,f246(x47901)) % 183.90/184.43 [4791]~P67(x47911)+P16(x47911,x47911,f80(x47911)) % 183.90/184.43 [4593]~E(x45931,f2(a875))+E(f333(f103(a1),x45931),f2(a1)) % 183.90/184.43 [4600]~P90(x46001)+E(f333(f106(x46001),a82),f2(x46001)) % 183.90/184.43 [4603]~E(f598(x46031),f2(a875))+E(f333(f167(a875),x46031),f2(a875)) % 183.90/184.43 [4604]~P107(x46041)+E(f249(x46041,f247(x46041)),f245(x46041)) % 183.90/184.43 [4605]~P107(x46051)+E(f250(x46051,f247(x46051)),f246(x46051)) % 183.90/184.43 [4606]~P87(x46061)+E(f81(x46061,f2(x46061)),f2(x46061)) % 183.90/184.43 [4615]~P141(x46151)+E(f333(f103(x46151),f77(a875)),f77(x46151)) % 183.90/184.43 [4616]~P141(x46161)+E(f333(f103(x46161),f2(a875)),f2(x46161)) % 183.90/184.43 [4617]~P138(x46171)+E(f333(f105(x46171),f77(a1)),f77(x46171)) % 183.90/184.43 [4618]~P138(x46181)+E(f333(f105(x46181),f2(a1)),f2(x46181)) % 183.90/184.43 [4619]E(x46191,f2(a875))+~E(f333(f103(a1),x46191),f2(a1)) % 183.90/184.43 [4644]~P114(x46441)+E(f333(f74(x46441),f77(x46441)),f77(x46441)) % 183.90/184.43 [4645]~P83(x46451)+E(f333(f74(x46451),f2(x46451)),f2(x46451)) % 183.90/184.43 [4646]~P93(x46461)+E(f333(f78(x46461),f196(x46461)),f256(x46461)) % 183.90/184.43 [4647]~P93(x46471)+E(f333(f78(x46471),f256(x46471)),f196(x46471)) % 183.90/184.43 [4648]~P72(x46481)+E(f333(f78(x46481),f2(x46481)),f2(x46481)) % 183.90/184.43 [4649]~P78(x46491)+E(f333(f167(x46491),f116(x46491)),f2(x46491)) % 183.90/184.43 [4670]~P36(x46701)+P38(f333(f174(a1),x46701)) % 183.90/184.43 [4702]~P90(x47021)+E(f333(f78(x47021),f77(x47021)),f333(f106(x47021),a100)) % 183.90/184.43 [4719]~P90(x47191)+P30(x47191,f333(f106(x47191),a82)) % 183.90/184.43 [4736]~P57(x47361)+E(f333(f174(x47361),f55(x47361)),f256(f882(x47361,a870))) % 183.90/184.43 [4746]P36(x47461)+~P38(f333(f174(a1),x47461)) % 183.90/184.43 [4747]~P57(x47471)+P1(f333(f138(x47471),f55(x47471))) % 183.90/184.43 [4792]E(f333(f103(a1),f333(a107,x47921)),x47921)+P1(f333(a201,x47921)) % 183.90/184.43 [4809]~P107(x48091)+E(f92(x48091,x48091,f5(x48091)),f93(x48091)) % 183.90/184.43 [4861]~P111(x48611)+E(f259(x48611,f77(x48611),f80(x48611)),f258(x48611)) % 183.90/184.43 [4891]~P90(x48911)+~P30(x48911,f333(f106(x48911),a100)) % 183.90/184.43 [5033]E(f333(f74(a1),x50331),x50331)+P1(f333(f333(f248(a1),x50331),f2(a1))) % 183.90/184.43 [5051]~E(f333(a107,x50511),f2(a875))+P1(f333(f333(f247(a1),x50511),f2(a1))) % 183.90/184.43 [5113]~P1(f333(a201,x51131))+P1(f333(f333(f248(a1),x51131),f2(a1))) % 183.90/184.43 [5153]~P138(x51531)+P1(f333(f333(f335(x51531),f77(x51531)),f112(x51531))) % 183.90/184.43 [5154]~P141(x51541)+P1(f333(f333(f335(x51541),f77(x51541)),f194(x51541))) % 183.90/184.43 [5155]~P138(x51551)+P1(f333(f333(f335(x51551),f2(x51551)),f112(x51551))) % 183.90/184.43 [5156]~P141(x51561)+P1(f333(f333(f335(x51561),f2(x51561)),f194(x51561))) % 183.90/184.43 [5157]~P120(x51571)+P1(f333(f333(f248(x51571),f2(x51571)),f77(x51571))) % 183.90/184.43 [5158]~P120(x51581)+P1(f333(f333(f247(x51581),f2(x51581)),f77(x51581))) % 183.90/184.43 [5210]E(x52101,f2(a875))+~P1(f333(f333(f247(a875),x52101),f2(a875))) % 183.90/184.43 [5253]E(f333(a107,x52531),f2(a875))+~P1(f333(f333(f247(a1),x52531),f2(a1))) % 183.90/184.43 [5316]P1(f333(a201,x53161))+~P1(f333(f333(f248(a1),x53161),f2(a1))) % 183.90/184.43 [5321]~P106(x53211)+P16(x53211,f876(x53211),f149(x53211,x53211,f5(x53211))) % 183.90/184.43 [5338]P38(x53381)+~P1(f333(f333(f247(a1),f2(a1)),f341(x53381))) % 183.90/184.43 [5344]E(f333(f74(a1),x53441),f333(f78(a1),x53441))+~P1(f333(f333(f248(a1),x53441),f2(a1))) % 183.90/184.43 [5516]~P120(x55161)+~P1(f333(f333(f248(x55161),f77(x55161)),f2(x55161))) % 183.90/184.43 [5517]~P120(x55171)+~P1(f333(f333(f247(x55171),f77(x55171)),f2(x55171))) % 183.90/184.43 [5527]~E(x55271,f2(a1))+P1(f333(f333(f248(a1),f333(f74(a1),x55271)),f77(a1))) % 183.90/184.43 [5528]~E(x55281,f2(a875))+P1(f333(f333(f247(a1),f333(f103(a1),x55281)),f2(a1))) % 183.90/184.43 [5649]~P78(x56491)+E(f143(x56491,x56491,f79(x56491),f2(x56491)),f167(x56491)) % 183.90/184.43 [5819]~P100(x58191)+P25(a875,x58191,f103(x58191),f256(f882(a875,a870))) % 183.90/184.43 [6014]E(x60141,f2(a875))+~P1(f333(f333(f247(a1),f333(f103(a1),x60141)),f2(a1))) % 183.90/184.43 [6015]E(x60151,f2(a1))+~P1(f333(f333(f248(a1),f333(f74(a1),x60151)),f77(a1))) % 183.90/184.43 [6806]~P1(f333(f333(f248(a1),x68061),f2(a1)))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x68061),x68061)),f2(a1))) % 183.90/184.43 [7355]P1(f333(f333(f248(a1),x73551),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x73551),x73551)),f2(a1))) % 183.90/184.43 [7917]E(x79171,f333(a3,f2(a875)))+P1(f333(f333(f248(a875),f333(f333(f22(a875),f333(a19,x79171)),f333(a115,f2(a875)))),f333(a19,x79171))) % 183.90/184.43 [8687]~P1(f333(f333(f248(a1),x86871),f2(a1)))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86871),x86871)),a100)),f2(a1))) % 183.90/184.43 [8773]~P1(f333(f333(f248(a1),x87731),f2(a1)))+P1(f333(f333(f248(a1),f333(f333(f79(a1),f333(f333(f79(a1),f77(a1)),x87731)),x87731)),f2(a1))) % 183.90/184.43 [9099]P1(f333(f333(f248(a1),x90991),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90991),x90991)),a100)),f2(a1))) % 183.90/184.43 [9162]P1(f333(f333(f248(a1),x91621),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),f333(f333(f79(a1),f77(a1)),x91621)),x91621)),f2(a1))) % 183.90/184.43 [4690]~E(a82,x46901)+E(f333(f333(f79(a1),x46901),x46901),a82) % 183.90/184.43 [4691]~E(x46911,a82)+E(f333(f333(f79(a1),x46911),x46911),a82) % 183.90/184.43 [4705]E(x47051,f2(a1))+E(f333(f333(f38(a1),x47051),x47051),f77(a1)) % 183.90/184.43 [4838]E(x48381,a82)+~E(f333(f333(f79(a1),x48381),x48381),a82) % 183.90/184.43 [4839]E(a82,x48391)+~E(f333(f333(f79(a1),x48391),x48391),a82) % 183.90/184.43 [4851]~P4(x48511)+E(f40(x48511,f196(f882(x48511,a870))),f256(x48511)) % 183.90/184.43 [4852]~P4(x48521)+E(f40(x48521,f256(f882(x48521,a870))),f196(x48521)) % 183.90/184.43 [4853]~P4(x48531)+E(f39(x48531,f196(f882(x48531,a870))),f196(x48531)) % 183.90/184.43 [4854]~P4(x48541)+E(f39(x48541,f256(f882(x48541,a870))),f256(x48541)) % 183.90/184.43 [4855]~P106(x48551)+E(f140(x48551,f196(f882(x48551,a870))),f116(x48551)) % 183.90/184.43 [4991]E(x49911,f2(a875))+P1(f333(f333(f248(a875),f2(a875)),x49911)) % 183.90/184.43 [5010]~P5(x50101)+P1(f333(f333(f247(a1),f2(a1)),x50101)) % 183.90/184.43 [5042]~E(f333(f106(a875),x50421),f2(a875))+P1(f333(f333(f247(a1),x50421),a82)) % 183.90/184.43 [5047]P38(x50471)+P1(f333(f333(f335(a1),f341(x50471)),x50471)) % 183.90/184.43 [5048]E(x50481,f333(a3,f2(a875)))+P1(f333(f333(f247(a102),f77(a102)),x50481)) % 183.90/184.43 [5087]P1(f333(a201,x50871))+P1(f333(f333(f247(a1),f2(a1)),x50871)) % 183.90/184.43 [5135]E(f333(f103(a1),f333(a107,x51351)),f2(a1))+P1(f333(f333(f247(a1),f2(a1)),x51351)) % 183.90/184.43 [5195]E(f333(f103(a1),f333(f106(a875),x51951)),f333(f106(a1),x51951))+P1(f333(a201,f333(f106(a1),x51951))) % 183.90/184.43 [5216]E(f333(f106(a875),x52161),f2(a875))+~P1(f333(a201,f333(f106(a1),x52161))) % 183.90/184.43 [5217]E(f333(f106(a875),x52171),f2(a875))+~P1(f333(f333(f247(a1),x52171),a82)) % 183.90/184.43 [5250]P5(x52501)+~P1(f333(f333(f247(a1),f2(a1)),x52501)) % 183.90/184.43 [5324]E(f333(a115,f343(x53241)),x53241)+~P1(f333(f333(f248(a875),f2(a875)),x53241)) % 183.90/184.43 [5332]E(f333(a115,f333(f106(a875),x53321)),f77(a875))+~P1(f333(a201,f333(f106(a1),x53321))) % 183.90/184.43 [5340]E(f333(f103(a1),f407(x53401)),x53401)+~P1(f333(f333(f248(a1),f2(a1)),x53401)) % 183.90/184.43 [5347]~E(x53471,f333(a3,f2(a875)))+~P1(f333(f333(f247(a102),f77(a102)),x53471)) % 183.90/184.43 [5354]E(f333(f103(a1),f333(f106(a875),x53541)),f2(a1))+~P1(f333(a201,f333(f106(a1),x53541))) % 183.90/184.43 [5380]E(f333(f167(a875),x53801),f2(a875))+P1(f333(f333(f335(a875),f598(x53801)),f333(f174(a875),x53801))) % 183.90/184.43 [5401]E(f333(f103(a1),f333(a107,x54011)),x54011)+~P1(f333(f333(f247(a1),f2(a1)),x54011)) % 183.90/184.43 [5410]~P1(f333(a201,x54101))+~P1(f333(f333(f247(a1),f2(a1)),x54101)) % 183.90/184.43 [5509]E(f333(f333(f79(a875),f77(a875)),f333(f106(a875),x55091)),f77(a875))+~P1(f333(f333(f248(a1),x55091),a82)) % 183.90/184.43 [5569]E(x55691,f2(a875))+~P1(f333(f333(f248(a875),x55691),f333(a115,f2(a875)))) % 183.90/184.43 [5608]E(f333(f333(f22(a875),f333(f106(a875),x56081)),f77(a875)),f2(a875))+~P1(f333(f333(f247(a1),x56081),a82)) % 183.90/184.43 [5609]E(f333(f333(f79(a875),f333(f106(a875),x56091)),f77(a875)),f77(a875))+~P1(f333(f333(f248(a1),x56091),a82)) % 183.90/184.43 [5619]~P38(x56191)+E(f333(f37(a875),f333(f312(a1,a875,a107),x56191)),f333(f37(a1),x56191)) % 183.90/184.43 [5650]~P106(x56501)+E(f249(x56501,f333(f7(x56501,x56501,a870),f247(x56501))),f246(x56501)) % 183.90/184.43 [5651]~P106(x56511)+E(f250(x56511,f333(f7(x56511,x56511,a870),f247(x56511))),f245(x56511)) % 183.90/184.43 [5661]E(f44(a875,f333(a115,f2(a875)),f333(f106(a875),x56611)),f333(a115,f2(a875)))+~P1(f333(a201,f333(f106(a1),x56611))) % 183.90/184.43 [5670]P1(f333(f333(f248(a1),f2(a1)),x56701))+~P1(f333(f333(f247(a1),f77(a1)),x56701)) % 183.90/184.43 [5671]~P1(f333(f333(f248(a1),f2(a1)),x56711))+P1(f333(f333(f247(a1),f77(a1)),x56711)) % 183.90/184.43 [5682]E(f333(a115,f333(f333(f22(a875),x56821),f77(a875))),x56821)+~P1(f333(f333(f248(a875),f2(a875)),x56821)) % 183.90/184.43 [5738]P1(f333(f333(f248(a875),f2(a875)),f407(x57381)))+~P1(f333(f333(f248(a1),f2(a1)),x57381)) % 183.90/184.43 [5797]E(f44(a1,f333(f106(a1),a100),x57971),f333(f333(f22(a1),x57971),f77(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x57971)) % 183.90/184.43 [5831]~P1(f333(f333(f248(a1),a82),x58311))+P1(f333(f333(f248(a875),f2(a875)),f333(f106(a875),x58311))) % 183.90/184.43 [5881]P1(f333(f333(f248(a875),f2(a875)),f333(a107,x58811)))+~P1(f333(f333(f248(a1),f2(a1)),x58811)) % 183.90/184.43 [5931]~P1(f333(f333(f248(a875),f2(a875)),x59311))+P1(f333(f333(f248(a1),f2(a1)),f333(f103(a1),x59311))) % 183.90/184.43 [5969]~P1(f333(f333(f248(a875),f2(a875)),f333(a107,x59691)))+P1(f333(f333(f248(a1),f2(a1)),x59691)) % 183.90/184.43 [5984]~P38(x59841)+E(f333(f312(a875,a1,f103(a1)),f333(f312(a1,a875,a107),x59841)),x59841) % 183.90/184.43 [5995]P1(f333(f333(f248(a1),a82),x59951))+~P1(f333(f333(f248(a875),f2(a875)),f333(f106(a875),x59951))) % 183.90/184.43 [6043]~P57(x60431)+E(f333(f333(f152(f879(x60431)),f209(x60431)),f333(f333(f155(x60431,f879(x60431)),f240(x60431)),f55(x60431))),f55(f879(x60431))) % 183.90/184.43 [6054]P1(f333(f333(f248(a875),f2(a875)),x60541))+~P1(f333(f333(f248(a1),f2(a1)),f333(f103(a1),x60541))) % 183.90/184.43 [6163]E(f333(f312(a875,a1,f103(a1)),f333(f254(a875),f333(a107,x61631))),f333(f303(a1,f2(a1)),x61631))+~P1(f333(f333(f247(a1),f2(a1)),x61631)) % 183.90/184.43 [6179]~P120(x61791)+P1(f333(f333(f248(x61791),f2(x61791)),f333(f333(f79(x61791),f77(x61791)),f77(x61791)))) % 183.90/184.43 [6230]P1(f333(f333(f248(a875),f333(a115,f2(a875))),f333(a107,x62301)))+~P1(f333(f333(f248(a1),f77(a1)),x62301)) % 183.90/184.43 [6325]E(x63251,f2(a1))+P1(f333(f48(f2(a1),x63251),f333(f333(f268(a1,a1),f2(a1)),f2(a1)))) % 183.90/184.43 [6489]~P1(f333(f333(f248(a875),f333(a115,f2(a875))),f333(a107,x64891)))+P1(f333(f333(f248(a1),f77(a1)),x64891)) % 183.90/184.43 [6918]~P112(x69181)+P37(x69181,f333(f253(f881(x69181,x69181)),f333(f272(x69181,x69181,a870),f248(x69181)))) % 183.90/184.43 [5556]E(f333(f106(a875),f333(f333(f22(a1),x55561),a100)),f333(a115,f333(f106(a875),x55561)))+P1(f333(a201,f333(f106(a1),x55561))) % 183.90/184.43 [5572]~P36(x55721)+E(f333(f333(f155(a875,a1),f103(a1)),f333(f333(f155(a1,a875),a107),x55721)),x55721) % 183.90/184.43 [5688]E(f333(f78(a1),f333(f103(a1),f333(a115,f486(x56881)))),x56881)+~P1(f333(f333(f248(a1),x56881),f2(a1))) % 183.90/184.43 [5698]E(f333(f333(f79(a875),f77(a875)),f333(f106(a875),x56981)),f333(f106(a875),f333(f333(f22(a1),x56981),a100)))+P1(f333(f333(f248(a1),x56981),a82)) % 183.90/184.43 [5740]E(f333(f333(f38(a1),f333(f106(a1),a100)),x57401),f333(f106(a1),a100))+~P1(f333(f333(f248(a1),f2(a1)),x57401)) % 183.90/184.43 [5827]E(f333(f333(f22(a875),f333(f106(a875),x58271)),f77(a875)),f333(f106(a875),f333(f333(f79(a1),x58271),a100)))+P1(f333(f333(f247(a1),x58271),a82)) % 183.90/184.43 [5828]E(f333(f333(f79(a875),f333(f106(a875),x58281)),f77(a875)),f333(f106(a875),f333(f333(f22(a1),x58281),a100)))+P1(f333(f333(f248(a1),x58281),a82)) % 183.90/184.43 [5869]E(f333(a107,f333(f333(f79(a1),f77(a1)),x58691)),f333(a115,f333(a107,x58691)))+~P1(f333(f333(f247(a1),f2(a1)),x58691)) % 183.90/184.43 [5903]E(f333(a115,f333(f333(f22(a875),x59031),f333(a115,f2(a875)))),x59031)+~P1(f333(f333(f248(a875),f2(a875)),x59031)) % 183.90/184.43 [6114]E(f44(a875,f333(a115,f2(a875)),f333(f106(a875),x61141)),f333(a107,f44(a1,f77(a1),f333(f106(a1),x61141))))+P1(f333(a201,f333(f106(a1),x61141))) % 183.90/184.43 [6153]~P1(f333(f333(f248(a1),a82),x61531))+P1(f333(f333(f248(a1),a82),f333(f333(f79(a1),x61531),x61531))) % 183.90/184.43 [6154]~P1(f333(f333(f248(a1),a100),x61541))+P1(f333(f333(f248(a1),a100),f333(f333(f79(a1),x61541),x61541))) % 183.90/184.43 [6155]~P1(f333(f333(f247(a1),a82),x61551))+P1(f333(f333(f247(a1),a82),f333(f333(f79(a1),x61551),x61551))) % 183.90/184.43 [6156]~P1(f333(f333(f248(a1),a100),x61561))+P1(f333(f333(f247(a1),a100),f333(f333(f79(a1),x61561),x61561))) % 183.90/184.43 [6157]~P1(f333(f333(f90(a1),a82),x61571))+P1(f333(f333(f90(a1),a82),f333(f333(f79(a1),x61571),x61571))) % 183.90/184.43 [6338]~P1(f333(f61(x63381),f256(f882(x63381,a870))))+P1(f333(f61(f879(x63381)),f256(f882(f879(x63381),a870)))) % 183.90/184.43 [6423]~P1(f333(f333(f247(a1),f2(a1)),x64231))+P1(f333(f333(f248(a1),f2(a1)),f333(f333(f79(a1),f77(a1)),x64231))) % 183.90/184.43 [6430]E(f333(f267(a1,a1),f46(f77(a1),f333(f106(a1),x64301))),f333(f333(f38(a1),f77(a1)),f333(f106(a1),x64301)))+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x64301))) % 183.90/184.43 [6450]E(f333(f271(a1,a1),f46(f77(a1),f333(f106(a1),x64501))),f44(a1,f77(a1),f333(f106(a1),x64501)))+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x64501))) % 183.90/184.43 [6461]P1(f333(f61(x64611),f256(f882(x64611,a870))))+~P1(f333(f61(f879(x64611)),f256(f882(f879(x64611),a870)))) % 183.90/184.43 [6490]P1(f333(f333(f248(a1),a82),x64901))+~P1(f333(f333(f248(a1),a82),f333(f333(f79(a1),x64901),x64901))) % 183.90/184.43 [6491]P1(f333(f333(f248(a1),a100),x64911))+~P1(f333(f333(f248(a1),a100),f333(f333(f79(a1),x64911),x64911))) % 183.90/184.43 [6492]P1(f333(f333(f248(a1),a100),x64921))+~P1(f333(f333(f247(a1),a100),f333(f333(f79(a1),x64921),x64921))) % 183.90/184.43 [6493]P1(f333(f333(f247(a1),a82),x64931))+~P1(f333(f333(f247(a1),a82),f333(f333(f79(a1),x64931),x64931))) % 183.90/184.43 [6494]P1(f333(f333(f90(a1),a82),x64941))+~P1(f333(f333(f90(a1),a82),f333(f333(f79(a1),x64941),x64941))) % 183.90/184.43 [6810]~P1(f333(f61(x68101),f256(f882(x68101,a870))))+P1(f333(f333(f248(a875),f2(a875)),f333(f37(x68101),f256(f882(x68101,a870))))) % 183.90/184.43 [7397]P1(f333(f61(a875),x73971))+~P1(f333(f61(a1),f333(f312(a875,a1,f103(a1)),x73971))) % 183.90/184.43 [8806]P24(a872,a883,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),a330),f333(a25,x88061)),f202(f333(a25,x88061)))),f196(f882(f874(a872),a870))))+~P1(f333(f333(f335(a873),x88061),f186(a873,a871,a27))) % 183.90/184.43 [5484]~E(a100,x54841)+E(f333(f333(f22(a1),f333(f333(f79(a1),x54841),x54841)),a100),a100) % 183.90/184.43 [5485]~E(x54851,a100)+E(f333(f333(f22(a1),f333(f333(f79(a1),x54851),x54851)),a100),a100) % 183.90/184.43 [5990]E(x59901,a100)+~E(f333(f333(f22(a1),f333(f333(f79(a1),x59901),x59901)),a100),a100) % 183.90/184.43 [5991]E(a100,x59911)+~E(f333(f333(f22(a1),f333(f333(f79(a1),x59911),x59911)),a100),a100) % 183.90/184.43 [6392]~E(f333(f106(a875),x63921),f2(a875))+P1(f333(a201,f333(f106(a1),f333(f333(f79(a1),x63921),a100)))) % 183.90/184.43 [6736]~P1(f333(a201,f333(f106(a1),x67361)))+P1(f333(a201,f333(f106(a1),f333(f333(f79(a1),x67361),x67361)))) % 183.90/184.43 [6737]~P1(f333(f333(f248(a1),x67371),a82))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x67371),x67371)),a82)) % 183.90/184.43 [6738]~P1(f333(f333(f247(a1),x67381),a100))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x67381),x67381)),a100)) % 183.90/184.43 [6739]~P1(f333(f333(f247(a1),x67391),a82))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x67391),x67391)),a82)) % 183.90/184.43 [6740]~P1(f333(f333(f247(a1),x67401),a100))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x67401),x67401)),a100)) % 183.90/184.43 [6741]~P1(f333(f333(f90(a1),x67411),a82))+P1(f333(f333(f90(a1),f333(f333(f79(a1),x67411),x67411)),a82)) % 183.90/184.43 [7065]E(f333(f106(a875),x70651),f2(a875))+~P1(f333(a201,f333(f106(a1),f333(f333(f79(a1),x70651),a100)))) % 183.90/184.43 [7304]~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x73041)))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),f333(f333(f79(a1),x73041),x73041)))) % 183.90/184.43 [7305]P1(f333(a201,f333(f106(a1),x73051)))+~P1(f333(a201,f333(f106(a1),f333(f333(f79(a1),x73051),x73051)))) % 183.90/184.43 [7306]P1(f333(f333(f248(a1),x73061),a82))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x73061),x73061)),a82)) % 183.90/184.43 [7307]P1(f333(f333(f247(a1),x73071),a82))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x73071),x73071)),a82)) % 183.90/184.43 [7308]P1(f333(f333(f247(a1),x73081),a100))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x73081),x73081)),a100)) % 183.90/184.43 [7309]P1(f333(f333(f247(a1),x73091),a100))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x73091),x73091)),a100)) % 183.90/184.43 [7310]P1(f333(f333(f90(a1),x73101),a82))+~P1(f333(f333(f90(a1),f333(f333(f79(a1),x73101),x73101)),a82)) % 183.90/184.43 [7681]E(f333(a109,f589(x76811)),x76811)+~P1(f333(f333(f335(f882(f881(a875,a875),a870)),x76811),a101)) % 183.90/184.43 [6311]~P90(x63111)+E(f333(f106(x63111),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f77(x63111)) % 183.90/184.43 [6788]~P1(f333(a201,f333(f106(a1),x67881)))+E(f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x67881),x67881)),a100)),f2(a875)) % 183.90/184.43 [7862]~P1(f333(f333(f248(a1),f333(f106(a1),x78621)),f2(a1)))+E(f333(f267(a1,a1),f333(a50,f49(f333(f78(a1),f77(a1)),f333(f78(a1),f333(f106(a1),x78621))))),f333(f333(f38(a1),f77(a1)),f333(f106(a1),x78621))) % 183.90/184.43 [7875]~P1(f333(f333(f248(a1),f333(f106(a1),x78751)),f2(a1)))+E(f333(f271(a1,a1),f333(a50,f49(f333(f78(a1),f77(a1)),f333(f78(a1),f333(f106(a1),x78751))))),f44(a1,f77(a1),f333(f106(a1),x78751))) % 183.90/184.43 [7923]~P1(f333(f333(f247(a1),a82),x79231))+P1(f333(f333(f248(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x79231),x79231)),a100))) % 183.90/184.43 [7924]~P1(f333(f333(f248(a1),a100),x79241))+P1(f333(f333(f248(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x79241),x79241)),a100))) % 183.90/184.43 [7925]~P1(f333(f333(f247(a1),a82),x79251))+P1(f333(f333(f247(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x79251),x79251)),a100))) % 183.90/184.43 [7926]~P1(f333(f333(f247(a1),a100),x79261))+P1(f333(f333(f247(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x79261),x79261)),a100))) % 183.90/184.43 [7927]~P1(f333(f333(f90(a1),a100),x79271))+P1(f333(f333(f90(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x79271),x79271)),a100))) % 183.90/184.43 [8237]~P90(x82371)+~P30(x82371,f333(f106(x82371),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))) % 183.90/184.43 [8418]P1(f333(f333(f248(a1),a100),x84181))+~P1(f333(f333(f248(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x84181),x84181)),a100))) % 183.90/184.43 [8419]P1(f333(f333(f247(a1),a82),x84191))+~P1(f333(f333(f248(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x84191),x84191)),a100))) % 183.90/184.43 [8420]P1(f333(f333(f247(a1),a82),x84201))+~P1(f333(f333(f247(a1),a82),f333(f333(f22(a1),f333(f333(f79(a1),x84201),x84201)),a100))) % 183.90/184.43 [8421]P1(f333(f333(f247(a1),a100),x84211))+~P1(f333(f333(f247(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x84211),x84211)),a100))) % 183.90/184.43 [8422]P1(f333(f333(f90(a1),a100),x84221))+~P1(f333(f333(f90(a1),a100),f333(f333(f22(a1),f333(f333(f79(a1),x84221),x84221)),a100))) % 183.90/184.43 [8731]E(f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x87311),x87311)),a100)),f333(f333(f85(a875,a875),f333(f106(a875),x87311)),f333(f333(f8(a875,a875,a875),a115),f333(f333(f18(a875,a875,a875),f79(a875)),f5(a875)))))+P1(f333(a201,f333(f106(a1),x87311))) % 183.90/184.43 [9577]E(x95771,f196(f882(f881(a875,a875),a870)))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x95771),f196(f882(f881(a875,a875),a870)))),a35)) % 183.90/184.43 [8662]~P1(f333(a201,f333(f106(a1),x86621)))+P1(f333(a201,f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86621),x86621)),a100)))) % 183.90/184.43 [8663]~P1(f333(f333(f248(a1),x86631),a82))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86631),x86631)),a100)),a82)) % 183.90/184.43 [8664]~P1(f333(f333(f248(a1),x86641),a100))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86641),x86641)),a100)),a100)) % 183.90/184.43 [8665]~P1(f333(f333(f248(a1),x86651),a82))+P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86651),x86651)),a100)),a82)) % 183.90/184.43 [8666]~P1(f333(f333(f247(a1),x86661),a100))+P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86661),x86661)),a100)),a100)) % 183.90/184.43 [8667]~P1(f333(f333(f90(a1),x86671),a100))+P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x86671),x86671)),a100)),a100)) % 183.90/184.43 [8766]~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x87661)))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x87661),x87661)),a100)))) % 183.90/184.43 [8928]~P90(x89281)+E(f333(f333(f79(x89281),f77(x89281)),f77(x89281)),f333(f106(x89281),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))) % 183.90/184.43 [9083]P1(f333(a201,f333(f106(a1),x90831)))+~P1(f333(a201,f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90831),x90831)),a100)))) % 183.90/184.43 [9084]P1(f333(f333(f248(a1),x90841),a82))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90841),x90841)),a100)),a82)) % 183.90/184.43 [9085]P1(f333(f333(f248(a1),x90851),a82))+~P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90851),x90851)),a100)),a82)) % 183.90/184.43 [9086]P1(f333(f333(f248(a1),x90861),a100))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90861),x90861)),a100)),a100)) % 183.90/184.43 [9087]P1(f333(f333(f247(a1),x90871),a100))+~P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90871),x90871)),a100)),a100)) % 183.90/184.43 [9088]P1(f333(f333(f90(a1),x90881),a100))+~P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90881),x90881)),a100)),a100)) % 183.90/184.43 [9623]~P1(f333(f61(f881(a875,a875)),x96231))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f196(f882(f881(a875,a875),a870))),x96231)),a68)) % 183.90/184.43 [9410]~P141(x94101)+E(f333(f333(f258(x94101),f77(x94101)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(x94101)) % 183.90/184.43 [9411]~P141(x94111)+E(f333(f333(f258(x94111),f2(x94111)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f2(x94111)) % 183.90/184.43 [9850]~P1(f333(f333(f248(a875),f77(a875)),x98501))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f38(a875),x98501),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.43 [9862]~P1(f333(f333(f248(a875),f2(a875)),x98621))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f38(a875),f333(f333(f79(a875),x98621),f77(a875))),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.43 [9904]~E(f44(a875,x99041,f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(a875))+P1(f333(f333(f248(a875),f2(a875)),f44(a875,x99041,f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.43 [9923]E(f44(a875,x99231,f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(a875))+~P1(f333(f333(f248(a875),f2(a875)),f44(a875,x99231,f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.43 [4623]~P37(x46231,x46232)+P52(x46231,x46232) % 183.90/184.43 [4624]~P43(x46241,x46242)+P52(x46241,x46242) % 183.90/184.43 [4585]~E(x45851,x45852)+E(f280(x45851,x45852),f77(a102)) % 183.90/184.43 [4588]E(f228(x45881,x45882),x45881)+~E(x45882,f2(a875)) % 183.90/184.43 [4595]~E(x45952,f116(x45951))+E(f153(x45951,x45952),f116(x45951)) % 183.90/184.43 [4614]~E(f153(x46142,x46141),f116(x46142))+E(x46141,f116(x46142)) % 183.90/184.43 [4628]~P2(x46282)+P2(f882(x46281,x46282)) % 183.90/184.43 [4629]~P62(x46292)+P62(f882(x46291,x46292)) % 183.90/184.43 [4630]~P95(x46302)+P63(f882(x46301,x46302)) % 183.90/184.43 [4631]~P62(x46312)+P98(f882(x46311,x46312)) % 183.90/184.43 [4632]~P62(x46322)+P99(f882(x46321,x46322)) % 183.90/184.43 [4633]~P64(x46332)+P64(f882(x46331,x46332)) % 183.90/184.43 [4634]~P96(x46342)+P96(f882(x46341,x46342)) % 183.90/184.43 [4635]~P4(x46352)+P4(f882(x46351,x46352)) % 183.90/184.43 [4636]~P104(x46362)+P104(f882(x46361,x46362)) % 183.90/184.43 [4637]~P95(x46372)+P97(f882(x46371,x46372)) % 183.90/184.43 [4638]~P105(x46382)+P105(f882(x46381,x46382)) % 183.90/184.43 [4639]~P107(x46392)+P107(f882(x46391,x46392)) % 183.90/184.43 [4640]~P108(x46402)+P108(f882(x46401,x46402)) % 183.90/184.43 [4641]~P86(x46412)+P86(f882(x46411,x46412)) % 183.90/184.43 [4642]~P93(x46422)+P93(f882(x46421,x46422)) % 183.90/184.43 [4643]~P95(x46432)+P95(f882(x46431,x46432)) % 183.90/184.43 [4655]E(x46551,x46552)+~E(f333(a25,x46551),f333(a25,x46552)) % 183.90/184.43 [4657]E(x46571,x46572)+~E(f333(a115,x46571),f333(a115,x46572)) % 183.90/184.43 [4658]E(x46581,x46582)+~E(f333(a109,x46581),f333(a109,x46582)) % 183.90/184.43 [4659]E(x46591,x46592)+~E(f333(a3,x46591),f333(a3,x46592)) % 183.90/184.43 [4661]E(x46611,x46612)+~E(f333(a19,x46611),f333(a19,x46612)) % 183.90/184.43 [4765]~P55(x47651)+E(f44(x47651,x47652,x47652),f2(x47651)) % 183.90/184.43 [4799]~P37(x47991,x47992)+P37(f876(x47991),f147(x47991,x47992)) % 183.90/184.43 [4800]~P37(x48001,x48002)+P37(f876(x48001),f146(x48001,x48002)) % 183.90/184.43 [4896]~P37(x48961,x48962)+P37(f882(x48961,a870),f324(x48961,x48962)) % 183.90/184.43 [4897]~P37(x48971,x48972)+P37(f882(x48971,a870),f325(x48971,x48972)) % 183.90/184.43 [5016]~P5(x50161)+P38(f304(a1,x50161,x50162)) % 183.90/184.43 [5116]~P37(x51161,x51162)+P54(x51161,f67(x51161,x51161,x51162)) % 183.90/184.43 [5613]~P82(x56131)+P25(x56131,x56131,f78(x56131),x56132) % 183.90/184.43 [4609]~E(x46092,f116(x46091))+E(f333(f169(x46091),x46092),f116(x46091)) % 183.90/184.43 [4610]~E(x46102,f116(x46101))+E(f333(f170(x46101),x46102),f116(x46101)) % 183.90/184.43 [4665]E(x46651,f333(a107,x46652))+~E(f333(f103(a1),x46651),x46652) % 183.90/184.43 [4668]E(x46681,f116(x46682))+~E(f333(f169(x46682),x46681),f116(x46682)) % 183.90/184.43 [4669]E(x46691,f116(x46692))+~E(f333(f170(x46692),x46691),f116(x46692)) % 183.90/184.43 [4687]~P90(x46871)+E(f333(f106(x46871),x46872),f333(f105(x46871),x46872)) % 183.90/184.43 [4694]~E(x46942,f209(x46941))+E(f239(x46941,x46942),f196(f882(x46941,a870))) % 183.90/184.43 [4696]~P3(x46961)+P1(f333(f61(x46961),x46962)) % 183.90/184.43 [4703]E(x47031,f209(x47032))+E(f333(f240(x47032),f685(x47032,x47031)),x47031) % 183.90/184.43 [4704]E(x47041,f209(x47042))+E(f333(f240(x47042),f716(x47042,x47041)),x47041) % 183.90/184.43 [4706]~E(f717(x47062,x47061),f116(x47061))+E(f182(x47061,x47062),f116(f876(x47061))) % 183.90/184.43 [4715]~E(x47152,f116(x47151))+E(f333(f174(x47151),x47152),f196(f882(x47151,a870))) % 183.90/184.43 [4716]~E(x47162,f116(x47161))+E(f196(f882(x47161,a870)),f333(f174(x47161),x47162)) % 183.90/184.43 [4718]E(x47181,x47182)+~E(f333(f103(a1),x47181),f333(f103(a1),x47182)) % 183.90/184.43 [4721]E(f226(x47211,x47212),f2(a875))+P1(f333(f61(x47211),x47212)) % 183.90/184.43 [4741]~P114(x47411)+E(f81(x47411,f81(x47411,x47412)),f81(x47411,x47412)) % 183.90/184.43 [4754]~P109(x47541)+E(f333(f333(f258(x47541),x47542),f77(a875)),x47542) % 183.90/184.43 [4755]~P77(x47551)+E(f333(f333(f258(x47551),x47552),f77(a875)),x47552) % 183.90/184.43 [4759]E(x47591,x47592)+E(f280(x47591,x47592),f333(f333(f79(a102),x47592),f77(a102))) % 183.90/184.43 [4762]E(f333(f37(x47621),x47622),f2(a875))+P1(f333(f61(x47621),x47622)) % 183.90/184.43 [4766]~E(f153(x47661,x47662),x47662)+P1(f333(f138(x47661),x47662)) % 183.90/184.43 [4769]~P63(x47691)+E(f333(f333(f113(x47691),x47692),f196(x47691)),x47692) % 183.90/184.43 [4770]~P72(x47701)+E(f333(f333(f22(x47701),x47702),f2(x47701)),x47702) % 183.90/184.43 [4771]~P97(x47711)+E(f333(f333(f104(x47711),x47712),f256(x47711)),x47712) % 183.90/184.43 [4772]~P66(x47721)+E(f333(f333(f79(x47721),x47722),f2(x47721)),x47722) % 183.90/184.43 [4773]~P109(x47731)+E(f333(f333(f79(x47731),x47732),f2(x47731)),x47732) % 183.90/184.43 [4774]~P78(x47741)+E(f333(f333(f79(x47741),x47742),f2(x47741)),x47742) % 183.90/184.43 [4775]~P109(x47751)+E(f333(f333(f80(x47751),x47752),f77(x47751)),x47752) % 183.90/184.43 [4776]~P73(x47761)+E(f333(f333(f80(x47761),x47762),f77(x47761)),x47762) % 183.90/184.43 [4777]~P77(x47771)+E(f333(f333(f80(x47771),x47772),f77(x47771)),x47772) % 183.90/184.43 [4778]~P55(x47781)+E(f333(f333(f38(x47781),x47782),f77(x47781)),x47782) % 183.90/184.43 [4779]~P117(x47791)+E(f333(f333(f291(x47791),x47792),f77(x47791)),x47792) % 183.90/184.43 [4780]~P109(x47801)+E(f333(f333(f258(x47801),x47802),f2(a875)),f77(x47801)) % 183.90/184.43 [4781]~P111(x47811)+E(f333(f333(f258(x47811),x47812),f2(a875)),f77(x47811)) % 183.90/184.43 [4782]~E(x47822,f196(f882(x47821,a870)))+E(f333(f37(x47821),x47822),f2(a875)) % 183.90/184.43 [4793]~P55(x47931)+E(f44(x47931,x47932,f2(x47931)),x47932) % 183.90/184.43 [4801]~P97(x48011)+E(f333(f333(f113(x48011),x48012),f256(x48011)),f256(x48011)) % 183.90/184.43 [4802]~P63(x48021)+E(f333(f333(f104(x48021),x48022),f196(x48021)),f196(x48021)) % 183.90/184.43 [4803]~P109(x48031)+E(f333(f333(f80(x48031),x48032),f2(x48031)),f2(x48031)) % 183.90/184.43 [4804]~P124(x48041)+E(f333(f333(f80(x48041),x48042),f2(x48041)),f2(x48041)) % 183.90/184.43 [4805]~P55(x48051)+E(f333(f333(f38(x48051),x48052),f2(x48051)),f2(x48051)) % 183.90/184.43 [4806]~P118(x48061)+E(f333(f333(f291(x48061),x48062),f2(x48061)),f2(x48061)) % 183.90/184.43 [4807]E(x48071,f209(x48072))+~E(f239(x48072,x48071),f196(f882(x48072,a870))) % 183.90/184.43 [4810]~P55(x48101)+E(f44(x48101,x48102,f77(x48101)),f2(x48101)) % 183.90/184.43 [4811]~P55(x48111)+E(f44(x48111,f2(x48111),x48112),f2(x48111)) % 183.90/184.43 [4840]E(x48401,f2(a875))+E(f54(x48402,x48401,f116(x48402)),f116(f876(x48402))) % 183.90/184.43 [4863]P37(x48631,x48632)+~E(f599(x48632,x48631),f196(f882(x48631,a870))) % 183.90/184.43 [4864]E(x48641,f116(x48642))+~E(f333(f174(x48642),x48641),f196(f882(x48642,a870))) % 183.90/184.43 [4865]E(x48651,f116(x48652))+~E(f196(f882(x48652,a870)),f333(f174(x48652),x48651)) % 183.90/184.43 [4868]~E(x48681,x48682)+P1(f333(f333(a330,x48681),x48682)) % 183.90/184.43 [4878]P1(x48781)+P1(f333(f333(a336,x48781),x48782)) % 183.90/184.43 [4879]E(x48791,f116(x48792))+E(f333(f333(f166(x48792),x48791),f2(a875)),f333(f142(x48792),x48791)) % 183.90/184.43 [4882]E(f153(x48821,x48822),x48822)+~P1(f333(f138(x48821),x48822)) % 183.90/184.43 [4887]~P1(x48872)+P1(f333(f333(a336,x48871),x48872)) % 183.90/184.43 [4888]~P1(x48882)+P1(f333(f333(a332,x48881),x48882)) % 183.90/184.43 [4889]~P1(x48891)+P1(f333(f333(a332,x48891),x48892)) % 183.90/184.43 [4899]~E(f686(x48992,x48991),f690(x48992,x48991))+P1(f333(f138(x48991),x48992)) % 183.90/184.43 [4906]E(f333(f253(x49061),x49062),f196(f882(x49061,a870)))+P1(f333(x49062,f339(x49062))) % 183.90/184.43 [4907]E(f196(f882(x49071,a870)),f333(f253(x49071),x49072))+P1(f333(x49072,f340(x49072))) % 183.90/184.43 [4973]~P114(x49731)+E(f333(f333(f80(x49731),x49732),f81(x49731,x49732)),f333(f74(x49731),x49732)) % 183.90/184.43 [4984]~E(x49841,f2(a1))+E(f45(x49841,x49842),f333(f333(f268(a1,a1),f2(a1)),f2(a1))) % 183.90/184.43 [5015]~P52(x50151,x50152)+P52(x50151,f333(f288(x50151,x50151),x50152)) % 183.90/184.43 [5038]E(x50381,x50382)+~P1(f333(f333(a330,x50381),x50382)) % 183.90/184.43 [5049]P1(x50491)+~P1(f333(f333(a331,x50492),x50491)) % 183.90/184.43 [5050]P1(x50501)+~P1(f333(f333(a331,x50501),x50502)) % 183.90/184.43 [5055]~P104(x50551)+P1(f333(f333(f247(x50551),x50552),f256(x50551))) % 183.90/184.43 [5059]E(x50591,x50592)+~E(f333(x50591,f406(x50592,x50591)),f333(x50592,f406(x50592,x50591))) % 183.90/184.43 [5089]E(x50891,f2(a875))+E(f228(x50891,f44(a875,x50892,x50891)),f228(x50892,x50891)) % 183.90/184.43 [5094]~P106(x50941)+P14(x50941,f333(f333(f152(x50941),x50942),f116(x50941))) % 183.90/184.43 [5096]E(x50961,f2(a1))+P1(f333(f48(x50962,x50961),f45(x50962,x50961))) % 183.90/184.43 [5114]~E(x51141,x51142)+P1(f333(f333(f248(a875),x51141),f333(a115,x51142))) % 183.90/184.43 [5124]~E(x51241,f2(a875))+P1(f333(f333(f248(a875),x51241),f333(a115,x51242))) % 183.90/184.43 [5134]P1(f333(x51341,x51342))+P1(f333(f333(f247(a1),f2(a1)),f401(x51341))) % 183.90/184.43 [5199]P52(x51991,x51992)+~P52(x51991,f333(f288(x51991,x51991),x51992)) % 183.90/184.43 [5203]~E(f44(a875,x52032,x52031),f2(a875))+E(f333(f333(f80(a875),x52031),f452(x52031,x52032)),x52032) % 183.90/184.43 [5204]~E(f44(a1,x52042,x52041),f2(a1))+E(f333(f333(f80(a1),x52041),f453(x52041,x52042)),x52042) % 183.90/184.43 [5229]~P1(f333(x52291,x52292))+P1(f333(f333(f247(a1),f2(a1)),f373(x52291))) % 183.90/184.43 [5241]E(f333(f333(f22(a875),f333(a107,x52411)),f333(a107,x52412)),f333(a107,x52411))+~P1(f333(a201,x52412)) % 183.90/184.43 [5271]E(f281(x52711,x52712),f77(a102))+~P1(f333(f333(f247(a102),x52711),f77(a102))) % 183.90/184.43 [5366]E(f333(f333(f166(x53661),x53662),f686(x53662,x53661)),f333(f333(f166(x53661),x53662),f690(x53662,x53661)))+P1(f333(f138(x53661),x53662)) % 183.90/184.43 [5411]~P1(f333(x54111,f89(x54112,x54111)))+P1(f333(x54111,f612(x54112,x54111))) % 183.90/184.43 [5474]P54(x54741,x54742)+~P1(f333(f321(x54741,x54742),f576(x54742,x54741))) % 183.90/184.43 [5620]~E(f333(a115,f44(a875,x56201,x56202)),x56202)+E(f44(a875,f333(a115,x56201),x56202),f2(a875)) % 183.90/184.43 [5677]P37(x56771,x56772)+P1(f333(f333(f335(x56771),f629(x56772,x56771)),f630(x56772,x56771))) % 183.90/184.43 [5684]~P138(x56841)+P1(f333(f333(f335(x56841),f333(f103(x56841),x56842)),f112(x56841))) % 183.90/184.43 [5685]~P141(x56851)+P1(f333(f333(f335(x56851),f333(f103(x56851),x56852)),f194(x56851))) % 183.90/184.43 [5686]~P138(x56861)+P1(f333(f333(f335(x56861),f333(f105(x56861),x56862)),f112(x56861))) % 183.90/184.43 [5687]~P90(x56871)+P1(f333(f333(f335(x56871),f333(f106(x56871),x56872)),f112(x56871))) % 183.90/184.43 [5830]E(f333(a115,f44(a875,x58301,x58302)),x58302)+E(f44(a875,f333(a115,x58301),x58302),f333(a115,f44(a875,x58301,x58302))) % 183.90/184.43 [6242]P37(x62421,x62422)+~P1(f333(f333(f335(x62421),f559(x62422,x62421)),f322(x62421,x62422))) % 183.90/184.43 [6277]~P120(x62771)+~P1(f333(f333(f248(x62771),f333(f103(x62771),x62772)),f2(x62771))) % 183.90/184.43 [6278]~P83(x62781)+~P1(f333(f333(f248(x62781),f333(f74(x62781),x62782)),f2(x62781))) % 183.90/184.43 [6365]P1(f333(f333(f248(a1),x63651),f44(a1,x63652,x63651)))+~P1(f333(f333(f248(a1),x63651),f2(a1))) % 183.90/184.43 [6463]E(f333(f333(f311(a875),f333(a115,x64631)),f304(a875,x64632,x64631)),f304(a875,x64632,f333(a115,x64631)))+~P1(f333(f333(f247(a875),x64632),f333(a115,x64631))) % 183.90/184.43 [6550]~P106(x65501)+P14(x65501,f151(x65501,x65501,f5(x65501),x65502)) % 183.90/184.43 [6680]E(f333(f169(x66801),x66802),x66802)+~P1(f333(f333(f247(a875),f333(f197(f876(x66801)),x66802)),f77(a875))) % 183.90/184.43 [6700]~P83(x67001)+P1(f333(f333(f247(x67001),f333(f78(x67001),f333(f74(x67001),x67002))),f2(x67001))) % 183.90/184.43 [6733]~P37(x67331,x67332)+P37(x67331,f333(f333(f290(x67331,x67331,x67331),x67332),f309(x67331,x67332))) % 183.90/184.43 [6956]~P1(f333(f333(f248(a1),x69562),f2(a1)))+P1(f333(f333(f247(a1),f44(a1,x69561,x69562)),f2(a1))) % 183.90/184.43 [7352]~P141(x73521)+E(f198(x73521,f333(f333(f7(x73521,x73521,x73521),f79(x73521)),f77(x73521)),x73522,f2(x73521)),f333(f103(x73521),x73522)) % 183.90/184.43 [7380]~P121(x73801)+~P1(f333(f333(f248(x73801),f333(f333(f80(x73801),x73802),x73802)),f2(x73801))) % 183.90/184.43 [10013]~P114(x100131)+~P1(f333(f333(f248(x100131),f333(f333(f258(x100131),x100132),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f2(x100131))) % 183.90/184.43 [4666]~E(x46662,f116(x46661))+E(f333(f197(f876(x46661)),x46662),f2(a875)) % 183.90/184.43 [4707]~E(x47071,f2(a875))+E(f333(f333(f79(a875),x47071),x47072),x47072) % 183.90/184.43 [4708]~E(x47082,f2(a875))+E(f333(f333(f80(a875),x47081),x47082),f2(a875)) % 183.90/184.43 [4710]~E(x47101,f2(a875))+E(f333(f333(f80(a875),x47101),x47102),f2(a875)) % 183.90/184.43 [4711]~E(x47112,f2(a875))+E(f333(f333(f258(a875),x47111),x47112),f77(a875)) % 183.90/184.43 [4712]~E(x47122,f2(a1))+E(f333(f333(f38(a1),x47121),x47122),f2(a1)) % 183.90/184.43 [4722]E(x47221,f116(x47222))+~E(f333(f197(f876(x47222)),x47221),f2(a875)) % 183.90/184.43 [4723]~P62(x47231)+E(f333(f333(f113(x47231),x47232),x47232),x47232) % 183.90/184.43 [4725]~P98(x47251)+E(f333(f333(f113(x47251),x47252),x47252),x47252) % 183.90/184.43 [4726]~P62(x47261)+E(f333(f333(f104(x47261),x47262),x47262),x47262) % 183.90/184.43 [4728]~P99(x47281)+E(f333(f333(f104(x47281),x47282),x47282),x47282) % 183.90/184.43 [4730]~P94(x47301)+E(f333(f333(f80(x47301),x47302),x47302),x47302) % 183.90/184.43 [4732]~P106(x47321)+E(f333(f333(f245(x47321),x47322),x47322),x47322) % 183.90/184.43 [4734]~P106(x47341)+E(f333(f333(f246(x47341),x47342),x47342),x47342) % 183.90/184.43 [4753]~P72(x47531)+E(f333(f333(f22(x47531),x47532),x47532),f2(x47531)) % 183.90/184.43 [4767]~P72(x47671)+E(f333(f78(x47671),f333(f78(x47671),x47672)),x47672) % 183.90/184.43 [4768]~P93(x47681)+E(f333(f78(x47681),f333(f78(x47681),x47682)),x47682) % 183.90/184.43 [4785]~E(x47852,f2(a875))+E(f333(f333(f258(a875),x47851),x47852),f333(a115,f2(a875))) % 183.90/184.43 [4819]~P63(x48191)+E(f333(f333(f113(x48191),f196(x48191)),x48192),x48192) % 183.90/184.43 [4820]~P97(x48201)+E(f333(f333(f104(x48201),f256(x48201)),x48202),x48202) % 183.90/184.43 [4821]~P66(x48211)+E(f333(f333(f79(x48211),f2(x48211)),x48212),x48212) % 183.90/184.43 [4822]~P109(x48221)+E(f333(f333(f79(x48221),f2(x48221)),x48222),x48222) % 183.90/184.43 [4823]~P78(x48231)+E(f333(f333(f79(x48231),f2(x48231)),x48232),x48232) % 183.90/184.43 [4824]~P109(x48241)+E(f333(f333(f80(x48241),f77(x48241)),x48242),x48242) % 183.90/184.43 [4825]~P73(x48251)+E(f333(f333(f80(x48251),f77(x48251)),x48252),x48252) % 183.90/184.43 [4826]~P77(x48261)+E(f333(f333(f80(x48261),f77(x48261)),x48262),x48262) % 183.90/184.43 [4844]~P97(x48441)+E(f333(f333(f113(x48441),f256(x48441)),x48442),f256(x48441)) % 183.90/184.43 [4845]~P63(x48451)+E(f333(f333(f104(x48451),f196(x48451)),x48452),f196(x48451)) % 183.90/184.43 [4846]~P109(x48461)+E(f333(f333(f80(x48461),f2(x48461)),x48462),f2(x48461)) % 183.90/184.43 [4847]~P124(x48471)+E(f333(f333(f80(x48471),f2(x48471)),x48472),f2(x48471)) % 183.90/184.43 [4848]~P77(x48481)+E(f333(f333(f258(x48481),f77(x48481)),x48482),f77(x48481)) % 183.90/184.43 [4849]~P55(x48491)+E(f333(f333(f38(x48491),f2(x48491)),x48492),f2(x48491)) % 183.90/184.43 [4850]~P117(x48501)+E(f333(f333(f291(x48501),f2(x48501)),x48502),f2(x48501)) % 183.90/184.43 [4858]E(x48581,f116(x48582))+E(f145(x48582,f333(f170(x48582),x48581)),f333(f142(x48582),x48581)) % 183.90/184.43 [4859]E(x48591,f116(x48592))+E(f333(f142(x48592),f333(f170(x48592),x48591)),f145(x48592,x48591)) % 183.90/184.43 [4860]E(x48601,f2(a875))+~E(f333(f333(f79(a875),x48602),x48601),x48602) % 183.90/184.43 [4866]~P138(x48661)+E(f333(f105(x48661),f333(f103(a1),x48662)),f333(f103(x48661),x48662)) % 183.90/184.43 [4867]~P90(x48671)+E(f333(f105(x48671),f333(f106(a1),x48672)),f333(f106(x48671),x48672)) % 183.90/184.43 [4874]E(x48741,f77(a875))+~E(f333(f333(f80(a875),x48742),x48741),f77(a875)) % 183.90/184.43 [4875]E(x48751,f77(a875))+~E(f333(f333(f80(a875),x48751),x48752),f77(a875)) % 183.90/184.43 [4876]E(x48761,f2(a875))+~E(f333(f333(f79(a875),x48762),x48761),f2(a875)) % 183.90/184.43 [4877]E(x48771,f2(a875))+~E(f333(f333(f79(a875),x48771),x48772),f2(a875)) % 183.90/184.43 [4892]~P114(x48921)+E(f333(f74(x48921),f333(f103(x48921),x48922)),f333(f103(x48921),x48922)) % 183.90/184.43 [4893]~P83(x48931)+E(f333(f74(x48931),f333(f74(x48931),x48932)),f333(f74(x48931),x48932)) % 183.90/184.43 [4894]~P83(x48941)+E(f333(f74(x48941),f333(f78(x48941),x48942)),f333(f74(x48941),x48942)) % 183.90/184.43 [4895]~P66(x48951)+E(f333(f167(x48951),f333(f170(x48951),x48952)),f333(f167(x48951),x48952)) % 183.90/184.43 [4900]~E(x49001,f333(a115,f2(a875)))+E(f333(f333(f258(a875),x49001),x49002),f333(a115,f2(a875))) % 183.90/184.43 [4909]~P72(x49091)+E(f333(f333(f22(x49091),f2(x49091)),x49092),f333(f78(x49091),x49092)) % 183.90/184.43 [4910]~E(x49102,f2(a875))+E(f140(a875,f333(f303(a875,x49101),x49102)),f116(a875)) % 183.90/184.43 [4919]~P90(x49191)+E(f333(f333(f79(x49191),x49192),f333(f106(x49191),a82)),x49192) % 183.90/184.43 [4920]E(x49201,f2(a1))+E(f46(f333(f74(a1),x49202),f333(f74(a1),x49201)),f52(x49202,x49201)) % 183.90/184.43 [4936]~E(x49361,x49362)+P1(f333(f333(f247(a875),x49361),x49362)) % 183.90/184.43 [4943]~E(x49431,f2(a102))+E(f333(f333(f79(a875),f333(a19,x49431)),x49432),x49432) % 183.90/184.43 [4944]~E(f333(f106(a1),x49442),f333(f103(a1),x49441))+E(x49441,f333(a107,f333(f106(a1),x49442))) % 183.90/184.43 [4953]~P5(x49531)+P5(f333(f333(f258(a1),x49531),x49532)) % 183.90/184.43 [4954]~P93(x49541)+E(f333(f333(f113(x49541),x49542),f333(f78(x49541),x49542)),f256(x49541)) % 183.90/184.43 [4955]~P93(x49551)+E(f333(f333(f104(x49551),x49552),f333(f78(x49551),x49552)),f196(x49551)) % 183.90/184.43 [4956]~P72(x49561)+E(f333(f333(f79(x49561),x49562),f333(f78(x49561),x49562)),f2(x49561)) % 183.90/184.43 [4981]E(x49811,f2(a875))+~E(f333(f78(a1),f333(f103(a1),x49812)),f333(f103(a1),x49811)) % 183.90/184.43 [4982]E(x49821,f2(a875))+~E(f333(f78(a1),f333(f103(a1),x49821)),f333(f103(a1),x49822)) % 183.90/184.43 [4992]E(f203(x49921,x49922),f2(a1))+P1(f333(f333(f247(a1),x49922),x49921)) % 183.90/184.43 [4993]E(f181(x49931,x49932),f116(a1))+P1(f333(f333(f247(a1),x49931),x49932)) % 183.90/184.43 [5006]E(x50061,f333(a115,f2(a875)))+~E(f333(f333(f80(a875),x50062),x50061),f333(a115,f2(a875))) % 183.90/184.43 [5007]E(x50071,f333(a115,f2(a875)))+~E(f333(f333(f80(a875),x50071),x50072),f333(a115,f2(a875))) % 183.90/184.43 [5008]~P105(x50081)+P1(f333(f333(f247(x50081),x50082),x50082)) % 183.90/184.43 [5009]~P92(x50091)+P1(f333(f333(f90(x50091),x50092),x50092)) % 183.90/184.43 [5012]~P90(x50121)+E(f333(f333(f80(x50121),x50122),f333(f106(x50121),a100)),f333(f78(x50121),x50122)) % 183.90/184.43 [5030]~P138(x50301)+E(f333(f78(x50301),f333(f105(x50301),x50302)),f333(f105(x50301),f333(f78(a1),x50302))) % 183.90/184.43 [5031]~P90(x50311)+E(f333(f78(x50311),f333(f106(x50311),x50312)),f333(f106(x50311),f333(f78(a1),x50312))) % 183.90/184.43 [5060]~E(x50601,f333(a115,x50602))+P1(f333(f333(f248(a875),f2(a875)),x50601)) % 183.90/184.43 [5077]~P106(x50771)+E(f333(f78(f882(x50771,a870)),f333(f254(x50771),x50772)),f333(f255(x50771),x50772)) % 183.90/184.43 [5078]~P106(x50781)+E(f333(f78(f882(x50781,a870)),f333(f305(x50781),x50782)),f333(f302(x50781),x50782)) % 183.90/184.43 [5079]~P106(x50791)+E(f333(f78(f882(x50791,a870)),f333(f255(x50791),x50792)),f333(f254(x50791),x50792)) % 183.90/184.43 [5080]~P106(x50801)+E(f333(f78(f882(x50801,a870)),f333(f302(x50801),x50802)),f333(f305(x50801),x50802)) % 183.90/184.43 [5088]~E(f333(f103(a1),x50882),x50881)+P1(f333(f333(f247(a1),f2(a1)),x50881)) % 183.90/184.43 [5095]~E(x50952,f2(a1))+E(f52(x50951,x50952),f333(f333(f268(a1,a1),f2(a1)),f333(f74(a1),x50951))) % 183.90/184.43 [5097]~P2(x50971)+P1(f333(f333(f247(x50971),f196(x50971)),x50972)) % 183.90/184.43 [5129]E(x51291,x51292)+~E(f333(f333(f79(a1),x51291),x51291),f333(f333(f79(a1),x51292),x51292)) % 183.90/184.43 [5133]~P1(f333(x51331,x51332))+P1(f333(x51331,f333(a107,f373(x51331)))) % 183.90/184.43 [5159]~P114(x51591)+E(f333(f333(f80(x51591),f81(x51591,x51592)),f333(f74(x51591),x51592)),x51592) % 183.90/184.43 [5160]E(x51601,x51602)+~P1(f333(f333(f202(a24),x51601),x51602)) % 183.90/184.43 [5167]~E(x51672,f2(a875))+E(f84(f881(a875,a875),f47(x51671,x51672)),f333(f333(f268(a875,a875),f2(a875)),x51671)) % 183.90/184.43 [5172]~E(x51721,x51722)+~P1(f333(f333(f248(a875),x51721),x51722)) % 183.90/184.43 [5173]~E(x51731,x51732)+~P1(f333(f333(f248(a1),x51731),x51732)) % 183.90/184.43 [5176]~P141(x51761)+E(f333(f333(f79(x51761),f77(x51761)),f333(f103(x51761),x51762)),f333(f103(x51761),f333(a115,x51762))) % 183.90/184.43 [5180]~E(x51801,f2(a875))+~P1(f333(f333(f248(a875),x51802),x51801)) % 183.90/184.43 [5196]E(f153(x51961,x51962),x51962)+~E(f333(f197(f876(x51961)),f153(x51961,x51962)),f333(f197(f876(x51961)),x51962)) % 183.90/184.43 [5197]E(f333(f37(x51971),f333(f174(x51971),x51972)),f333(f197(f876(x51971)),x51972))+~P1(f333(f138(x51971),x51972)) % 183.90/184.43 [5208]~P1(f333(x52081,f374(x52081)))+P1(f333(x52081,f333(f103(a1),x52082))) % 183.90/184.43 [5219]E(f281(x52191,x52192),f77(a102))+~P1(f333(f333(f248(a102),x52192),x52191)) % 183.90/184.43 [5220]E(f181(x52201,x52202),f116(a1))+~P1(f333(f333(f248(a1),x52202),x52201)) % 183.90/184.43 [5221]E(f126(x52211,x52212),f118(a1))+~P1(f333(f333(f248(a1),x52211),x52212)) % 183.90/184.43 [5222]~P108(x52221)+E(f304(x52221,x52222,x52222),f333(f333(f311(x52221),x52222),f196(f882(x52221,a870)))) % 183.90/184.43 [5244]~E(f333(f333(f22(a875),x52441),x52442),f2(a875))+P1(f333(f333(f247(a875),x52441),x52442)) % 183.90/184.43 [5245]~E(f333(f333(f22(a1),x52451),x52452),f2(a1))+P1(f333(f333(f90(a1),x52451),x52452)) % 183.90/184.43 [5268]~E(x52682,f2(a875))+E(f54(x52681,x52682,f116(x52681)),f333(f333(f152(f876(x52681)),f116(x52681)),f116(f876(x52681)))) % 183.90/184.43 [5272]~P105(x52721)+~P1(f333(f333(f248(x52721),x52722),x52722)) % 183.90/184.43 [5275]~E(f44(a1,x52751,x52752),f2(a1))+E(f44(a1,x52751,f333(f78(a1),x52752)),f2(a1)) % 183.90/184.43 [5277]~E(f44(a1,x52771,x52772),f2(a1))+E(f44(a1,f333(f78(a1),x52771),x52772),f2(a1)) % 183.90/184.43 [5286]E(f333(f303(a875,x52861),f333(a115,x52862)),f196(f882(a875,a870)))+P1(f333(f333(f247(a875),x52861),x52862)) % 183.90/184.43 [5307]E(f140(a875,f333(f303(a875,x53071),x53072)),f116(a875))+P1(f333(f333(f248(a875),x53071),x53072)) % 183.90/184.43 [5312]~E(f333(f37(x53121),f333(f174(x53121),x53122)),f333(f197(f876(x53121)),x53122))+P1(f333(f138(x53121),x53122)) % 183.90/184.43 [5317]~P1(f333(f138(x53171),x53172))+P1(f333(f138(x53171),f333(f169(x53171),x53172))) % 183.90/184.43 [5318]~P1(f333(f138(x53181),x53182))+P1(f333(f138(x53181),f333(f173(x53181),x53182))) % 183.90/184.43 [5319]~P1(f333(f138(x53191),x53192))+P1(f333(f138(x53191),f333(f170(x53191),x53192))) % 183.90/184.43 [5326]P1(f333(x53261,x53262))+~P1(f333(x53261,f333(a107,f401(x53261)))) % 183.90/184.43 [5327]P1(f333(f333(f247(a875),x53272),x53271))+P1(f333(f333(f247(a875),x53271),x53272)) % 183.90/184.43 [5328]P1(f333(f333(f247(a1),x53282),x53281))+P1(f333(f333(f247(a1),x53281),x53282)) % 183.90/184.43 [5330]~P83(x53301)+P1(f333(f333(f247(x53301),x53302),f333(f74(x53301),x53302))) % 183.90/184.43 [5333]P1(f333(x53331,f375(x53331)))+~P1(f333(x53331,f333(f103(a1),x53332))) % 183.90/184.43 [5358]E(f333(f333(f22(a875),x53581),x53582),f2(a875))+~P1(f333(f333(f247(a875),x53581),x53582)) % 183.90/184.43 [5359]E(f333(f333(f22(a1),x53591),x53592),f2(a1))+~P1(f333(f333(f90(a1),x53591),x53592)) % 183.90/184.43 [5360]E(f333(f333(f38(a875),x53601),x53602),f2(a875))+~P1(f333(f333(f248(a875),x53601),x53602)) % 183.90/184.43 [5378]E(f44(a875,x53781,x53782),x53781)+~P1(f333(f333(f248(a875),x53781),x53782)) % 183.90/184.43 [5387]E(f44(a1,x53871,f333(f78(a1),x53872)),f292(x53871,x53872))+P1(f333(f333(f247(a1),f2(a1)),x53872)) % 183.90/184.43 [5399]E(f333(f333(f22(a1),x53991),x53992),f203(x53991,x53992))+~P1(f333(f333(f247(a1),x53992),x53991)) % 183.90/184.43 [5418]P1(f333(f333(f247(a1),f2(a1)),f374(x54181)))+P1(f333(x54181,f333(f103(a1),x54182))) % 183.90/184.43 [5430]~P57(x54301)+P1(f333(f333(f335(x54301),x54302),f333(f174(x54301),f55(x54301)))) % 183.90/184.43 [5432]~P120(x54321)+P1(f333(f333(f247(x54321),f2(x54321)),f333(f103(x54321),x54322))) % 183.90/184.43 [5433]~P83(x54331)+P1(f333(f333(f247(x54331),f2(x54331)),f333(f74(x54331),x54332))) % 183.90/184.43 [5460]E(f333(f333(f79(a875),x54601),f804(x54602,x54601)),x54602)+~P1(f333(f333(f247(a875),x54601),x54602)) % 183.90/184.43 [5472]~E(f333(f106(a1),x54721),f333(f103(a1),x54722))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x54721))) % 183.90/184.43 [5475]E(f304(a1,x54751,x54752),f196(f882(a1,a870)))+~P1(f333(f333(f248(a1),x54752),x54751)) % 183.90/184.43 [5477]~P114(x54771)+E(f333(f333(f80(x54771),f333(f74(x54771),x54772)),f333(f74(x54771),x54772)),f333(f333(f80(x54771),x54772),x54772)) % 183.90/184.43 [5483]E(f140(a875,f333(f303(a875,x54831),f333(a115,x54832))),f116(a875))+P1(f333(f333(f247(a875),x54831),x54832)) % 183.90/184.43 [5487]E(f333(f333(f38(a1),x54871),x54872),f293(x54871,x54872))+~P1(f333(f333(f247(a1),f2(a1)),x54872)) % 183.90/184.43 [5507]P1(f333(f138(x55071),x55072))+~P1(f333(f138(x55071),f333(f169(x55071),x55072))) % 183.90/184.43 [5508]P1(f333(f138(x55081),x55082))+~P1(f333(f138(x55081),f333(f170(x55081),x55082))) % 183.90/184.43 [5529]P1(f333(f61(a875),x55291))+P1(f333(f333(f335(a875),f344(x55291,x55292)),x55291)) % 183.90/184.43 [5530]P1(f333(f61(a875),x55301))+P1(f333(f333(f335(a875),f354(x55301,x55302)),x55301)) % 183.90/184.43 [5533]P1(f333(f333(f248(a875),x55332),f333(a115,x55331)))+P1(f333(f333(f248(a875),x55331),x55332)) % 183.90/184.43 [5534]E(f44(a1,x55341,x55342),f292(x55341,x55342))+~P1(f333(f333(f247(a1),f2(a1)),x55342)) % 183.90/184.43 [5537]E(f140(a875,f333(f303(a875,x55371),x55372)),f116(a875))+~P1(f333(f333(f247(a875),x55372),x55371)) % 183.90/184.43 [5538]~P82(x55381)+E(f333(f312(x55381,x55381,f78(x55381)),f333(f254(x55381),x55382)),f333(f305(x55381),f333(f78(x55381),x55382))) % 183.90/184.43 [5539]~P82(x55391)+E(f333(f312(x55391,x55391,f78(x55391)),f333(f305(x55391),x55392)),f333(f254(x55391),f333(f78(x55391),x55392))) % 183.90/184.43 [5540]~P82(x55401)+E(f333(f312(x55401,x55401,f78(x55401)),f333(f255(x55401),x55402)),f333(f302(x55401),f333(f78(x55401),x55402))) % 183.90/184.43 [5541]~P82(x55411)+E(f333(f312(x55411,x55411,f78(x55411)),f333(f302(x55411),x55412)),f333(f255(x55411),f333(f78(x55411),x55412))) % 183.90/184.43 [5552]E(x55521,f196(f882(x55522,a870)))+P1(f333(f333(f335(x55522),f451(x55521,x55522)),x55521)) % 183.90/184.43 [5553]E(x55531,f196(f882(x55532,a870)))+P1(f333(f333(f335(x55532),f454(x55531,x55532)),x55531)) % 183.90/184.43 [5564]~P1(f333(f333(f248(a875),x55641),x55642))+P1(f333(f333(f247(a875),x55641),x55642)) % 183.90/184.43 [5565]~P1(f333(f333(f248(a1),x55651),x55652))+P1(f333(f333(f247(a1),x55651),x55652)) % 183.90/184.43 [5581]E(f46(x55811,x55812),f333(f333(f268(a1,a1),f2(a1)),x55811))+~P1(f333(f333(f248(a1),x55811),x55812)) % 183.90/184.43 [5583]E(f227(f333(f78(a1),x55831),f333(f78(a1),x55832)),f227(x55831,x55832))+~P1(f333(f333(f248(a1),x55832),f2(a1))) % 183.90/184.43 [5594]E(x55941,x55942)+~E(f333(a3,f333(a115,f333(a19,x55941))),f333(a3,f333(a115,f333(a19,x55942)))) % 183.90/184.43 [5599]E(f46(x55991,x55992),f333(f333(f268(a1,a1),f2(a1)),x55991))+~P1(f333(f333(f247(a1),x55992),f2(a1))) % 183.90/184.43 [5626]E(f44(a875,f333(f106(a875),x56261),f333(f106(a875),x56262)),f2(a875))+~P1(f333(a201,f333(f106(a1),x56261))) % 183.90/184.43 [5641]P1(f333(f333(f247(a1),f2(a1)),f375(x56411)))+~P1(f333(x56411,f333(f103(a1),x56412))) % 183.90/184.43 [5675]P38(f304(a1,x56751,x56752))+~P1(f333(f333(f247(a1),f2(a1)),x56751)) % 183.90/184.43 [5680]~P1(f333(f61(x56801),x56802))+P1(f333(f61(f882(x56801,a870)),f333(f310(x56801),x56802))) % 183.90/184.43 [5693]E(f333(f333(f79(a1),x56931),f333(f103(a1),f384(x56932,x56931))),x56932)+~P1(f333(f333(f247(a1),x56931),x56932)) % 183.90/184.43 [5701]P1(f333(f333(f247(a875),x57011),x57012))+P1(f333(f333(f247(a875),f333(a115,x57012)),x57011)) % 183.90/184.43 [5744]E(f333(f333(f38(a875),f333(f106(a875),x57441)),f333(f106(a875),x57442)),f2(a875))+~P1(f333(a201,f333(f106(a1),x57441))) % 183.90/184.43 [5745]E(f333(f333(f80(a875),f333(f106(a875),x57451)),f333(f106(a875),x57452)),f2(a875))+~P1(f333(f333(f248(a1),x57451),a82)) % 183.90/184.43 [5747]P1(f333(f333(f248(a875),x57471),f333(a115,x57472)))+~P1(f333(f333(f248(a875),x57471),x57472)) % 183.90/184.43 [5749]P1(f333(f333(f248(a875),x57491),f333(a115,x57492)))+~P1(f333(f333(f247(a875),x57491),x57492)) % 183.90/184.43 [5751]P1(f333(f333(f247(a875),x57511),f333(a115,x57512)))+~P1(f333(f333(f247(a875),x57511),x57512)) % 183.90/184.43 [5754]~E(x57541,x57542)+P1(f333(f333(f248(a1),x57541),f333(f333(f79(a1),x57542),f77(a1)))) % 183.90/184.43 [5757]E(f44(a1,x57571,x57572),f2(a1))+E(f333(f333(f22(a1),x57572),f44(a1,x57571,x57572)),f44(a1,f333(f78(a1),x57571),x57572)) % 183.90/184.43 [5766]E(x57661,f116(x57662))+P1(f333(f333(f335(x57662),f145(x57662,x57661)),f333(f174(x57662),x57661))) % 183.90/184.43 [5778]E(f84(f881(a875,a875),f47(x57781,x57782)),f333(f333(f268(a875,a875),f2(a875)),x57781))+~P1(f333(f333(f248(a875),x57781),x57782)) % 183.90/184.43 [5811]E(f333(f333(f22(a875),f333(f106(a875),x58111)),f333(f106(a875),x58112)),f333(f106(a875),x58111))+~P1(f333(f333(f248(a1),x58112),a82)) % 183.90/184.43 [5812]E(f333(f333(f79(a875),f333(f106(a875),x58121)),f333(f106(a875),x58122)),f333(f106(a875),x58122))+~P1(f333(f333(f248(a1),x58121),a82)) % 183.90/184.43 [5817]E(f333(a115,f333(f333(f79(a875),x58171),f805(x58172,x58171))),x58172)+~P1(f333(f333(f248(a875),x58171),x58172)) % 183.90/184.43 [5840]P1(f333(x58401,x58402))+~P1(f333(x58401,f333(a88,f588(x58402,x58401)))) % 183.90/184.43 [5848]~P1(f333(f333(f248(a875),x58481),f333(a115,x58482)))+P1(f333(f333(f247(a875),x58481),x58482)) % 183.90/184.43 [5894]E(f333(f333(f311(a875),x58941),f333(f303(a875,x58942),x58941)),f333(f303(a875,x58942),f333(a115,x58941)))+~P1(f333(f333(f247(a875),x58942),x58941)) % 183.90/184.43 [5896]E(x58961,f116(x58962))+E(f333(f333(f135(x58962),f117(x58962,x58961)),f333(f333(f152(x58962),f145(x58962,x58961)),f116(x58962))),x58961) % 183.90/184.43 [5910]P1(f333(f61(x59101),x59102))+~P1(f333(f333(f248(a875),f2(a875)),f333(f37(x59101),x59102))) % 183.90/184.43 [5912]~E(x59121,f196(f882(x59122,a870)))+~P1(f333(f333(f248(a875),f2(a875)),f333(f37(x59122),x59121))) % 183.90/184.43 [5924]~P1(f333(f333(f248(a875),x59241),x59242))+P1(f333(f333(f247(a875),f333(a115,x59241)),x59242)) % 183.90/184.43 [5932]~P106(x59321)+E(f151(x59321,x59321,f5(x59321),f153(x59321,x59322)),f140(x59321,f333(f174(x59321),x59322))) % 183.90/184.43 [5935]E(x59351,f116(x59352))+P1(f333(f333(f335(x59352),f333(f142(x59352),x59351)),f333(f174(x59352),x59351))) % 183.90/184.43 [5941]~P120(x59411)+P1(f333(f333(f248(x59411),x59412),f333(f333(f79(x59411),x59412),f77(x59411)))) % 183.90/184.43 [5943]~P83(x59431)+P1(f333(f333(f247(x59431),f333(f78(x59431),x59432)),f333(f74(x59431),x59432))) % 183.90/184.43 [5976]P1(f333(f61(a875),x59761))+~P1(f333(f333(f248(a875),f344(x59761,x59762)),x59762)) % 183.90/184.43 [5977]P1(f333(f61(a875),x59771))+~P1(f333(f333(f247(a875),f354(x59771,x59772)),x59772)) % 183.90/184.43 [5981]~P1(f333(f61(f881(x59811,x59811)),x59812))+P1(f333(f61(x59811),f333(f286(x59811),x59812))) % 183.90/184.43 [6035]~P1(f333(f333(f248(a875),x60352),f333(a115,x60351)))+~P1(f333(f333(f248(a875),x60351),x60352)) % 183.90/184.43 [6036]~P108(x60361)+E(f333(f333(f104(f882(x60361,a870)),f333(f302(x60361),x60362)),f333(f255(x60361),x60362)),f333(f333(f311(x60361),x60362),f196(f882(x60361,a870)))) % 183.90/184.43 [6049]P1(f333(f61(x60491),x60492))+~P1(f333(f61(f882(x60491,a870)),f333(f310(x60491),x60492))) % 183.90/184.43 [6074]P1(f333(f333(f248(a875),f333(a115,x60741)),f333(a115,x60742)))+~P1(f333(f333(f248(a875),x60741),x60742)) % 183.90/184.43 [6075]P1(f333(f333(f248(a875),f333(a19,x60751)),f333(a19,x60752)))+~P1(f333(f333(f248(a102),x60751),x60752)) % 183.90/184.43 [6076]P1(f333(f333(f248(a102),f333(a3,x60761)),f333(a3,x60762)))+~P1(f333(f333(f248(a875),x60761),x60762)) % 183.90/184.43 [6077]P1(f333(f333(f247(a875),f333(a115,x60771)),f333(a115,x60772)))+~P1(f333(f333(f247(a875),x60771),x60772)) % 183.90/184.43 [6078]P1(f333(f333(f247(a875),f333(a19,x60781)),f333(a19,x60782)))+~P1(f333(f333(f247(a102),x60781),x60782)) % 183.90/184.43 [6079]P1(f333(f333(f247(a102),f333(a3,x60791)),f333(a3,x60792)))+~P1(f333(f333(f247(a875),x60791),x60792)) % 183.90/184.43 [6082]E(x60821,x60822)+~E(f333(f312(a875,a1,f103(a1)),x60821),f333(f312(a875,a1,f103(a1)),x60822)) % 183.90/184.43 [6098]P1(f333(f333(f248(a875),x60981),x60982))+~P1(f333(f333(f248(a875),f333(a115,x60981)),x60982)) % 183.90/184.43 [6101]P1(f333(f333(f248(a875),x61011),x61012))+~P1(f333(f333(f247(a875),f333(a115,x61011)),x61012)) % 183.90/184.43 [6102]P1(f333(f333(f247(a875),x61021),x61022))+~P1(f333(f333(f247(a875),f333(a115,x61021)),x61022)) % 183.90/184.43 [6117]E(f44(a1,x61171,x61172),f2(a1))+E(f333(f333(f22(a1),f44(a1,x61171,x61172)),x61172),f44(a1,x61171,f333(f78(a1),x61172))) % 183.90/184.43 [6182]E(f333(f37(f882(x61821,a870)),f333(f310(x61821),x61822)),f333(f333(f258(a875),f333(a115,f333(a115,f2(a875)))),f333(f37(x61821),x61822)))+~P1(f333(f61(x61821),x61822)) % 183.90/184.43 [6185]E(x61851,f116(x61852))+E(f333(f333(f166(x61852),x61851),f333(f333(f22(a875),f333(f197(f876(x61852)),x61851)),f77(a875))),f145(x61852,x61851)) % 183.90/184.43 [6210]E(x62101,f116(x62102))+E(f333(f333(f135(x62102),f333(f173(x62102),x62101)),f333(f333(f152(x62102),f333(f142(x62102),x62101)),f116(x62102))),f333(f169(x62102),x62101)) % 183.90/184.43 [6239]~P1(f333(f61(x62391),f39(f882(x62391,a870),x62392)))+P1(f333(f61(f882(x62391,a870)),x62392)) % 183.90/184.43 [6262]P1(f333(f333(f247(a875),f333(f106(a875),x62621)),f333(f106(a875),x62622)))+~P1(f333(f333(f247(a1),x62621),a82)) % 183.90/184.43 [6279]~P1(f333(f333(f248(a1),x62791),x62792))+P1(f333(f333(f248(a1),x62791),f333(f333(f79(a1),x62792),f77(a1)))) % 183.90/184.43 [6280]~P1(f333(f333(f247(a1),x62801),x62802))+P1(f333(f333(f248(a1),x62801),f333(f333(f79(a1),x62802),f77(a1)))) % 183.90/184.43 [6281]~P1(f333(f333(f248(a1),x62811),x62812))+P1(f333(f333(f247(a1),x62811),f333(f333(f22(a1),x62812),f77(a1)))) % 183.90/184.43 [6284]~P1(f333(f333(f248(a875),x62841),x62842))+P1(f333(f333(f248(a1),f333(f103(a1),x62841)),f333(f103(a1),x62842))) % 183.90/184.43 [6285]~P1(f333(f333(f248(a1),x62851),x62852))+P1(f333(f333(f248(a1),f333(f106(a1),x62851)),f333(f106(a1),x62852))) % 183.90/184.43 [6286]~P1(f333(f333(f247(a1),x62861),x62862))+P1(f333(f333(f247(a875),f333(f106(a875),x62861)),f333(f106(a875),x62862))) % 183.90/184.43 [6288]~P1(f333(f333(f247(a875),x62881),x62882))+P1(f333(f333(f247(a1),f333(f103(a1),x62881)),f333(f103(a1),x62882))) % 183.90/184.43 [6289]~P1(f333(f333(f247(a1),x62891),x62892))+P1(f333(f333(f247(a1),f333(f106(a1),x62891)),f333(f106(a1),x62892))) % 183.90/184.43 [6290]~P1(f333(f333(f90(a1),x62901),x62902))+P1(f333(f333(f90(a1),f333(f106(a1),x62901)),f333(f106(a1),x62902))) % 183.90/184.43 [6308]~P1(f333(f333(f247(a875),x63081),x63082))+~P1(f333(f333(f247(a875),f333(a115,x63082)),x63081)) % 183.90/184.43 [6352]~P1(f333(f333(f248(a875),f333(a115,x63521)),f333(a115,x63522)))+P1(f333(f333(f248(a875),x63521),x63522)) % 183.90/184.43 [6353]~P1(f333(f333(f248(a102),f333(a3,x63531)),f333(a3,x63532)))+P1(f333(f333(f248(a875),x63531),x63532)) % 183.90/184.43 [6354]~P1(f333(f333(f248(a875),f333(a107,x63541)),f333(a107,x63542)))+P1(f333(f333(f248(a1),x63541),x63542)) % 183.90/184.43 [6355]~P1(f333(f333(f248(a875),f333(a19,x63551)),f333(a19,x63552)))+P1(f333(f333(f248(a102),x63551),x63552)) % 183.90/184.43 [6356]~P1(f333(f333(f247(a875),f333(a115,x63561)),f333(a115,x63562)))+P1(f333(f333(f247(a875),x63561),x63562)) % 183.90/184.43 [6357]~P1(f333(f333(f247(a102),f333(a3,x63571)),f333(a3,x63572)))+P1(f333(f333(f247(a875),x63571),x63572)) % 183.90/184.43 [6358]~P1(f333(f333(f247(a875),f333(a19,x63581)),f333(a19,x63582)))+P1(f333(f333(f247(a102),x63581),x63582)) % 183.90/184.43 [6398]~P1(f333(f333(f248(a875),f333(a107,x63982)),f333(a107,x63981)))+P1(f333(f333(f248(a1),f2(a1)),x63981)) % 183.90/184.43 [6429]P1(f333(f333(f247(a1),f2(a1)),f44(a1,x64291,x64292)))+~P1(f333(f333(f248(a1),f2(a1)),x64292)) % 183.90/184.43 [6586]P37(x65861,x65862)+~E(f333(f333(f290(x65861,x65861,x65861),x65862),x65862),f196(f882(f881(x65861,x65861),a870))) % 183.90/184.43 [6598]~P37(x65981,x65982)+P37(x65981,f333(f333(f290(x65981,x65981,x65981),x65982),x65982)) % 183.90/184.43 [6610]P1(f333(f333(f248(a1),x66101),x66102))+~P1(f333(f333(f247(a1),x66101),f333(f333(f22(a1),x66102),f77(a1)))) % 183.90/184.43 [6611]P1(f333(f333(f247(a1),x66111),x66112))+~P1(f333(f333(f248(a1),x66111),f333(f333(f79(a1),x66112),f77(a1)))) % 183.90/184.43 [6614]P1(f333(f333(f248(a875),x66141),x66142))+~P1(f333(f333(f248(a1),f333(f103(a1),x66141)),f333(f103(a1),x66142))) % 183.90/184.43 [6615]P1(f333(f333(f248(a1),x66151),x66152))+~P1(f333(f333(f248(a875),f333(f106(a875),x66151)),f333(f106(a875),x66152))) % 183.90/184.43 [6616]P1(f333(f333(f248(a1),x66161),x66162))+~P1(f333(f333(f248(a1),f333(f106(a1),x66161)),f333(f106(a1),x66162))) % 183.90/184.43 [6618]P1(f333(f333(f247(a875),x66181),x66182))+~P1(f333(f333(f247(a1),f333(f103(a1),x66181)),f333(f103(a1),x66182))) % 183.90/184.43 [6619]P1(f333(f333(f247(a1),x66191),x66192))+~P1(f333(f333(f247(a1),f333(f106(a1),x66191)),f333(f106(a1),x66192))) % 183.90/184.43 [6620]P1(f333(f333(f90(a1),x66201),x66202))+~P1(f333(f333(f90(a1),f333(f106(a1),x66201)),f333(f106(a1),x66202))) % 183.90/184.43 [6713]~E(f729(x67132,x67131),f116(x67131))+E(f333(f143(f876(x67131),f876(x67131),f135(x67131),f116(x67131)),x67132),f116(x67131)) % 183.90/184.43 [6714]~E(f730(x67142,x67141),f116(x67141))+E(f333(f143(f876(x67141),f876(x67141),f135(x67141),f116(x67141)),x67142),f116(x67141)) % 183.90/184.43 [6721]~P4(x67211)+E(f333(f143(x67211,x67211,f104(x67211),f256(x67211)),x67212),f40(x67211,f333(f174(x67211),x67212))) % 183.90/184.43 [6722]~P4(x67221)+E(f333(f143(x67221,x67221,f113(x67221),f196(x67221)),x67222),f39(x67221,f333(f174(x67221),x67222))) % 183.90/184.43 [6734]E(x67341,f2(a102))+E(f333(f333(f79(a875),f333(a19,f333(f333(f22(a102),x67341),f77(a102)))),f333(a115,x67342)),f333(f333(f79(a875),f333(a19,x67341)),x67342)) % 183.90/184.43 [6784]P1(f333(f333(f248(a1),f333(f333(f22(a1),x67841),x67842)),f2(a1)))+~P1(f333(f333(f248(a1),x67841),x67842)) % 183.90/184.43 [6812]~P106(x68121)+E(f333(f333(f113(f882(x68121,a870)),f333(f333(f311(x68121),x68122),f196(f882(x68121,a870)))),f333(f305(x68121),x68122)),f333(f255(x68121),x68122)) % 183.90/184.43 [6887]~P54(x68871,x68872)+P37(x68871,f333(f253(f881(x68871,x68871)),f333(f272(x68871,x68871,a870),x68872))) % 183.90/184.43 [6888]~P54(x68881,x68882)+P52(x68881,f333(f253(f881(x68881,x68881)),f333(f272(x68881,x68881,a870),x68882))) % 183.90/184.43 [6889]E(x68891,f196(f882(x68892,a870)))+~P1(f333(f333(f247(f882(x68892,a870)),x68891),f196(f882(x68892,a870)))) % 183.90/184.43 [6972]~P1(f333(f333(f248(a875),f2(a875)),x69722))+P1(f333(f333(f248(a875),f44(a875,x69721,x69722)),x69722)) % 183.90/184.43 [6974]~P1(f333(f333(f248(a1),f2(a1)),x69742))+P1(f333(f333(f248(a1),f44(a1,x69741,x69742)),x69742)) % 183.90/184.43 [6975]~P1(f333(f333(f248(a875),f2(a875)),x69752))+P1(f333(f333(f247(a875),f44(a875,x69751,x69752)),x69752)) % 183.90/184.43 [6976]~P1(f333(f333(f247(a1),f2(a1)),x69761))+P1(f333(f333(f247(a1),f44(a1,x69761,x69762)),x69761)) % 183.90/184.43 [7054]~P108(x70541)+E(f333(f333(f22(f882(x70541,a870)),f333(f333(f311(x70541),x70542),f196(f882(x70541,a870)))),f333(f254(x70541),x70542)),f333(f333(f311(x70541),x70542),f196(f882(x70541,a870)))) % 183.90/184.43 [7127]~P48(x71271,x71272)+P39(x71271,f256(f882(x71271,a870)),f333(f253(f881(x71271,x71271)),f333(f272(x71271,x71271,a870),x71272))) % 183.90/184.43 [7128]P1(f333(x71281,x71282))+P1(f333(f333(f335(f882(f881(a875,a875),a870)),f588(x71282,x71281)),a101)) % 183.90/184.43 [7173]E(f333(f333(f135(a875),f140(a875,f333(f303(a875,x71731),x71732))),f333(f333(f152(a875),x71732),f116(a875))),f140(a875,f333(f303(a875,x71731),f333(a115,x71732))))+~P1(f333(f333(f247(a875),x71731),x71732)) % 183.90/184.43 [7314]E(x73141,f2(a875))+~E(f333(f143(a875,a875,f79(a875),x73141),x73142),f2(a875)) % 183.90/184.43 [7342]~P1(f333(f333(f248(a1),f333(f333(f22(a1),x73421),x73422)),f2(a1)))+P1(f333(f333(f248(a1),x73421),x73422)) % 183.90/184.43 [7371]P37(x73711,x73712)+~P37(x73711,f333(f333(f290(x73711,x73711,x73711),x73712),x73712)) % 183.90/184.43 [7400]~P1(f333(f333(f247(a875),f333(a115,x74001)),x74002))+P1(f193(a870,a251,f333(f247(a875),x74001),x74002)) % 183.90/184.43 [7559]P25(a875,a875,f333(f333(f7(a875,a875,a875),f22(a875)),x75591),x75592)+P1(f333(f333(f335(a875),f490(x75591,x75592)),x75592)) % 183.90/184.43 [7615]E(f333(f333(f333(f65(a875,x76151,f79(a875)),f333(f16(a875,x76151),f77(a875))),f2(a875)),x76152),f333(f37(x76151),x76152))+~P1(f333(f61(x76151),x76152)) % 183.90/184.43 [7657]P25(a875,a875,f333(f333(f7(a875,a875,a875),f22(a875)),x76571),x76572)+~P1(f333(f333(f247(a875),x76571),f490(x76571,x76572))) % 183.90/184.43 [7717]P37(x77171,x77172)+P1(f333(f333(f247(f882(x77171,a870)),f599(x77172,x77171)),f333(f287(x77171,x77171,x77172),f599(x77172,x77171)))) % 183.90/184.43 [7722]P54(x77221,x77222)+~P37(x77221,f333(f253(f881(x77221,x77221)),f333(f272(x77221,x77221,a870),x77222))) % 183.90/184.43 [7795]P1(f333(f333(f247(a875),f333(a115,x77951)),x77952))+~P1(f193(a870,a251,f333(f247(a875),x77951),x77952)) % 183.90/184.43 [7850]P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x78501),x78502)),f309(a875,a323)))+~P1(f333(f333(f247(a875),x78501),x78502)) % 183.90/184.43 [7947]P48(x79471,x79472)+~P39(x79471,f256(f882(x79471,a870)),f333(f253(f881(x79471,x79471)),f333(f272(x79471,x79471,a870),x79472))) % 183.90/184.43 [8008]~P1(f333(f138(x80081),x80082))+P1(f333(f138(f882(x80081,a870)),f333(f333(f155(f876(x80081),f882(x80081,a870)),f174(x80081)),f53(x80081,x80082)))) % 183.90/184.43 [8214]~P37(x82141,f333(f288(x82141,x82141),x82142))+P37(x82141,f333(f288(x82141,x82141),f333(f333(f290(x82141,x82141,x82141),x82142),f309(x82141,x82142)))) % 183.90/184.43 [8335]P1(f333(f61(f881(x83351,x83351)),f333(f333(f290(x83351,x83351,x83351),x83352),f309(x83351,x83352))))+~P1(f333(f61(f881(x83351,x83351)),x83352)) % 183.90/184.43 [8366]E(x83661,f2(a1))+P1(f333(f48(x83662,x83661),f333(f333(f268(a1,a1),f333(f333(f38(a1),x83662),x83661)),f44(a1,x83662,x83661)))) % 183.90/184.43 [8377]~P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x83771),x83772)),f309(a875,a323)))+P1(f333(f333(f247(a875),x83771),x83772)) % 183.90/184.43 [8395]~P78(x83951)+E(f333(f143(x83951,x83951,f333(f7(x83951,x83951,x83951),f79(x83951)),f2(x83951)),f333(f170(x83951),x83952)),f333(f143(x83951,x83951,f79(x83951),f2(x83951)),x83952)) % 183.90/184.43 [8571]~P106(x85711)+E(f333(f143(f876(x85711),x85711,f333(f7(x85711,f876(x85711),f876(x85711)),f149(x85711,x85711,f5(x85711))),f116(x85711)),x85712),f151(x85711,x85711,f5(x85711),x85712)) % 183.90/184.43 [8672]~P52(x86721,f333(f253(f881(x86721,x86721)),f333(f272(x86721,x86721,a870),x86722)))+P52(x86721,f333(f253(f881(x86721,x86721)),f333(f272(x86721,x86721,a870),f257(x86721,x86721,x86722)))) % 183.90/184.43 [8686]P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x86861),x86862)),f333(f333(f290(a875,a875,a875),a323),f309(a875,a323))))+~P1(f333(f333(f248(a875),x86861),x86862)) % 183.90/184.43 [8729]~P1(f333(f61(f881(x87291,x87291)),f333(f333(f290(x87291,x87291,x87291),x87292),f309(x87291,x87292))))+P1(f333(f61(f881(x87291,x87291)),x87292)) % 183.90/184.43 [8780]~P52(x87801,f333(f253(f881(x87801,x87801)),f333(f272(x87801,x87801,a870),f257(x87801,x87801,x87802))))+P52(x87801,f333(f253(f881(x87801,x87801)),f333(f272(x87801,x87801,a870),x87802))) % 183.90/184.43 [8985]P52(x89851,x89852)+P1(f333(f333(f335(f881(x89851,x89851)),f333(f333(f268(x89851,x89851),f620(x89852,x89851)),f620(x89852,x89851))),f333(f333(f290(x89851,x89851,x89851),x89852),f309(x89851,x89852)))) % 183.90/184.43 [8986]P52(x89861,x89862)+P1(f333(f333(f335(f881(x89861,x89861)),f333(f333(f268(x89861,x89861),f634(x89862,x89861)),f634(x89862,x89861))),f333(f333(f290(x89861,x89861,x89861),x89862),f309(x89861,x89862)))) % 183.90/184.43 [9102]~P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x91021),x91022)),f333(f333(f290(a875,a875,a875),a323),f309(a875,a323))))+P1(f333(f333(f248(a875),x91021),x91022)) % 183.90/184.43 [5073]~P90(x50731)+E(f333(f333(f79(x50731),f333(f106(x50731),a82)),x50732),x50732) % 183.90/184.43 [5102]~P93(x51021)+E(f333(f333(f113(x51021),f333(f78(x51021),x51022)),x51022),f256(x51021)) % 183.90/184.43 [5103]~P93(x51031)+E(f333(f333(f104(x51031),f333(f78(x51031),x51032)),x51032),f196(x51031)) % 183.90/184.43 [5104]~P65(x51041)+E(f333(f333(f79(x51041),f333(f78(x51041),x51042)),x51042),f2(x51041)) % 183.90/184.43 [5105]~P72(x51051)+E(f333(f333(f79(x51051),f333(f78(x51051),x51052)),x51052),f2(x51051)) % 183.90/184.43 [5137]~P90(x51371)+E(f333(f333(f80(x51371),f333(f106(x51371),a100)),x51372),f333(f78(x51371),x51372)) % 183.90/184.43 [5300]~P113(x53001)+E(f333(f333(f80(x53001),f333(f78(x53001),f77(x53001))),x53002),f333(f78(x53001),x53002)) % 183.90/184.43 [5343]E(f333(f74(a1),x53431),f77(a1))+~E(f333(f74(a1),f333(f333(f80(a1),x53431),x53432)),f77(a1)) % 183.90/184.43 [5435]~P90(x54351)+E(f333(f333(f79(x54351),f77(x54351)),f333(f106(x54351),x54352)),f333(f106(x54351),f333(f333(f22(a1),x54352),a100))) % 183.90/184.43 [5488]~P62(x54881)+E(f13(x54881,f333(f333(f311(x54881),x54882),f196(f882(x54881,a870)))),x54882) % 183.90/184.43 [5489]~P62(x54891)+E(f10(x54891,f333(f333(f311(x54891),x54892),f196(f882(x54891,a870)))),x54892) % 183.90/184.43 [5490]~P4(x54901)+E(f40(x54901,f333(f333(f311(x54901),x54902),f196(f882(x54901,a870)))),x54902) % 183.90/184.43 [5491]~P4(x54911)+E(f39(x54911,f333(f333(f311(x54911),x54912),f196(f882(x54911,a870)))),x54912) % 183.90/184.43 [5492]~P106(x54921)+E(f14(x54921,f333(f333(f311(x54921),x54922),f196(f882(x54921,a870)))),x54922) % 183.90/184.43 [5493]~P106(x54931)+E(f15(x54931,f333(f333(f311(x54931),x54932),f196(f882(x54931,a870)))),x54932) % 183.90/184.43 [5515]E(f333(f333(f79(a875),x55151),f333(f333(f22(a875),x55152),x55151)),x55152)+P1(f333(f333(f248(a875),x55152),x55151)) % 183.90/184.43 [5547]E(x55471,f116(x55472))+P1(f333(f333(f248(a875),f2(a875)),f333(f197(f876(x55472)),x55471))) % 183.90/184.43 [5672]~P106(x56721)+E(f11(x56721,f245(x56721),f333(f333(f311(x56721),x56722),f196(f882(x56721,a870)))),x56722) % 183.90/184.43 [5673]~P106(x56731)+E(f12(x56731,f246(x56731),f333(f333(f311(x56731),x56732),f196(f882(x56731,a870)))),x56732) % 183.90/184.43 [5734]E(f333(f333(f22(a875),x57341),f333(f333(f22(a875),x57341),x57342)),x57342)+~P1(f333(f333(f247(a875),x57342),x57341)) % 183.90/184.43 [5735]E(f333(f333(f79(a875),x57351),f333(f333(f22(a875),x57352),x57351)),x57352)+~P1(f333(f333(f247(a875),x57351),x57352)) % 183.90/184.43 [5756]E(f44(a875,f333(f333(f22(a875),x57561),x57562),x57562),f44(a875,x57561,x57562))+P1(f333(f333(f248(a875),x57561),x57562)) % 183.90/184.43 [5767]E(f333(f78(a1),f333(f333(f38(a1),x57671),f333(f78(a1),x57672))),f293(x57671,x57672))+P1(f333(f333(f247(a1),f2(a1)),x57672)) % 183.90/184.43 [5769]~E(x57692,f2(a875))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f258(a875),x57691),x57692))) % 183.90/184.43 [5820]~P90(x58201)+E(f333(f333(f79(x58201),f333(f78(x58201),f77(x58201))),f333(f106(x58201),x58202)),f333(f106(x58201),f333(f333(f79(a1),x58202),a100))) % 183.90/184.43 [5821]E(f333(f333(f258(a875),f333(f106(a875),x58211)),x58212),f333(f333(f258(a875),f2(a875)),x58212))+~P1(f333(a201,f333(f106(a1),x58211))) % 183.90/184.43 [5916]E(f333(f142(a875),f140(a875,f333(f303(a875,x59161),x59162))),x59161)+~P1(f333(f333(f248(a875),x59161),x59162)) % 183.90/184.43 [5936]E(f333(f333(f80(a875),f333(f106(a875),x59361)),f333(f106(a875),x59362)),f333(f106(a875),f333(f333(f80(a1),x59361),x59362)))+P1(f333(f333(f248(a1),x59361),a82)) % 183.90/184.43 [5942]~P121(x59421)+P1(f333(f333(f247(x59421),f2(x59421)),f333(f333(f80(x59421),x59422),x59422))) % 183.90/184.43 [5954]E(f333(f333(f22(a875),f333(a115,x59541)),x59542),f333(a115,f333(f333(f22(a875),x59541),x59542)))+~P1(f333(f333(f247(a875),x59542),x59541)) % 183.90/184.43 [5957]E(f44(a875,f333(f333(f22(a875),x59571),x59572),x59572),f44(a875,x59571,x59572))+~P1(f333(f333(f247(a875),x59572),x59571)) % 183.90/184.43 [6010]E(f333(f333(f258(a875),f333(a107,x60101)),x60102),f333(a107,f333(f333(f258(a1),x60101),x60102)))+~P1(f333(f333(f247(a1),f2(a1)),x60101)) % 183.90/184.43 [6026]P1(f333(f138(x60261),x60262))+P1(f333(f333(f248(a875),f686(x60262,x60261)),f333(f197(f876(x60261)),x60262))) % 183.90/184.43 [6027]P1(f333(f138(x60271),x60272))+P1(f333(f333(f248(a875),f690(x60272,x60271)),f333(f197(f876(x60271)),x60272))) % 183.90/184.43 [6042]~E(x60421,f116(x60422))+~P1(f333(f333(f248(a875),f2(a875)),f333(f197(f876(x60422)),x60421))) % 183.90/184.43 [6056]E(f145(a875,f140(a875,f333(f303(a875,x60561),x60562))),f333(f333(f22(a875),x60562),f77(a875)))+~P1(f333(f333(f248(a875),x60561),x60562)) % 183.90/184.43 [6059]E(f333(f333(f79(a1),x60591),f333(f103(a1),f333(a115,f377(x60592,x60591)))),x60592)+~P1(f333(f333(f248(a1),x60591),x60592)) % 183.90/184.43 [6066]E(x60661,f2(a875))+E(f333(f333(f80(a875),x60662),f333(f333(f258(a875),x60662),f333(f333(f22(a875),x60661),f77(a875)))),f333(f333(f258(a875),x60662),x60661)) % 183.90/184.43 [6092]E(f333(f333(f80(a875),f333(a107,x60921)),f333(a107,x60922)),f333(a107,f333(f333(f80(a1),x60921),x60922)))+~P1(f333(f333(f247(a1),f2(a1)),x60921)) % 183.90/184.43 [6093]E(f333(f333(f38(a875),f333(a107,x60931)),f333(a107,x60932)),f333(a107,f333(f333(f38(a1),x60931),x60932)))+~P1(f333(f333(f247(a1),f2(a1)),x60931)) % 183.90/184.43 [6107]~P109(x61071)+E(f333(f333(f79(x61071),x61072),x61072),f333(f333(f80(x61071),f333(f333(f79(x61071),f77(x61071)),f77(x61071))),x61072)) % 183.90/184.43 [6124]E(f333(f333(f22(a1),f333(f103(a1),x61241)),f333(f103(a1),x61242)),f333(f103(a1),f333(f333(f22(a875),x61241),x61242)))+~P1(f333(f333(f247(a875),x61242),x61241)) % 183.90/184.43 [6126]E(f333(f333(f268(a1,a1),f333(f106(a1),a100)),f333(f333(f79(a1),x61261),x61262)),f49(x61261,x61262))+~P1(f333(f333(f247(a1),x61262),f2(a1))) % 183.90/184.43 [6160]E(f182(x61601,x61602),f116(f876(x61601)))+P1(f333(f333(f335(f876(x61601)),f717(x61602,x61601)),f333(f174(f876(x61601)),x61602))) % 183.90/184.43 [6169]E(f119(a1,f333(f127(a1),x61691),f126(x61692,f333(f333(f79(a1),x61691),f77(a1)))),f126(x61692,x61691))+P1(f333(f333(f248(a1),x61692),x61691)) % 183.90/184.43 [6245]E(f333(f333(f152(a1),x62451),f181(f333(f333(f79(a1),x62451),f77(a1)),x62452)),f181(x62451,x62452))+~P1(f333(f333(f247(a1),x62451),x62452)) % 183.90/184.43 [6282]~P1(f333(f333(f248(a875),x62822),x62821))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f22(a875),x62821),x62822))) % 183.90/184.43 [6313]~P1(f333(f333(f248(a875),x63131),f333(a107,x63132)))+P1(f333(f333(f248(a1),f333(f103(a1),x63131)),x63132)) % 183.90/184.43 [6342]~P106(x63421)+E(f333(f333(f113(f882(x63421,a870)),f333(f254(x63421),x63422)),f333(f333(f311(x63421),x63422),f196(f882(x63421,a870)))),f333(f302(x63421),x63422)) % 183.90/184.43 [6345]~P1(f333(f333(f248(a875),f2(a875)),x63451))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f258(a875),x63451),x63452))) % 183.90/184.43 [6346]~P1(f333(f333(f247(a1),f2(a1)),x63461))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f258(a1),x63461),x63462))) % 183.90/184.43 [6374]~E(f333(x63741,f2(a875)),f2(a875))+E(f333(f333(f6(a875,a875),x63741),f304(a875,f333(a115,f2(a875)),x63742)),f333(f333(f6(a875,a875),x63741),f304(a875,f2(a875),x63742))) % 183.90/184.43 [6437]~P90(x64371)+E(f333(f333(f80(x64371),f333(f333(f79(x64371),f77(x64371)),f77(x64371))),f333(f106(x64371),x64372)),f333(f106(x64371),f333(f333(f79(a1),x64372),x64372))) % 183.90/184.43 [6452]E(f333(f333(f311(a1),x64521),f304(a1,f333(f333(f79(a1),x64521),f77(a1)),x64522)),f304(a1,x64521,x64522))+P1(f333(f333(f248(a1),x64522),x64521)) % 183.90/184.43 [6453]P1(f333(f333(f248(a875),x64531),f333(a107,x64532)))+~P1(f333(f333(f248(a1),f333(f103(a1),x64531)),x64532)) % 183.90/184.43 [6554]E(f333(a107,f333(f333(f38(a1),f333(f106(a1),x65541)),f333(f106(a1),x65542))),f333(f333(f38(a875),f333(f106(a875),x65541)),f333(f106(a875),x65542)))+P1(f333(a201,f333(f106(a1),x65541))) % 183.90/184.43 [6612]P1(f333(f333(f248(a875),x66121),x66122))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f22(a875),x66122),x66121))) % 183.90/184.43 [6656]P1(f333(f333(f248(a875),f2(a875)),x66561))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f80(a875),x66562),x66561))) % 183.90/184.43 [6657]P1(f333(f333(f248(a875),f2(a875)),x66571))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f80(a875),x66571),x66572))) % 183.90/184.43 [6674]~P1(f333(f333(f247(a1),x66741),f2(a1)))+E(f333(f333(f80(a875),f333(a107,f333(f78(a1),x66741))),f333(a107,f333(f78(a1),x66742))),f333(a107,f333(f333(f80(a1),x66741),x66742))) % 183.90/184.43 [6732]~E(x67322,f196(f882(x67321,a870)))+P1(f333(f333(f247(f882(x67321,a870)),x67322),f333(f78(f882(x67321,a870)),x67322))) % 183.90/184.43 [6795]~P90(x67951)+E(f333(f333(f79(x67951),f333(f333(f79(x67951),f2(x67951)),f333(f106(x67951),x67952))),f333(f106(x67951),x67952)),f333(f106(x67951),f333(f333(f79(a1),x67952),x67952))) % 183.90/184.43 [6852]~P1(f333(f333(f248(a1),x68521),x68522))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x68521),f77(a1))),x68522)) % 183.90/184.43 [6919]E(x69191,f2(a875))+~P1(f333(f333(f247(a1),f333(f103(a1),x69192)),f333(f78(a1),f333(f103(a1),x69191)))) % 183.90/184.43 [6920]E(x69201,f2(a875))+~P1(f333(f333(f247(a1),f333(f103(a1),x69201)),f333(f78(a1),f333(f103(a1),x69202)))) % 183.90/184.43 [7025]E(f333(f333(f268(a1,a1),f333(f106(a1),a100)),f333(f333(f79(a1),x70251),x70252)),f49(x70251,x70252))+~P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),x70251),x70252))) % 183.90/184.43 [7067]~P26(x70671,x70672)+P37(x70671,f333(f267(f882(f881(x70671,x70671),a870),f882(f881(x70671,x70671),a870)),x70672)) % 183.90/184.43 [7085]~P1(f333(f333(f247(a875),f333(a115,f2(a875))),x70851))+P1(f333(f333(f247(a875),f333(a115,f2(a875))),f333(f333(f258(a875),x70851),x70852))) % 183.90/184.43 [7248]~P1(f333(f333(f248(a1),x72481),x72482))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x72481),x72481)),f333(f333(f79(a1),x72482),x72482))) % 183.90/184.43 [7260]~P1(f333(f333(f247(a1),x72601),x72602))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x72601),x72601)),f333(f333(f79(a1),x72602),x72602))) % 183.90/184.43 [7261]~P1(f333(f333(f90(a1),x72611),x72612))+P1(f333(f333(f90(a1),f333(f333(f79(a1),x72611),x72611)),f333(f333(f79(a1),x72612),x72612))) % 183.90/184.43 [7316]~P1(f333(f333(f248(a875),f2(a875)),x73161))+P1(f333(f333(f248(a875),f333(f333(f22(a875),x73161),f333(a115,x73162))),x73161)) % 183.90/184.43 [7353]P1(f333(f333(f247(a875),f333(a115,f2(a875))),x73531))+~P1(f333(f333(f247(a875),f333(a115,f2(a875))),f333(f333(f80(a875),x73532),x73531))) % 183.90/184.43 [7354]P1(f333(f333(f247(a875),f333(a115,f2(a875))),x73541))+~P1(f333(f333(f247(a875),f333(a115,f2(a875))),f333(f333(f80(a875),x73541),x73542))) % 183.90/184.43 [7358]P1(f333(f333(f247(a875),f333(f333(f166(a875),x73581),x73582)),f333(f167(a875),x73581)))+~P1(f333(f333(f248(a875),x73582),f333(f197(f876(a875)),x73581))) % 183.90/184.43 [7399]P1(f333(f333(f248(a1),x73991),x73992))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x73991),f77(a1))),x73992)) % 183.90/184.43 [7444]P1(f333(f61(x74441),f256(f882(x74441,a870))))+~P1(f333(f61(f882(x74442,x74441)),f256(f882(f882(x74442,x74441),a870)))) % 183.90/184.43 [7445]P1(f333(f61(x74451),f256(f882(x74451,a870))))+~P1(f333(f61(f880(x74452,x74451)),f256(f882(f880(x74452,x74451),a870)))) % 183.90/184.43 [7446]P1(f333(f61(x74461),f256(f882(x74461,a870))))+~P1(f333(f61(f880(x74461,x74462)),f256(f882(f880(x74461,x74462),a870)))) % 183.90/184.43 [7488]E(x74881,f196(f882(x74882,a870)))+~P1(f333(f333(f247(f882(x74882,a870)),x74881),f333(f78(f882(x74882,a870)),x74881))) % 183.90/184.43 [7625]E(f333(f143(f876(x76251),f876(x76251),f135(x76251),f116(x76251)),x76252),f116(x76251))+P1(f333(f333(f335(f876(x76251)),f729(x76252,x76251)),f333(f174(f876(x76251)),x76252))) % 183.90/184.43 [7626]E(f333(f143(f876(x76261),f876(x76261),f135(x76261),f116(x76261)),x76262),f116(x76261))+P1(f333(f333(f335(f876(x76261)),f730(x76262,x76261)),f333(f174(f876(x76261)),x76262))) % 183.90/184.43 [7869]P1(f333(f333(f248(a1),x78691),x78692))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x78691),x78691)),f333(f333(f79(a1),x78692),x78692))) % 183.90/184.43 [7872]P1(f333(f333(f247(a1),x78721),x78722))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x78721),x78721)),f333(f333(f79(a1),x78722),x78722))) % 183.90/184.43 [7873]P1(f333(f333(f90(a1),x78731),x78732))+~P1(f333(f333(f90(a1),f333(f333(f79(a1),x78731),x78731)),f333(f333(f79(a1),x78732),x78732))) % 183.90/184.43 [7967]~P109(x79671)+E(f333(f333(f80(x79671),f333(f333(f79(x79671),f77(x79671)),f77(x79671))),f333(f333(f6(a875,x79671),f103(x79671)),f304(a875,f77(a875),x79672))),f333(f333(f80(x79671),f333(f103(x79671),x79672)),f333(f333(f79(x79671),f333(f103(x79671),x79672)),f77(x79671)))) % 183.90/184.43 [8024]P1(f333(f333(f335(a875),x80241),x80242))+~P1(f333(f333(f335(a1),f333(f103(a1),x80241)),f333(f312(a875,a1,f103(a1)),x80242))) % 183.90/184.43 [8185]~P1(f333(f61(x81851),x81852))+E(f333(f312(a875,x81851,f491(x81852,x81851)),f333(f253(a875),f333(f333(f7(a875,a875,a870),f248(a875)),f492(x81852,x81851)))),x81852) % 183.90/184.43 [8474]P41(x84741,x84742)+P1(f333(f333(f335(f881(x84741,x84741)),f333(f333(f268(x84741,x84741),f536(x84742,x84741)),f536(x84742,x84741))),x84742)) % 183.90/184.43 [8612]~P90(x86121)+E(f333(f333(f22(x86121),f77(x86121)),f333(f106(x86121),x86122)),f333(f106(x86121),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f78(a1),x86122)))) % 183.90/184.43 [8725]~P1(f333(f333(f248(f882(a875,a870)),x87251),x87252))+P1(f333(f333(f248(f882(a1,a870)),f333(f312(a875,a1,f103(a1)),x87251)),f333(f312(a875,a1,f103(a1)),x87252))) % 183.90/184.43 [8754]~P1(f333(f333(f248(a1),x87541),x87542))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x87541),x87541)),a100)),f333(f333(f79(a1),x87542),x87542))) % 183.90/184.43 [8756]~P1(f333(f333(f248(a1),x87561),x87562))+P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x87561),x87561)),a100)),f333(f333(f79(a1),x87562),x87562))) % 183.90/184.43 [8827]~P1(f333(f333(f335(a875),x88271),f333(f174(a875),x88272)))+P1(f333(f333(f247(a875),x88271),f333(f143(a875,a875,f79(a875),f2(a875)),x88272))) % 183.90/184.43 [8921]P45(x89211,x89212)+~P1(f333(f333(f335(f881(x89211,x89211)),f333(f333(f268(x89211,x89211),f538(x89212,x89211)),f538(x89212,x89211))),x89212)) % 183.90/184.43 [9068]~P1(f333(f333(f248(f882(a1,a870)),f333(f312(a875,a1,f103(a1)),x90681)),f333(f312(a875,a1,f103(a1)),x90682)))+P1(f333(f333(f248(f882(a875,a870)),x90681),x90682)) % 183.90/184.43 [9069]~P1(f333(f333(f247(f882(a1,a870)),f333(f312(a875,a1,f103(a1)),x90691)),f333(f312(a875,a1,f103(a1)),x90692)))+P1(f333(f333(f247(f882(a875,a870)),x90691),x90692)) % 183.90/184.43 [9149]P1(f333(f333(f248(a1),x91491),x91492))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x91491),x91491)),a100)),f333(f333(f79(a1),x91492),x91492))) % 183.90/184.43 [9151]P1(f333(f333(f248(a1),x91511),x91512))+~P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x91511),x91511)),a100)),f333(f333(f79(a1),x91512),x91512))) % 183.90/184.43 [10033]~P101(x100331)+E(f119(f876(x100331),f333(f127(f876(x100331)),f116(x100331)),f333(f333(f333(f99(f877(f876(x100331))),f333(f333(f248(a1),f2(a1)),x100332)),f333(f121(f881(x100331,f876(x100331)),f876(x100331),f132(x100331,f876(x100331),f133(x100331,f333(f333(f22(a1),x100332),f77(a1))),f133(f876(x100331),f333(f333(f22(a1),x100332),f77(a1))))),f333(f272(x100331,f876(x100331),f877(f876(x100331))),f333(f333(f8(f882(f876(x100331),f876(x100331)),f882(f876(x100331),f877(f876(x100331))),x100331),f333(f8(f876(x100331),f877(f876(x100331)),f876(x100331)),f127(f876(x100331)))),f152(x100331))))),f118(f876(x100331)))),f133(f876(x100331),x100332)) % 183.90/184.43 [10055]~P1(f333(f61(x100551),x100552))+E(f333(f197(f876(x100551)),f89(f876(x100551),f333(f333(f18(f876(x100551),a870,a870),f333(f333(f8(a870,f882(a870,a870),f876(x100551)),a331),f333(f333(f7(f876(x100551),f882(x100551,a870),a870),f333(f333(f8(f882(x100551,a870),f882(f882(x100551,a870),a870),f876(x100551)),a330),f174(x100551))),x100552))),f138(x100551)))),f226(x100551,x100552)) % 183.90/184.43 [10191]~P24(a872,x101911,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),a330),x101912),f202(x101912))),f196(f882(f874(a872),a870))))+P24(a872,x101911,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),f333(f333(f8(f882(a872,f882(a872,a870)),f882(a872,a870),a872),f333(f8(f882(a872,a870),a870,a872),f87(a872))),f333(f333(f8(f882(a872,a870),f882(a872,f882(a872,a870)),a872),f333(f7(a872,f882(a872,a870),f882(a872,a870)),f333(f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870)),f333(f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f333(f8(a870,f882(a870,a870),a872),a336)),f202(x101912))))),a330))),x101912),a330)),f196(f882(f874(a872),a870)))) % 183.90/184.43 [6055]E(f333(f333(f79(a875),f333(f333(f22(a875),x60551),x60552)),x60552),x60551)+~P1(f333(f333(f247(a875),x60552),x60551)) % 183.90/184.43 [6120]E(f333(f333(f38(a875),f333(f333(f80(a875),x61201),x61202)),x61202),x61201)+~P1(f333(f333(f248(a875),f2(a875)),x61202)) % 183.90/184.43 [6121]E(f333(f333(f38(a875),f333(f333(f80(a875),x61211),x61212)),x61211),x61212)+~P1(f333(f333(f248(a875),f2(a875)),x61211)) % 183.90/184.43 [6125]~P66(x61251)+E(f333(f333(f6(a875,x61251),f333(f166(x61251),x61252)),f333(f303(a875,f2(a875)),f333(f197(f876(x61251)),x61252))),f333(f167(x61251),x61252)) % 183.90/184.43 [6237]E(f44(a875,f333(a115,f333(f333(f80(a875),x62371),x62372)),x62371),f77(a875))+~P1(f333(f333(f248(a875),f77(a875)),x62371)) % 183.90/184.43 [6243]E(f333(a115,f333(f333(f79(a875),f333(f106(a875),x62431)),x62432)),f333(f333(f79(a875),f77(a875)),x62432))+~P1(f333(a201,f333(f106(a1),x62431))) % 183.90/184.43 [6271]E(f333(a107,f333(f333(f258(a1),f333(f106(a1),x62711)),x62712)),f333(f333(f258(a875),f333(f106(a875),x62711)),x62712))+P1(f333(a201,f333(f106(a1),x62711))) % 183.90/184.43 [6506]E(f333(f333(f22(a875),x65061),f333(f106(a875),f333(f333(f79(a1),x65062),a100))),f333(f333(f22(a875),f333(a115,x65061)),f333(f106(a875),x65062)))+~P1(f333(f333(f248(a1),a82),x65062)) % 183.90/184.43 [6585]E(x65851,f2(a875))+E(f333(a115,f333(f333(f79(a875),f333(f333(f22(a875),x65851),f77(a875))),x65852)),f333(f333(f79(a875),x65851),x65852)) % 183.90/184.43 [6626]E(x66261,f2(a1))+P1(f333(f333(f248(a1),f2(a1)),f333(f333(f258(a1),f333(f74(a1),x66261)),x66262))) % 183.90/184.43 [6641]~E(x66412,f2(a875))+P1(f333(f333(f248(a1),f2(a1)),f333(f333(f258(a1),f333(f74(a1),x66411)),x66412))) % 183.90/184.43 [6678]E(x66781,f2(a875))+E(f333(f333(f79(a875),x66782),f333(f333(f80(a875),f333(f333(f22(a875),x66781),f77(a875))),x66782)),f333(f333(f80(a875),x66781),x66782)) % 183.90/184.43 [6726]~P1(f333(f333(f247(a1),x67261),x67262))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x67261),a100)),x67262)) % 183.90/184.43 [6855]E(f333(f333(f152(a875),x68551),f140(a875,f333(f303(a875,f333(a115,x68551)),x68552))),f140(a875,f333(f303(a875,x68551),x68552)))+~P1(f333(f333(f248(a875),x68551),x68552)) % 183.90/184.43 [7058]E(x70581,x70582)+~E(f333(f333(f22(a1),f333(f333(f79(a1),x70581),x70581)),a100),f333(f333(f22(a1),f333(f333(f79(a1),x70582),x70582)),a100)) % 183.90/184.43 [7061]E(x70611,f116(x70612))+E(f277(x70612,f333(f333(f155(x70612,f881(a102,x70612)),f333(f268(a102,x70612),f77(a102))),x70611)),f284(x70612,x70611)) % 183.90/184.43 [7285]P1(f333(f333(f247(a1),x72851),x72852))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x72851),a100)),x72852)) % 183.90/184.43 [7772]~P1(f333(f333(f248(a875),x77721),x77722))+P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x77721),x77722)),a252)) % 183.90/184.43 [7996]~P1(f333(f333(f248(a102),f2(a102)),x79961))+P1(f333(f333(f248(a102),f333(f267(a102,f881(a102,a102)),f333(f278(x79961),x79962))),x79961)) % 183.90/184.43 [8313]~P83(x83131)+P1(f333(f333(f247(x83131),f333(f74(x83131),f333(f167(x83131),x83132))),f333(f167(x83131),f333(f333(f155(x83131,x83131),f74(x83131)),x83132)))) % 183.90/184.43 [8337]P1(f333(f333(f248(a875),x83371),x83372))+~P1(f333(f333(f335(f881(a875,a875)),f333(f333(f268(a875,a875),x83371),x83372)),a252)) % 183.90/184.43 [8497]E(f333(f333(f268(x84971,x84971),f632(x84972,x84971)),f632(x84972,x84971)),x84972)+~P1(f333(f333(f335(f881(x84971,x84971)),x84972),f309(x84971,f196(f882(f881(x84971,x84971),a870))))) % 183.90/184.43 [8538]E(f333(f303(a875,x85381),f333(f333(f79(a875),x85381),f333(f37(a875),x85382))),x85382)+~P1(f333(f333(f247(f882(a875,a870)),x85382),f333(f303(a875,x85381),f333(f333(f79(a875),x85381),f333(f37(a875),x85382))))) % 183.90/184.43 [8866]E(f333(f333(f38(a1),f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x88661),x88661)),a100))),f333(f106(a1),f333(f333(f79(a1),x88662),x88662))),f333(f333(f38(a1),f333(f106(a1),x88661)),f333(f106(a1),x88662)))+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x88662))) % 183.90/184.43 [8996]E(f179(f876(x89961),f333(f333(f8(a870,a870,f876(x89961)),a328),f333(f333(f7(f876(x89961),f876(x89961),a870),a330),f116(x89961))),x89962),f182(x89961,f182(x89961,x89962)))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x89961),a875),f197(f876(x89961))),x89962))) % 183.90/184.43 [8999]E(f333(f333(f38(a1),f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x89991),x89991)),a100))),f333(f106(a1),f333(f333(f79(a1),x89992),x89992))),f333(f333(f38(a1),f333(f333(f79(a1),f333(f106(a1),x89991)),f77(a1))),f333(f106(a1),x89992)))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x89992))) % 183.90/184.43 [9830]P1(f333(a201,x98302))+E(f333(f333(f85(a1,a875),f333(f333(f22(a1),x98301),x98302)),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f2(a875))),a107)),f333(f333(f22(a875),f333(a107,x98301)),f333(a107,x98302))) % 183.90/184.43 [9838]E(f333(f333(f85(a1,a875),f333(f106(a1),f333(f333(f79(a1),x98381),f333(f78(a1),x98382)))),f333(f333(f18(a1,a875,a875),f333(f333(f7(a1,a875,f882(a875,a875)),f333(f333(f8(a870,f882(a875,f882(a875,a875)),a1),f99(a875)),a201)),f2(a875))),a107)),f333(f333(f22(a875),f333(f106(a875),x98381)),f333(f106(a875),x98382)))+P1(f333(f333(f248(a1),x98382),a82)) % 183.90/184.43 [9839]~P26(x98391,x98392)+P1(f333(f333(f247(f882(f881(x98391,x98391),a870)),f333(f333(f290(x98391,x98391,x98391),f333(f267(f882(f881(x98391,x98391),a870),f882(f881(x98391,x98391),a870)),x98392)),f333(f271(f882(f881(x98391,x98391),a870),f882(f881(x98391,x98391),a870)),x98392))),f333(f267(f882(f881(x98391,x98391),a870),f882(f881(x98391,x98391),a870)),x98392))) % 183.90/184.43 [9905]~E(f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,f882(a875,a870),a870),f335(a875)),x99051))),f333(f333(f7(a875,a875,a870),f248(a875)),f333(a115,x99052))))),f2(a875))+~P1(f333(f333(f335(a875),f2(a875)),x99051)) % 183.90/184.43 [9961]E(f44(a1,f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x99611),x99611)),a100)),f333(f106(a1),f333(f333(f79(a1),x99612),x99612))),f333(f333(f79(a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a1,f333(f106(a1),x99611),f333(f106(a1),x99612)))),f77(a1)))+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x99612))) % 183.90/184.43 [9970]E(f44(a1,f333(f106(a1),f333(f333(f22(a1),f333(f333(f79(a1),x99701),x99701)),a100)),f333(f106(a1),f333(f333(f79(a1),x99702),x99702))),f333(f333(f22(a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a1,f333(f333(f79(a1),f333(f106(a1),x99701)),f77(a1)),f333(f106(a1),x99702)))),f77(a1)))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x99702))) % 183.90/184.43 [10022]~P4(x100221)+E(f39(x100221,f333(f253(x100221),f333(f333(f8(f882(x100221,a870),a870,x100221),f87(x100221)),f333(f333(f8(f882(x100221,a870),f882(x100221,a870),x100221),f333(f18(x100221,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100221),a336),f333(f333(f7(x100221,f882(x100221,a870),a870),f335(x100221)),x100222)))),f247(x100221))))),f40(x100221,x100222)) % 183.90/184.43 [10048]~P37(x100481,x100482)+P54(x100481,f333(f333(f7(x100481,f882(f881(x100481,x100481),a870),f882(x100481,a870)),f333(f333(f8(f882(x100481,f882(f882(f881(x100481,x100481),a870),a870)),f882(f882(f881(x100481,x100481),a870),f882(x100481,a870)),x100481),f7(x100481,f882(f881(x100481,x100481),a870),a870)),f333(f333(f8(f882(x100481,f881(x100481,x100481)),f882(x100481,f882(f882(f881(x100481,x100481),a870),a870)),x100481),f333(f8(f881(x100481,x100481),f882(f882(f881(x100481,x100481),a870),a870),x100481),f335(f881(x100481,x100481)))),f268(x100481,x100481)))),x100482)) % 183.90/184.43 [10049]~P7(x100491,f256(f882(x100491,a870)),x100492)+P6(x100491,f333(f333(f7(x100491,f882(f881(x100491,x100491),a870),f882(x100491,a870)),f333(f333(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)),f333(f333(f8(f882(x100491,f881(x100491,x100491)),f882(x100491,f882(f882(f881(x100491,x100491),a870),a870)),x100491),f333(f8(f881(x100491,x100491),f882(f882(f881(x100491,x100491),a870),a870),x100491),f335(f881(x100491,x100491)))),f268(x100491,x100491)))),x100492)) % 183.90/184.43 [10086]P37(x100861,x100862)+~P54(x100861,f333(f333(f7(x100861,f882(f881(x100861,x100861),a870),f882(x100861,a870)),f333(f333(f8(f882(x100861,f882(f882(f881(x100861,x100861),a870),a870)),f882(f882(f881(x100861,x100861),a870),f882(x100861,a870)),x100861),f7(x100861,f882(f881(x100861,x100861),a870),a870)),f333(f333(f8(f882(x100861,f881(x100861,x100861)),f882(x100861,f882(f882(f881(x100861,x100861),a870),a870)),x100861),f333(f8(f881(x100861,x100861),f882(f882(f881(x100861,x100861),a870),a870),x100861),f335(f881(x100861,x100861)))),f268(x100861,x100861)))),x100862)) % 183.90/184.43 [10087]P7(x100871,f256(f882(x100871,a870)),x100872)+~P6(x100871,f333(f333(f7(x100871,f882(f881(x100871,x100871),a870),f882(x100871,a870)),f333(f333(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)),f333(f333(f8(f882(x100871,f881(x100871,x100871)),f882(x100871,f882(f882(f881(x100871,x100871),a870),a870)),x100871),f333(f8(f881(x100871,x100871),f882(f882(f881(x100871,x100871),a870),a870),x100871),f335(f881(x100871,x100871)))),f268(x100871,x100871)))),x100872)) % 183.90/184.43 [7236]E(f333(f333(f79(a875),f333(f106(a875),f333(f333(f22(a1),x72361),a100))),x72362),f333(a115,f333(f333(f79(a875),f333(f106(a875),x72361)),x72362)))+P1(f333(a201,f333(f106(a1),x72361))) % 183.90/184.43 [7685]~P90(x76851)+E(f333(f333(f79(x76851),f333(f333(f79(x76851),f77(x76851)),f333(f106(x76851),x76852))),f333(f106(x76851),x76852)),f333(f106(x76851),f333(f333(f22(a1),f333(f333(f79(a1),x76852),x76852)),a100))) % 183.90/184.43 [8339]~P1(f333(f333(f247(a1),x83391),x83392))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x83391),x83391)),f333(f333(f22(a1),f333(f333(f79(a1),x83392),x83392)),a100))) % 183.90/184.43 [8341]~P1(f333(f333(f247(a1),x83411),x83412))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x83411),x83411)),f333(f333(f22(a1),f333(f333(f79(a1),x83412),x83412)),a100))) % 183.90/184.43 [8758]P1(f333(f333(f247(a1),x87581),x87582))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),x87581),x87581)),f333(f333(f22(a1),f333(f333(f79(a1),x87582),x87582)),a100))) % 183.90/184.43 [8760]P1(f333(f333(f247(a1),x87601),x87602))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x87601),x87601)),f333(f333(f22(a1),f333(f333(f79(a1),x87602),x87602)),a100))) % 183.90/184.43 [9056]~P1(f333(f333(f248(a1),x90561),x90562))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90561),x90561)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x90562),x90562)),a100))) % 183.90/184.43 [9058]~P1(f333(f333(f247(a1),x90581),x90582))+P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90581),x90581)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x90582),x90582)),a100))) % 183.90/184.43 [9059]~P1(f333(f333(f90(a1),x90591),x90592))+P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x90591),x90591)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x90592),x90592)),a100))) % 183.90/184.43 [9322]P1(f333(f333(f248(a1),x93221),x93222))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),x93221),x93221)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x93222),x93222)),a100))) % 183.90/184.43 [9324]P1(f333(f333(f247(a1),x93241),x93242))+~P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),x93241),x93241)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x93242),x93242)),a100))) % 183.90/184.43 [9325]P1(f333(f333(f90(a1),x93251),x93252))+~P1(f333(f333(f90(a1),f333(f333(f22(a1),f333(f333(f79(a1),x93251),x93251)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),x93252),x93252)),a100))) % 183.90/184.43 [9357]~P1(f333(f61(x93571),x93572))+P1(f333(f61(f882(x93571,a870)),f333(f253(f882(x93571,a870)),f333(f333(f7(f882(x93571,a870),f882(x93571,a870),a870),f247(f882(x93571,a870))),x93572)))) % 183.90/184.43 [9405]~E(f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),x94051),f196(f882(f881(a875,a875),a870)))),f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),x94052),f196(f882(f881(a875,a875),a870)))))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x94051),x94052)),a111)) % 183.90/184.43 [9489]E(f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),x94891),f196(f882(f881(a875,a875),a870)))),f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),x94892),f196(f882(f881(a875,a875),a870)))))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x94891),x94892)),a111)) % 183.90/184.43 [9525]P1(f333(f333(f247(a1),f2(a1)),f657(x95251,x95252)))+E(f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95251)),f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95252))) % 183.90/184.43 [10032]~P4(x100321)+E(f40(x100321,f333(f253(x100321),f333(f333(f8(f882(x100321,a870),a870,x100321),f87(x100321)),f333(f333(f8(f882(x100321,a870),f882(x100321,a870),x100321),f333(f18(x100321,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100321),a336),f333(f333(f7(x100321,f882(x100321,a870),a870),f335(x100321)),x100322)))),f333(f7(x100321,x100321,a870),f247(x100321)))))),f39(x100321,x100322)) % 183.90/184.43 [10054]P1(f333(f333(f335(a875),f2(a875)),x100541))+E(f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),a875),f335(a875)),a115)),x100541))),f333(f333(f7(a875,a875,a870),f248(a875)),x100542)))),f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,f882(a875,a870),a870),f335(a875)),x100541))),f333(f333(f7(a875,a875,a870),f248(a875)),f333(a115,x100542)))))) % 183.90/184.43 [7553]~P90(x75531)+E(f333(f333(f80(x75531),x75532),f333(f106(x75531),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),x75532) % 183.90/184.43 [7820]~P90(x78201)+E(f333(f333(f79(x78201),f333(f106(x78201),x78202)),f77(x78201)),f333(f106(x78201),f333(f333(f79(a1),x78202),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))) % 183.90/184.43 [7965]P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x79652)))+E(f333(f333(f258(a1),x79651),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x79652),x79652)),a100))),f77(a1)) % 183.90/184.43 [9383]~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x93832)))+E(f333(f333(f258(a1),x93831),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x93832),x93832)),a100))),f333(f333(f85(a1,a1),f333(f333(f258(a1),x93831),f333(f106(a875),x93832))),f333(f333(f18(a1,a1,a1),f333(f333(f8(a1,f882(a1,a1),a1),f80(a1)),f333(f80(a1),x93831))),f5(a1)))) % 183.90/184.43 [9745]~P1(f333(f333(f247(a875),f669(x97452,x97451)),f333(x97451,f669(x97452,x97451))))+P1(f333(f61(a875),f333(f253(a875),f333(f333(f7(a875,a875,a870),f333(f333(f8(a875,f882(a875,a870),a875),f247(a875)),x97451)),x97452)))) % 183.90/184.43 [9895]~P1(f333(f333(f248(a875),f333(f106(a875),x98951)),f333(a115,x98952)))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x98951),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),f248(a875)),a107)),x98952)))) % 183.90/184.43 [9896]~P1(f333(f333(f247(a875),f333(f106(a875),x98961)),f333(a115,x98962)))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x98961),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),f247(a875)),a107)),x98962)))) % 183.90/184.43 [9945]P1(f333(f333(f248(a875),f333(f106(a875),x99451)),f333(a115,x99452)))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x99451),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),f248(a875)),a107)),x99452)))) % 183.90/184.43 [9946]P1(f333(f333(f247(a875),f333(f106(a875),x99461)),f333(a115,x99462)))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x99461),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),f247(a875)),a107)),x99462)))) % 183.90/184.43 [9976]~P1(f333(f333(f248(a875),f333(a115,x99762)),f333(f106(a875),x99761)))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x99761),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f8(a875,a870,a1),f333(f248(a875),x99762)),a107))))) % 183.90/184.43 [9977]~P1(f333(f333(f247(a875),f333(a115,x99772)),f333(f106(a875),x99771)))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x99771),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f8(a875,a870,a1),f333(f247(a875),x99772)),a107))))) % 183.90/184.43 [10020]P1(f333(f333(f248(a875),f333(a115,x100201)),f333(f106(a875),x100202)))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100202),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f8(a875,a870,a1),f333(f248(a875),x100201)),a107))))) % 183.90/184.43 [10021]P1(f333(f333(f247(a875),f333(a115,x100211)),f333(f106(a875),x100212)))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100212),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f8(a875,a870,a1),f333(f247(a875),x100211)),a107))))) % 183.90/184.43 [10094]~P1(f333(f333(f335(a875),f2(a875)),x100941))+E(f333(a115,f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,f882(a875,a870),a870),f333(f333(f8(a875,f882(f882(a875,a870),a870),a875),f335(a875)),a115)),x100941))),f333(f333(f7(a875,a875,a870),f248(a875)),x100942))))),f333(f37(a875),f333(f253(a875),f333(f333(f18(a875,a870,a870),f333(f333(f8(a870,f882(a870,a870),a875),a331),f333(f333(f7(a875,f882(a875,a870),a870),f335(a875)),x100941))),f333(f333(f7(a875,a875,a870),f248(a875)),f333(a115,x100942)))))) % 183.90/184.43 [8522]~P90(x85221)+E(f333(f333(f80(x85221),f333(f106(x85221),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),x85222),x85222) % 183.90/184.43 [8580]~P90(x85801)+E(f333(f333(f79(x85801),f77(x85801)),f333(f106(x85801),x85802)),f333(f106(x85801),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),x85802))) % 183.90/184.43 [8638]~P90(x86381)+E(f333(f333(f22(x86381),f333(f106(x86381),x86382)),f77(x86381)),f333(f106(x86381),f333(f333(f79(a1),x86382),f333(f78(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.43 [8776]~P1(f333(f333(f248(a875),f333(f106(a875),a82)),x87762))+E(f333(f333(f22(a875),x87761),f333(f333(f22(a875),x87762),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f22(a875),f333(a115,x87761)),x87762)) % 183.90/184.43 [9421]~P109(x94211)+E(f333(f333(f80(x94211),x94212),x94212),f333(f333(f258(x94211),x94212),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.43 [9422]~P77(x94221)+E(f333(f333(f258(x94221),x94222),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f80(x94221),x94222),x94222)) % 183.90/184.43 [9424]~P90(x94241)+E(f333(f333(f80(x94241),x94242),f333(f106(x94241),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f79(x94241),x94242),x94242)) % 183.90/184.43 [9664]~P114(x96641)+E(f333(f333(f258(x96641),f333(f74(x96641),x96642)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f258(x96641),x96642),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.43 [9665]~P138(x96651)+E(f333(f333(f258(x96651),f333(f78(x96651),x96652)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f258(x96651),x96652),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.43 [9661]~P90(x96611)+E(f333(f333(f80(x96611),f333(f106(x96611),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x96612),f333(f333(f79(x96611),x96612),x96612)) % 183.90/184.43 [9785]~P114(x97851)+E(f333(f74(x97851),f333(f333(f258(x97851),x97852),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x97851),x97852),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.43 [9847]~P114(x98471)+P1(f333(f333(f247(x98471),f2(x98471)),f333(f333(f258(x98471),x98472),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.43 [10011]~E(f333(a115,x100112),f333(f106(a875),x100111))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100111),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),a330),a107)),x100112))))) % 183.90/184.43 [10012]~E(f333(f106(a875),x100121),f333(a115,x100122))+P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100121),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),a330),a107)),x100122))))) % 183.90/184.43 [10057]E(f333(a115,x100571),f333(f106(a875),x100572))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100572),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),a330),a107)),x100571))))) % 183.90/184.43 [10058]E(f333(f106(a875),x100581),f333(a115,x100582))+~P1(f333(f333(f85(a1,a870),f333(f106(a1),f333(f333(f79(a1),x100581),a100))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a336),f333(f333(f8(a870,a870,a1),a328),a201))),f333(f333(f7(a1,a875,a870),f333(f333(f8(a875,f882(a875,a870),a1),a330),a107)),x100582))))) % 183.90/184.43 [9844]~P90(x98441)+E(f333(f333(f258(x98441),f333(f106(x98441),a100)),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x98442)),f77(x98441)) % 183.90/184.43 [9845]~P138(x98451)+E(f333(f333(f258(x98451),f333(f78(x98451),f77(x98451))),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x98452)),f77(x98451)) % 183.90/184.43 [9849]~P77(x98491)+E(f333(f333(f258(x98491),x98492),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),a100))),f333(f333(f80(x98491),f333(f333(f80(x98491),x98492),x98492)),x98492)) % 183.90/184.43 [10036]~P1(f333(f333(f247(a1),f2(a1)),x100362))+E(f44(a1,f333(f333(f79(a1),f77(a1)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100361)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100362)),f333(f333(f79(a1),f77(a1)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a1,x100361,x100362)))) % 183.90/184.43 [10060]~P1(f333(f333(f247(a1),f2(a1)),x100602))+E(f333(f333(f38(a1),f333(f333(f79(a1),f77(a1)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100601))),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100602)),f333(f333(f38(a1),x100601),x100602)) % 183.90/184.43 [10062]~P1(f333(f333(f247(a1),x100622),f2(a1)))+E(f333(f333(f38(a1),f333(f333(f79(a1),f77(a1)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100621))),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100622)),f333(f333(f38(a1),f333(f333(f79(a1),x100621),f77(a1))),x100622)) % 183.90/184.43 [10063]~P1(f333(f333(f247(a1),x100632),f2(a1)))+E(f44(a1,f333(f333(f79(a1),f77(a1)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100631)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100632)),f333(f333(f22(a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f44(a1,f333(f333(f79(a1),x100631),f77(a1)),x100632))),f77(a1))) % 183.90/184.43 [9936]~P90(x99361)+E(f333(f333(f258(x99361),f333(f106(x99361),a100)),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99362))),f333(f106(x99361),a100)) % 183.90/184.43 [9938]~P138(x99381)+E(f333(f333(f258(x99381),f333(f78(x99381),f77(x99381))),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99382))),f333(f78(x99381),f77(x99381))) % 183.90/184.43 [5110]~P24(x51101,x51102,x51103)+P28(x51101,x51102,x51103) % 183.90/184.43 [8039]~E(x80392,x80393)+P34(x80391,x80391,a330,x80392,x80393) % 183.90/184.43 [8593]E(x85931,x85932)+~P34(x85933,x85933,a330,x85931,x85932) % 183.90/184.43 [4757]E(f171(x47571,x47572,x47573),f116(x47571))+~E(x47572,f2(a875)) % 183.90/184.43 [4922]~E(f171(x49222,x49221,x49223),f116(x49222))+E(x49221,f2(a875)) % 183.90/184.43 [5115]~P37(x51151,x51153)+P37(x51151,f327(x51151,x51152,x51153)) % 183.90/184.43 [5280]P27(x52801,x52802,x52803)+~P27(x52801,f333(a115,x52802),x52803) % 183.90/184.43 [5367]~P7(x53671,x53672,x53673)+P7(f876(x53671),f162(x53671,x53672),f159(x53671,x53673)) % 183.90/184.43 [5368]~P39(x53681,x53682,x53683)+P39(f876(x53681),f162(x53681,x53682),f159(x53681,x53683)) % 183.90/184.43 [5480]P49(x54801,x54802,x54803)+~E(f613(x54803,x54802,x54801),f614(x54803,x54802,x54801)) % 183.90/184.43 [5481]P50(x54811,x54812,x54813)+~E(f627(x54813,x54812,x54811),f628(x54813,x54812,x54811)) % 183.90/184.43 [6412]P28(x64121,x64122,x64123)+~P27(x64121,f600(x64123,x64122,x64121),f607(x64123,x64122,x64121)) % 183.90/184.43 [4663]~E(x46631,f209(x46632))+~E(x46631,f333(f240(x46632),x46633)) % 183.90/184.43 [4713]~E(f333(f170(x47132),x47131),x47133)+E(x47131,f333(f170(x47132),x47133)) % 183.90/184.43 [4714]~E(x47142,f333(f170(x47141),x47143))+E(f333(f170(x47141),x47142),x47143) % 183.90/184.43 [4763]E(x47631,x47632)+~E(f333(f240(x47633),x47631),f333(f240(x47633),x47632)) % 183.90/184.43 [4764]E(x47641,x47642)+~E(f333(f170(x47643),x47641),f333(f170(x47643),x47642)) % 183.90/184.43 [4969]~P6(x49693,x49691)+P1(f333(f333(x49691,x49692),x49692)) % 183.90/184.43 [4970]~P48(x49703,x49701)+P1(f333(f333(x49701,x49702),x49702)) % 183.90/184.43 [4972]~P54(x49721,x49722)+P1(f333(f321(x49721,x49722),x49723)) % 183.90/184.43 [5034]~P37(x50341,x50342)+P37(f876(x50341),f333(f144(x50341,x50342),x50343)) % 183.90/184.43 [5039]~P1(f333(x50392,x50393))+~E(f333(f253(x50391),x50392),f196(f882(x50391,a870))) % 183.90/184.43 [5040]~P1(f333(x50402,x50403))+~E(f196(f882(x50401,a870)),f333(f253(x50401),x50402)) % 183.90/184.43 [5052]E(x50521,f2(a875))+E(f145(x50522,f171(x50522,x50521,x50523)),x50523) % 183.90/184.43 [5070]~P1(f333(x50701,x50703))+P1(f333(x50701,f89(x50702,x50701))) % 183.90/184.43 [5082]E(x50821,f2(a875))+E(f333(f142(x50822),f171(x50822,x50821,x50823)),x50823) % 183.90/184.43 [5188]~E(x51882,x51883)+P1(f333(f333(f335(x51881),x51882),f333(a330,x51883))) % 183.90/184.43 [5200]P1(f333(x52001,x52002))+~P1(f333(x52001,f575(x52001,x52003))) % 183.90/184.43 [5201]~E(x52012,f2(a875))+E(f333(f174(x52011),f171(x52011,x52012,x52013)),f196(f882(x52011,a870))) % 183.90/184.43 [5246]E(f333(f170(x52461),x52462),f333(f333(f152(x52461),x52463),f116(x52461)))+~E(x52462,f333(f333(f152(x52461),x52463),f116(x52461))) % 183.90/184.43 [5247]~E(x52473,f333(f333(f152(x52471),x52472),f116(x52471)))+E(f333(f333(f152(x52471),x52472),f116(x52471)),f333(f170(x52471),x52473)) % 183.90/184.43 [5273]~E(x52733,f333(f16(f879(x52732),x52731),f209(x52732)))+E(f186(x52731,x52732,x52733),f196(f882(x52731,a870))) % 183.90/184.43 [5295]~P33(x52951,x52952,x52953)+P33(x52951,x52952,f333(f170(x52951),x52953)) % 183.90/184.43 [5296]~P31(x52961,x52962,x52963)+P31(x52961,x52962,f333(f170(x52961),x52963)) % 183.90/184.43 [5299]E(f333(f37(x52991),f342(x52992,x52993,x52991)),x52992)+~E(f333(f37(x52991),x52993),f333(a115,x52992)) % 183.90/184.43 [5305]~P37(x53051,x53053)+P1(f333(f333(f335(x53051),x53052),f322(x53051,x53053))) % 183.90/184.43 [5309]~E(f333(f170(x53092),x53091),f333(f333(f152(x53092),x53093),f116(x53092)))+E(x53091,f333(f333(f152(x53092),x53093),f116(x53092))) % 183.90/184.43 [5310]~E(f333(f333(f152(x53102),x53103),f116(x53102)),f333(f170(x53102),x53101))+E(x53101,f333(f333(f152(x53102),x53103),f116(x53102))) % 183.90/184.43 [5325]E(x53251,f333(f16(f879(x53252),x53253),f209(x53252)))+~E(f186(x53253,x53252,x53251),f196(f882(x53253,a870))) % 183.90/184.43 [5331]E(f84(f881(a875,a875),f47(x53311,x53312)),x53313)+~P1(f333(f47(x53311,x53312),x53313)) % 183.90/184.43 [5339]~E(x53393,f333(f240(x53391),x53392))+P1(f333(f333(f335(x53391),x53392),f239(x53391,x53393))) % 183.90/184.43 [5371]P33(x53711,x53712,x53713)+~P33(x53711,x53712,f333(f170(x53711),x53713)) % 183.90/184.43 [5372]P31(x53721,x53722,x53723)+~P31(x53721,x53722,f333(f170(x53721),x53723)) % 183.90/184.43 [5434]~E(x54342,f116(x54341))+P1(f333(f333(f335(f876(x54341)),x54342),f162(x54341,x54343))) % 183.90/184.43 [5441]~P39(x54411,x54412,x54413)+P39(x54411,x54412,f333(f288(x54411,x54411),x54413)) % 183.90/184.43 [5442]~P50(x54421,x54422,x54423)+P50(x54421,x54422,f333(f288(x54421,x54421),x54423)) % 183.90/184.43 [5461]~P55(x54611)+E(f44(x54611,f44(x54611,x54612,x54613),x54613),f44(x54611,x54612,x54613)) % 183.90/184.43 [5558]E(x55581,x55582)+~P1(f333(f333(f335(x55583),x55581),f333(a330,x55582))) % 183.90/184.43 [5604]~P141(x56041)+E(f198(x56041,x56042,f2(a875),x56043),x56043) % 183.90/184.43 [5624]P39(x56241,x56242,x56243)+~P39(x56241,x56242,f333(f288(x56241,x56241),x56243)) % 183.90/184.43 [5625]P50(x56251,x56252,x56253)+~P50(x56251,x56252,f333(f288(x56251,x56251),x56253)) % 183.90/184.43 [5629]~P106(x56292)+E(f151(x56291,x56292,x56293,f116(x56291)),f116(x56291)) % 183.90/184.43 [5642]E(f172(x56421,x56422,f153(x56421,x56423)),f153(x56421,f172(x56421,x56422,x56423)))+~P1(f333(f138(x56421),x56423)) % 183.90/184.43 [5648]E(x56481,f333(f240(x56482),x56483))+~P1(f333(f333(f335(x56482),x56483),f239(x56482,x56481))) % 183.90/184.43 [5743]E(f333(f137(x57431,x57432),x57433),f116(x57431))+P1(f333(x57432,f727(x57433,x57432,x57431))) % 183.90/184.43 [5886]~P1(f333(f138(x58861),x58862))+P1(f333(f138(x58861),f178(x58861,x58862,x58863))) % 183.90/184.43 [5887]~P1(f333(f138(x58871),x58873))+P1(f333(f138(x58871),f172(x58871,x58872,x58873))) % 183.90/184.43 [5888]~P1(f333(f138(x58881),x58883))+P1(f333(f138(x58881),f179(x58881,x58882,x58883))) % 183.90/184.43 [5889]~P1(f333(f138(x58891),x58893))+P1(f333(f138(x58891),f141(x58891,x58892,x58893))) % 183.90/184.43 [5890]~P143(x58901,x58903,x58902)+P1(f333(x58901,f44(a1,x58902,x58903))) % 183.90/184.43 [5907]~P33(x59073,x59071,x59072)+P1(f333(x59071,f777(x59072,x59071,x59073))) % 183.90/184.43 [5908]~P35(x59083,x59081,x59082)+P1(f333(x59081,f806(x59082,x59081,x59083))) % 183.90/184.43 [5930]E(f333(f137(x59301,x59302),x59303),f179(x59301,x59302,x59303))+P1(f333(x59302,f756(x59303,x59302,x59301))) % 183.90/184.43 [5972]~P1(f333(f138(x59721),x59723))+P1(f333(f138(f876(x59721)),f54(x59721,x59722,x59723))) % 183.90/184.43 [6005]~P108(x60051)+E(f333(f333(f104(f882(x60051,a870)),f333(f254(x60051),x60052)),f304(x60051,x60052,x60053)),f196(f882(x60051,a870))) % 183.90/184.43 [6006]~P108(x60061)+E(f333(f333(f104(f882(x60061,a870)),f333(f302(x60061),x60062)),f307(x60061,x60062,x60063)),f196(f882(x60061,a870))) % 183.90/184.43 [6007]~P108(x60071)+E(f333(f333(f104(f882(x60071,a870)),f333(f302(x60071),x60072)),f306(x60071,x60072,x60073)),f196(f882(x60071,a870))) % 183.90/184.43 [6233]E(f333(f137(x62331,x62332),x62333),x62333)+~P1(f333(x62332,f728(x62333,x62332,x62331))) % 183.90/184.43 [6235]E(f333(f333(f311(x62351),f366(x62352,x62353,x62351)),f342(x62352,x62353,x62351)),x62353)+~E(f333(f37(x62351),x62353),f333(a115,x62352)) % 183.90/184.43 [6251]P143(x62511,x62512,x62513)+~P1(f333(x62511,f44(a1,x62513,x62512))) % 183.90/184.43 [6298]P31(x62981,x62982,x62983)+~P1(f333(x62982,f794(x62983,x62982,x62981))) % 183.90/184.43 [6299]P31(x62991,x62992,x62993)+~P1(f333(x62992,f800(x62992,x62993,x62991))) % 183.90/184.43 [6300]P31(x63001,x63002,x63003)+~P1(f333(x63002,f801(x63003,x63002,x63001))) % 183.90/184.43 [6302]E(f179(x63021,x63022,x63023),x63023)+~P1(f333(x63022,f752(x63023,x63022,x63021))) % 183.90/184.43 [6381]~P1(f333(x63812,f595(x63813,x63812,x63811)))+P1(f333(f261(x63811,x63812),x63813)) % 183.90/184.43 [6382]~P1(f333(x63822,f720(x63823,x63822,x63821)))+P1(f333(f161(x63821,x63822),x63823)) % 183.90/184.43 [6627]~P1(f333(f321(x66271,x66272),f525(x66273,x66272,x66271)))+P1(f333(f321(x66271,x66272),x66273)) % 183.90/184.43 [6628]~P1(f333(f321(x66281,x66282),f549(x66283,x66282,x66281)))+P1(f333(f321(x66281,x66282),x66283)) % 183.90/184.43 [7237]~P55(x72371)+E(f333(f333(f79(x72371),f333(f333(f80(x72371),x72372),f333(f333(f38(x72371),x72373),x72372))),f44(x72371,x72373,x72372)),x72373) % 183.90/184.43 [7709]E(f333(f333(f268(x77091,x77091),f553(x77092,x77093,x77091)),f553(x77092,x77093,x77091)),x77093)+~P1(f333(f333(f335(f881(x77091,x77091)),x77093),f265(x77091,x77092))) % 183.90/184.43 [7828]~P1(f333(f333(f335(x78281),f557(x78283,x78282,x78281)),f322(x78281,x78283)))+P1(f333(f333(f335(x78281),x78282),f322(x78281,x78283))) % 183.90/184.43 [7829]~P1(f333(f333(f335(x78291),f617(x78293,x78292,x78291)),f322(x78291,x78293)))+P1(f333(f333(f335(x78291),x78292),f322(x78291,x78293))) % 183.90/184.43 [7830]~P1(f333(f333(f335(x78301),f619(x78303,x78302,x78301)),f322(x78301,x78303)))+P1(f333(f333(f335(x78301),x78302),f322(x78301,x78303))) % 183.90/184.43 [8020]~P55(x80201)+E(f333(f333(f79(x80201),f333(f333(f80(x80201),f333(f333(f38(x80201),x80202),x80203)),x80203)),f44(x80201,x80202,x80203)),x80202) % 183.90/184.43 [8065]~E(f333(f37(x80651),x80652),f333(a115,x80653))+~P1(f333(f333(f335(x80651),f366(x80653,x80652,x80651)),f342(x80653,x80652,x80651))) % 183.90/184.43 [8688]P1(f333(f333(f247(f882(f881(x86881,x86881),a870)),f309(x86881,x86882)),f309(x86881,x86883)))+~P1(f333(f333(f247(f882(f881(x86881,x86881),a870)),x86882),f309(x86881,x86883))) % 183.90/184.43 [8965]E(x89651,f116(x89652))+~P1(f333(f333(f335(f881(f876(x89652),f876(x89652))),f333(f333(f268(f876(x89652),f876(x89652)),x89651),f116(x89652))),f159(x89652,x89653))) % 183.90/184.43 [8990]E(x89901,f116(x89902))+~P1(f333(f333(f335(f881(f876(x89902),f876(x89902))),f333(f333(f268(f876(x89902),f876(x89902)),f116(x89902)),x89901)),f159(x89902,x89903))) % 183.90/184.43 [9113]E(f333(f333(f152(x91131),f707(x91132,x91133,x91131)),f708(x91132,x91133,x91131)),x91133)+~P1(f333(f333(f335(f881(f876(x91131),f876(x91131))),f333(f333(f268(f876(x91131),f876(x91131)),f116(x91131)),x91133)),f148(x91131,x91132))) % 183.90/184.43 [9350]~P121(x93501)+~P1(f333(f333(f248(x93501),f333(f333(f79(x93501),f333(f333(f80(x93501),x93502),x93502)),f333(f333(f80(x93501),x93503),x93503))),f2(x93501))) % 183.90/184.43 [9400]P1(f333(f61(x94001),x94002))+~P1(f333(f333(f335(f881(f882(x94001,a870),f882(x94001,a870))),f333(f333(f268(f882(x94001,a870),f882(x94001,a870)),x94003),x94002)),f308(x94001))) % 183.90/184.43 [9686]~P46(x96861,x96862,x96863)+P1(f333(f333(f248(a1),f333(f333(f72(f881(a1,a1),a1,x96861,f267(a1,a1)),f224(x96861)),f235(x96861,x96862,f232(x96861,x96863)))),f2(a1))) % 183.90/184.43 [9687]~P47(x96871,x96872,x96873)+P1(f333(f333(f247(a1),f333(f333(f72(f881(a1,a1),a1,x96871,f267(a1,a1)),f224(x96871)),f235(x96871,x96872,f232(x96871,x96873)))),f2(a1))) % 183.90/184.43 [9814]P46(x98141,x98142,x98143)+~P1(f333(f333(f248(a1),f333(f333(f72(f881(a1,a1),a1,x98141,f267(a1,a1)),f224(x98141)),f235(x98141,x98142,f232(x98141,x98143)))),f2(a1))) % 183.90/184.43 [9815]P47(x98151,x98152,x98153)+~P1(f333(f333(f247(a1),f333(f333(f72(f881(a1,a1),a1,x98151,f267(a1,a1)),f224(x98151)),f235(x98151,x98152,f232(x98151,x98153)))),f2(a1))) % 183.90/184.43 [10137]~P114(x101371)+~P1(f333(f333(f248(x101371),f333(f333(f79(x101371),f333(f333(f258(x101371),x101372),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101371),x101373),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f2(x101371))) % 183.90/184.43 [4744]~E(x47443,f116(x47441))+E(f333(f333(f135(x47441),x47442),x47443),x47442) % 183.90/184.43 [4745]~E(x47452,f116(x47451))+E(f333(f333(f135(x47451),x47452),x47453),x47453) % 183.90/184.43 [4752]~E(x47522,f2(a875))+E(f333(f333(f177(x47521),x47522),x47523),f116(x47521)) % 183.90/184.43 [4758]~E(x47583,f116(x47581))+E(f333(f333(f177(x47581),x47582),x47583),f116(x47581)) % 183.90/184.43 [4798]~E(x47981,x47983)+E(x47981,f333(f333(f135(x47982),f116(x47982)),x47983)) % 183.90/184.43 [4885]~P2(x48852)+E(f333(f196(f882(x48851,x48852)),x48853),f196(x48852)) % 183.90/184.43 [4886]~P104(x48862)+E(f333(f256(f882(x48861,x48862)),x48863),f256(x48862)) % 183.90/184.43 [4904]E(x49041,f116(x49042))+~E(f333(f333(f135(x49042),x49043),x49041),x49043) % 183.90/184.43 [4905]E(x49051,f116(x49052))+~E(f333(f333(f135(x49052),x49051),x49053),x49053) % 183.90/184.43 [4913]E(x49131,f116(x49132))+~E(f333(f333(f135(x49132),x49133),x49131),f116(x49132)) % 183.90/184.43 [4914]E(x49141,f116(x49142))+~E(f333(f333(f135(x49142),x49141),x49143),f116(x49142)) % 183.90/184.43 [4939]~E(x49392,f2(a875))+E(f333(f333(f80(a875),x49391),x49392),f333(f333(f80(a875),x49393),x49392)) % 183.90/184.43 [4941]~E(x49411,f2(a875))+E(f333(f333(f80(a875),x49411),x49412),f333(f333(f80(a875),x49411),x49413)) % 183.90/184.43 [4994]~P62(x49941)+E(f333(f333(f113(x49941),x49942),x49943),f333(f333(f113(x49941),x49943),x49942)) % 183.90/184.43 [4996]~P98(x49961)+E(f333(f333(f113(x49961),x49962),x49963),f333(f333(f113(x49961),x49963),x49962)) % 183.90/184.43 [4997]~P62(x49971)+E(f333(f333(f104(x49971),x49972),x49973),f333(f333(f104(x49971),x49973),x49972)) % 183.90/184.43 [4999]~P99(x49991)+E(f333(f333(f104(x49991),x49992),x49993),f333(f333(f104(x49991),x49993),x49992)) % 183.90/184.43 [5000]~P109(x50001)+E(f333(f333(f79(x50001),x50002),x50003),f333(f333(f79(x50001),x50003),x50002)) % 183.90/184.43 [5001]~P109(x50011)+E(f333(f333(f80(x50011),x50012),x50013),f333(f333(f80(x50011),x50013),x50012)) % 183.90/184.43 [5003]~P106(x50031)+E(f333(f333(f245(x50031),x50032),x50033),f333(f333(f245(x50031),x50033),x50032)) % 183.90/184.43 [5005]~P106(x50051)+E(f333(f333(f246(x50051),x50052),x50053),f333(f333(f246(x50051),x50053),x50052)) % 183.90/184.43 [5065]E(f44(a875,x50651,x50652),f2(a875))+~E(x50651,f333(f333(f80(a875),x50652),x50653)) % 183.90/184.43 [5066]E(f44(a1,x50661,x50662),f2(a1))+~E(x50661,f333(f333(f80(a1),x50662),x50663)) % 183.90/184.43 [5127]E(x51271,x51272)+~E(f333(f333(f79(a875),x51273),x51271),f333(f333(f79(a875),x51273),x51272)) % 183.90/184.43 [5128]E(x51281,x51282)+~E(f333(f333(f79(a875),x51281),x51283),f333(f333(f79(a875),x51282),x51283)) % 183.90/184.43 [5138]~P93(x51381)+E(f333(f333(f104(x51381),x51382),f333(f78(x51381),x51383)),f333(f333(f22(x51381),x51382),x51383)) % 183.90/184.43 [5139]~P65(x51391)+E(f333(f333(f79(x51391),x51392),f333(f78(x51391),x51393)),f333(f333(f22(x51391),x51392),x51393)) % 183.90/184.43 [5140]~P72(x51401)+E(f333(f333(f79(x51401),x51402),f333(f78(x51401),x51403)),f333(f333(f22(x51401),x51402),x51403)) % 183.90/184.43 [5141]~P113(x51411)+E(f333(f333(f79(x51411),x51412),f333(f78(x51411),x51413)),f333(f333(f22(x51411),x51412),x51413)) % 183.90/184.43 [5142]~P72(x51421)+E(f333(f333(f22(x51421),x51422),f333(f78(x51421),x51423)),f333(f333(f79(x51421),x51422),x51423)) % 183.90/184.43 [5181]~P1(f333(x51813,x51812))+P1(f333(f333(f335(x51811),x51812),x51813)) % 183.90/184.43 [5183]~P66(x51832)+E(f333(f333(f6(x51831,x51832),x51833),f196(f882(x51831,a870))),f2(x51832)) % 183.90/184.43 [5185]~P73(x51852)+E(f333(f333(f9(x51851,x51852),x51853),f196(f882(x51851,a870))),f77(x51852)) % 183.90/184.43 [5234]~E(x52342,f333(f333(f79(a875),x52341),x52343))+P1(f333(f333(f247(a875),x52341),x52342)) % 183.90/184.43 [5237]~E(x52372,f196(f882(x52371,a870)))+E(f333(f333(f60(x52371),x52372),x52373),f196(f882(f882(x52371,a870),a870))) % 183.90/184.43 [5238]~E(x52382,f196(f882(x52381,a870)))+E(f196(f882(f882(x52381,a870),a870)),f333(f333(f60(x52381),x52382),x52383)) % 183.90/184.43 [5314]~E(f333(f264(x53142,x53143),x53141),f196(f882(x53143,a870)))+E(x53141,f196(f882(f881(x53142,x53143),a870))) % 183.90/184.43 [5315]~E(f333(f266(x53152,x53153),x53151),f196(f882(x53152,a870)))+E(x53151,f196(f882(f881(x53152,x53153),a870))) % 183.90/184.43 [5345]E(f333(f264(x53451,x53452),x53453),f196(f882(x53452,a870)))+~E(x53453,f196(f882(f881(x53451,x53452),a870))) % 183.90/184.43 [5346]E(f333(f266(x53461,x53462),x53463),f196(f882(x53461,a870)))+~E(x53463,f196(f882(f881(x53461,x53462),a870))) % 183.90/184.43 [5349]E(f283(x53491,x53492,x53493),f333(f333(f22(a102),x53492),x53493))+P1(f333(f333(f248(a102),x53492),x53493)) % 183.90/184.43 [5365]P1(f333(x53651,x53652))+~P1(f333(f333(f335(x53653),x53652),x53651)) % 183.90/184.43 [5404]E(x54041,x54042)+~E(f333(f78(f882(x54043,a870)),x54041),f333(f78(f882(x54043,a870)),x54042)) % 183.90/184.43 [5409]E(f315(x54091,x54092,x54093),f209(f876(a329)))+~P1(f333(f333(f248(a1),x54092),x54093)) % 183.90/184.43 [5414]~E(x54141,f196(f882(x54142,a870)))+~P1(f333(f333(f335(x54142),x54143),x54141)) % 183.90/184.43 [5443]~E(x54432,f333(f333(f79(a1),x54431),f333(f103(a1),x54433)))+P1(f333(f333(f247(a1),x54431),x54432)) % 183.90/184.43 [5459]E(f333(f333(f311(x54591),x54592),x54593),x54593)+~P1(f333(f333(f335(x54591),x54592),x54593)) % 183.90/184.43 [5470]E(x54701,f196(f882(x54702,a870)))+~E(f333(f333(f60(x54702),x54701),x54703),f196(f882(f882(x54702,a870),a870))) % 183.90/184.43 [5471]E(x54711,f196(f882(x54712,a870)))+~E(f196(f882(f882(x54712,a870),a870)),f333(f333(f60(x54712),x54711),x54713)) % 183.90/184.43 [5478]~P103(x54781)+E(f333(f333(f80(x54781),f333(f78(x54781),x54782)),f333(f78(x54781),x54783)),f333(f333(f80(x54781),x54782),x54783)) % 183.90/184.43 [5479]~P58(x54791)+E(f333(f333(f291(x54791),f333(f78(x54791),x54792)),f333(f78(x54791),x54793)),f333(f333(f291(x54791),x54792),x54793)) % 183.90/184.43 [5511]~P1(f333(x55113,x55112))+P1(f333(f333(f335(x55111),x55112),f333(f253(x55111),x55113))) % 183.90/184.43 [5532]E(x55321,f2(a875))+E(f333(f174(x55322),f171(x55322,x55321,x55323)),f333(f333(f311(x55322),x55323),f196(f882(x55322,a870)))) % 183.90/184.43 [5551]E(f172(x55511,x55512,x55513),x55513)+P1(f333(f333(f335(x55511),x55512),f333(f174(x55511),x55513))) % 183.90/184.43 [5633]~P1(f333(f138(x56331),x56333))+P1(f333(f138(x56331),f333(f137(x56331,x56332),x56333))) % 183.90/184.43 [5678]~P55(x56781)+E(f333(f333(f38(x56781),f44(x56781,x56782,x56783)),x56783),f2(x56781)) % 183.90/184.43 [5697]E(f178(x56971,f333(f333(f152(x56971),x56972),f116(x56971)),x56973),f116(x56971))+P1(f333(f333(f335(a875),f2(a875)),x56973)) % 183.90/184.43 [5703]E(x57031,f2(a875))+E(f333(f173(x57032),f171(x57032,x57031,x57033)),f171(x57032,f333(f333(f22(a875),x57031),f77(a875)),x57033)) % 183.90/184.43 [5753]E(f333(f333(f152(x57531),x57532),x57533),f141(x57531,x57532,x57533))+P1(f333(f333(f335(x57531),x57532),f333(f174(x57531),x57533))) % 183.90/184.43 [5762]E(x57621,x57622)+~E(f333(f333(f80(a875),f333(a115,x57623)),x57621),f333(f333(f80(a875),f333(a115,x57623)),x57622)) % 183.90/184.43 [5763]~E(x57632,f333(f333(f79(a1),x57631),f333(f103(a1),f333(a115,x57633))))+P1(f333(f333(f248(a1),x57631),x57632)) % 183.90/184.43 [5868]~E(x58683,f116(x58681))+E(f333(f333(f333(f191(f876(x58681),f876(x58681)),x58682),f169(x58681)),x58683),f116(x58681)) % 183.90/184.43 [5872]P1(f333(x58721,x58722))+~P1(f333(f333(f335(x58723),x58722),f333(f253(x58723),x58721))) % 183.90/184.43 [5902]E(x59021,x59022)+~E(f333(f333(f311(x59023),x59021),f196(f882(x59023,a870))),f333(f333(f311(x59023),x59022),f196(f882(x59023,a870)))) % 183.90/184.43 [5913]~P108(x59131)+E(f333(f333(f104(f882(x59131,a870)),f333(f254(x59131),x59132)),f333(f303(x59131,x59132),x59133)),f196(f882(x59131,a870))) % 183.90/184.43 [5956]E(f141(x59561,x59562,x59563),x59563)+~P1(f333(f333(f335(x59561),x59562),f333(f174(x59561),x59563))) % 183.90/184.43 [5980]~P82(x59801)+E(f333(f312(x59801,x59801,f78(x59801)),f333(f303(x59801,x59802),x59803)),f306(x59801,f333(f78(x59801),x59803),f333(f78(x59801),x59802))) % 183.90/184.43 [5989]E(f333(f197(f876(x59891)),f172(x59891,x59892,x59893)),f333(f197(f876(x59891)),x59893))+P1(f333(f333(f335(x59891),x59892),f333(f174(x59891),x59893))) % 183.90/184.43 [6041]~P108(x60411)+E(f333(f333(f104(f882(x60411,a870)),f333(f303(x60411,x60412),x60413)),f333(f255(x60411),x60413)),f196(f882(x60411,a870))) % 183.90/184.43 [6064]~P82(x60641)+E(f333(f312(x60641,x60641,f78(x60641)),f307(x60641,x60642,x60643)),f307(x60641,f333(f78(x60641),x60643),f333(f78(x60641),x60642))) % 183.90/184.43 [6065]~P82(x60651)+E(f333(f312(x60651,x60651,f78(x60651)),f304(x60651,x60652,x60653)),f304(x60651,f333(f78(x60651),x60653),f333(f78(x60651),x60652))) % 183.90/184.43 [6122]E(f178(x61221,f333(f333(f152(x61221),x61222),f116(x61221)),x61223),f333(f333(f152(x61221),x61222),f116(x61221)))+~P1(f333(f333(f335(a875),f2(a875)),x61223)) % 183.90/184.43 [6129]~P82(x61291)+E(f333(f312(x61291,x61291,f78(x61291)),f306(x61291,x61292,x61293)),f333(f303(x61291,f333(f78(x61291),x61293)),f333(f78(x61291),x61292))) % 183.90/184.43 [6149]~P56(x61491)+E(f44(x61491,f333(f78(x61491),f44(x61491,x61492,x61493)),x61493),f44(x61491,f333(f78(x61491),x61492),x61493)) % 183.90/184.43 [6248]~P1(f333(f61(f881(x62482,x62481)),x62483))+P1(f333(f61(x62481),f333(f264(x62482,x62481),x62483))) % 183.90/184.43 [6249]~P1(f333(f61(f881(x62491,x62492)),x62493))+P1(f333(f61(x62491),f333(f266(x62491,x62492),x62493))) % 183.90/184.43 [6255]~P108(x62551)+E(f333(f333(f104(f882(x62551,a870)),f307(x62551,x62552,x62553)),f333(f255(x62551),x62553)),f196(f882(x62551,a870))) % 183.90/184.43 [6256]~P108(x62561)+E(f333(f333(f104(f882(x62561,a870)),f306(x62561,x62562,x62563)),f333(f305(x62561),x62563)),f196(f882(x62561,a870))) % 183.90/184.43 [6257]~P108(x62571)+E(f333(f333(f104(f882(x62571,a870)),f304(x62571,x62572,x62573)),f333(f305(x62571),x62573)),f196(f882(x62571,a870))) % 183.90/184.43 [6323]E(f333(f333(f166(x63231),x63232),f653(x63232,x63233,x63231)),x63233)+~P1(f333(f333(f335(x63231),x63233),f333(f174(x63231),x63232))) % 183.90/184.43 [6462]E(x64621,f116(x64622))+~E(f333(f333(f333(f191(f876(x64622),f876(x64622)),x64623),f169(x64622)),x64621),f116(x64622)) % 183.90/184.43 [6564]~P1(f333(f61(f881(x65642,x65641)),x65643))+P1(f333(f61(f881(x65641,x65642)),f333(f288(x65642,x65641),x65643))) % 183.90/184.43 [6715]P50(x67151,x67152,x67153)+P1(f333(f333(f335(x67151),f628(x67153,x67152,x67151)),x67152)) % 183.90/184.43 [6716]P50(x67161,x67162,x67163)+P1(f333(f333(f335(x67161),f627(x67163,x67162,x67161)),x67162)) % 183.90/184.43 [6728]P1(f333(f321(x67281,x67282),x67283))+P1(f333(f333(x67282,f525(x67283,x67282,x67281)),x67283)) % 183.90/184.43 [6729]P1(f333(f321(x67291,x67292),x67293))+P1(f333(f333(x67292,f549(x67293,x67292,x67291)),x67293)) % 183.90/184.43 [6760]E(f333(f197(f876(x67601)),f172(x67601,x67602,x67603)),f333(f333(f22(a875),f333(f197(f876(x67601)),x67603)),f77(a875)))+~P1(f333(f333(f335(x67601),x67602),f333(f174(x67601),x67603))) % 183.90/184.43 [6800]P1(f333(f261(x68001,x68002),x68003))+P1(f333(f333(f335(x68001),f595(x68003,x68002,x68001)),x68003)) % 183.90/184.43 [6811]~P1(f333(f61(f881(x68112,x68111)),f333(f288(x68111,x68112),x68113)))+P1(f333(f61(f881(x68111,x68112)),x68113)) % 183.90/184.43 [6867]~P1(f333(f333(f335(x68671),x68672),f333(f174(x68671),f117(x68671,x68673))))+P1(f333(f333(f335(x68671),x68672),f333(f174(x68671),x68673))) % 183.90/184.43 [6872]P28(x68721,x68722,x68723)+P1(f333(f333(f335(f874(x68721)),f607(x68723,x68722,x68721)),x68723)) % 183.90/184.43 [6902]E(f333(f137(x69021,x69022),x69023),x69023)+P1(f333(f333(f335(x69021),f728(x69023,x69022,x69021)),f333(f174(x69021),x69023))) % 183.90/184.43 [6917]E(f333(f137(x69171,x69172),x69173),f116(x69171))+P1(f333(f333(f335(x69171),f727(x69173,x69172,x69171)),f333(f174(x69171),x69173))) % 183.90/184.43 [6940]P31(x69401,x69402,x69403)+P1(f333(f333(f335(x69401),f794(x69403,x69402,x69401)),f333(f174(x69401),x69403))) % 183.90/184.43 [6941]P31(x69411,x69412,x69413)+P1(f333(f333(f335(x69411),f801(x69413,x69412,x69411)),f333(f174(x69411),x69413))) % 183.90/184.43 [6942]P31(x69421,x69422,x69423)+P1(f333(f333(f335(x69421),f800(x69422,x69423,x69421)),f333(f174(x69421),x69423))) % 183.90/184.43 [6945]E(f179(x69451,x69452,x69453),x69453)+P1(f333(f333(f335(x69451),f752(x69453,x69452,x69451)),f333(f174(x69451),x69453))) % 183.90/184.43 [7026]P1(f333(f161(x70261,x70262),x70263))+P1(f333(f333(f335(x70261),f720(x70263,x70262,x70261)),f333(f174(x70261),x70263))) % 183.90/184.43 [7035]~P33(x70351,x70353,x70352)+P1(f333(f333(f335(x70351),f777(x70352,x70353,x70351)),f333(f174(x70351),x70352))) % 183.90/184.43 [7036]~P35(x70361,x70363,x70362)+P1(f333(f333(f335(x70361),f806(x70362,x70363,x70361)),f333(f174(x70361),x70362))) % 183.90/184.43 [7071]P1(f333(f333(f335(x70711),x70712),f655(x70713,x70712,x70711)))+~P1(f333(f333(f335(x70711),x70712),f39(f882(x70711,a870),x70713))) % 183.90/184.43 [7072]~P66(x70721)+E(f333(f333(f79(x70721),f333(f333(f6(a875,x70721),x70722),f333(f254(a875),x70723))),f333(x70722,x70723)),f333(f333(f6(a875,x70721),x70722),f333(f254(a875),f333(a115,x70723)))) % 183.90/184.43 [7161]~P33(x71612,x71611,x71613)+P1(f333(x71611,f333(f333(f166(x71612),x71613),f790(x71613,x71611,x71612)))) % 183.90/184.43 [7174]~P1(f333(f333(f335(x71741),x71742),f831(x71742,x71743,x71741)))+P1(f333(f333(f335(x71741),x71742),f40(f882(x71741,a870),x71743))) % 183.90/184.43 [7204]~P66(x72041)+E(f333(f333(f79(x72041),f333(f333(f6(a875,x72041),x72042),f333(f302(a875),x72043))),f333(x72042,f333(a115,x72043))),f333(f333(f6(a875,x72041),x72042),f333(f302(a875),f333(a115,x72043)))) % 183.90/184.43 [7339]P1(f333(f333(f335(f876(x73391)),x73392),f162(x73391,x73393)))+P1(f333(f333(f335(x73391),f678(x73393,x73392,x73391)),f333(f174(x73391),x73392))) % 183.90/184.43 [7356]~P1(f333(f333(f335(f876(x73561)),x73562),f162(x73561,f322(x73561,x73563))))+P1(f333(f333(f335(f876(x73561)),x73562),f322(f876(x73561),f158(x73561,x73563)))) % 183.90/184.43 [7381]~P1(f333(f333(f335(f876(x73811)),x73812),f322(f876(x73811),f158(x73811,x73813))))+P1(f333(f333(f335(f876(x73811)),x73812),f162(x73811,f322(x73811,x73813)))) % 183.90/184.43 [7417]E(f333(f333(f333(f191(f876(x74171),f876(x74171)),x74172),f169(x74171)),x74173),x74173)+~P1(f333(f333(f247(a875),f333(f197(f876(x74171)),x74173)),f77(a875))) % 183.90/184.43 [7453]E(f333(f333(f135(x74531),f796(x74532,x74533,x74531)),f333(f333(f152(x74531),x74533),f797(x74532,x74533,x74531))),x74532)+~P1(f333(f333(f335(x74531),x74533),f333(f174(x74531),x74532))) % 183.90/184.43 [7454]E(f333(f333(f135(x74541),f791(x74542,x74543,x74541)),f333(f333(f152(x74541),x74543),f792(x74542,x74543,x74541))),x74542)+~P1(f333(f333(f335(x74541),x74543),f333(f174(x74541),x74542))) % 183.90/184.43 [7455]E(f333(f333(f135(x74551),f798(x74552,x74553,x74551)),f333(f333(f152(x74551),x74553),f799(x74552,x74553,x74551))),x74552)+~P1(f333(f333(f335(x74551),x74553),f333(f174(x74551),x74552))) % 183.90/184.43 [7479]~P25(x74791,x74792,x74793,f256(f882(x74791,a870)))+P25(f876(x74791),f876(x74792),f333(f155(x74791,x74792),x74793),f256(f882(f876(x74791),a870))) % 183.90/184.43 [7628]E(x76281,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x76282)),x76283)),f333(f271(a875,a875),x76282)))+~P1(f333(f47(x76281,x76283),x76282)) % 183.90/184.43 [7636]P25(x76361,x76362,x76363,f256(f882(x76361,a870)))+~P25(f876(x76361),f876(x76362),f333(f155(x76361,x76362),x76363),f256(f882(f876(x76361),a870))) % 183.90/184.43 [7675]~P1(f333(f333(f202(x76751),x76752),x76753))+P1(f333(f333(f333(f333(a204,x76751),x76752),f470(x76753,x76752,x76751)),x76753)) % 183.90/184.43 [7680]P1(f333(f333(f335(f882(x76801,a870)),f831(x76802,x76803,x76801)),x76803))+P1(f333(f333(f335(x76801),x76802),f40(f882(x76801,a870),x76803))) % 183.90/184.43 [7776]P1(f333(f333(f335(f876(x77761)),x77762),f162(x77761,x77763)))+~P1(f333(f333(f335(x77761),f678(x77763,x77762,x77761)),x77763)) % 183.90/184.43 [7877]P31(x78771,x78772,x78773)+~P1(f333(x78772,f333(f333(f166(x78771),x78773),f795(x78773,x78772,x78771)))) % 183.90/184.43 [7902]E(x79021,x79022)+~E(f333(f333(f7(x79023,f882(x79023,a870),a870),f335(x79023)),x79021),f333(f333(f7(x79023,f882(x79023,a870),a870),f335(x79023)),x79022)) % 183.90/184.43 [7908]~P1(f333(f333(f335(f881(x79081,x79081)),x79083),f265(x79081,x79082)))+P1(f333(f333(f335(x79081),f553(x79082,x79083,x79081)),x79082)) % 183.90/184.43 [7910]~P1(f333(f333(f335(x79101),x79103),f39(f882(x79101,a870),x79102)))+P1(f333(f333(f335(f882(x79101,a870)),f655(x79102,x79103,x79101)),x79102)) % 183.90/184.43 [8093]~P1(f333(f333(f335(x80931),x80932),f333(f174(x80931),f791(x80933,x80932,x80931))))+~P1(f333(f333(f335(x80931),x80932),f333(f174(x80931),x80933))) % 183.90/184.43 [8094]~P1(f333(f333(f335(x80941),x80942),f333(f174(x80941),f799(x80943,x80942,x80941))))+~P1(f333(f333(f335(x80941),x80942),f333(f174(x80941),x80943))) % 183.90/184.43 [8184]E(f333(f242(f879(f876(a329)),f876(a329),f315(x81841,x81842,f333(f333(f79(a1),x81843),f77(a1))),f240(f876(a329))),f333(x81841,x81843)),f315(x81841,x81842,x81843))+P1(f333(f333(f248(a1),x81842),x81843)) % 183.90/184.43 [8286]E(x82861,f116(x82862))+P1(f333(f333(f335(x82862),f333(f267(x82862,f881(a102,a102)),f333(f284(x82862,x82861),x82863))),f333(f174(x82862),x82861))) % 183.90/184.43 [8382]~P68(x83821)+E(f333(f143(x83821,x83821,f333(f7(x83821,x83821,x83821),f79(x83821)),x83822),f333(f170(x83821),x83823)),f333(f143(x83821,x83821,f79(x83821),x83822),x83823)) % 183.90/184.43 [8872]~P106(x88721)+E(f333(f174(x88721),f150(x88721,x88721,f5(x88721),x88722,x88723)),f333(f333(f311(x88721),x88722),f333(f174(x88721),x88723))) % 183.90/184.43 [8883]P1(f333(f333(f248(a875),f2(a875)),f635(x88831,x88832,x88833)))+~P1(f333(f333(f335(f881(x88833,x88833)),x88832),f333(f333(f290(x88833,x88833,x88833),x88831),f309(x88833,x88831)))) % 183.90/184.43 [9173]~P52(x91731,x91732)+~P1(f333(f333(f335(f881(x91731,x91731)),f333(f333(f268(x91731,x91731),x91733),x91733)),f333(f333(f290(x91731,x91731,x91731),x91732),f309(x91731,x91732)))) % 183.90/184.43 [9305]~E(f333(f333(f104(f882(f881(x93051,x93051),a870)),f333(f288(x93051,x93051),x93052)),f309(x93051,x93052)),f196(f882(f881(x93051,x93051),a870)))+~P1(f333(f333(f335(f881(x93051,x93051)),f333(f333(f268(x93051,x93051),x93053),x93053)),f333(f333(f290(x93051,x93051,x93051),x93052),f309(x93051,x93052)))) % 183.90/184.43 [9484]~P1(f333(f61(x94841),x94842))+P1(f333(f333(f247(a875),f333(f37(x94841),f333(f333(f22(f882(x94841,a870)),x94842),f333(f333(f311(x94841),x94843),f196(f882(x94841,a870)))))),f333(f37(x94841),x94842))) % 183.90/184.43 [5054]~E(x50543,f116(x50541))+E(f145(x50541,f333(f333(f152(x50541),x50542),x50543)),x50542) % 183.90/184.43 [5062]~E(x50623,f116(x50621))+E(f117(x50621,f333(f333(f152(x50621),x50622),x50623)),f116(x50621)) % 183.90/184.43 [5091]E(x50911,f116(x50912))+E(f145(x50912,f333(f333(f152(x50912),x50913),x50911)),f145(x50912,x50911)) % 183.90/184.43 [5093]E(x50931,f116(x50932))+E(f145(x50932,f333(f333(f135(x50932),x50933),x50931)),f145(x50932,x50931)) % 183.90/184.43 [5098]~E(x50983,f116(x50981))+E(f117(x50981,f333(f333(f135(x50981),x50982),x50983)),f117(x50981,x50982)) % 183.90/184.43 [5100]~E(x51003,f116(x51001))+E(f145(x51001,f333(f333(f135(x51001),x51002),x51003)),f145(x51001,x51002)) % 183.90/184.43 [5132]E(x51321,f116(x51322))+E(f333(f142(x51322),f333(f333(f135(x51322),x51321),x51323)),f333(f142(x51322),x51321)) % 183.90/184.43 [5161]~E(x51612,f116(x51611))+E(f333(f142(x51611),f333(f333(f135(x51611),x51612),x51613)),f333(f142(x51611),x51613)) % 183.90/184.43 [5211]~P62(x52111)+E(f333(f333(f113(x52111),x52112),f333(f333(f104(x52111),x52112),x52113)),x52112) % 183.90/184.43 [5212]~P62(x52121)+E(f333(f333(f104(x52121),x52122),f333(f333(f113(x52121),x52122),x52123)),x52122) % 183.90/184.43 [5213]~P106(x52131)+E(f333(f333(f245(x52131),x52132),f333(f333(f246(x52131),x52132),x52133)),x52132) % 183.90/184.43 [5214]~P106(x52141)+E(f333(f333(f246(x52141),x52142),f333(f333(f245(x52141),x52142),x52143)),x52142) % 183.90/184.43 [5232]~P55(x52321)+E(f44(x52321,f333(f333(f80(x52321),x52322),x52323),x52323),f2(x52321)) % 183.90/184.43 [5233]~P55(x52331)+E(f44(x52331,f333(f333(f80(x52331),x52332),x52333),x52332),f2(x52331)) % 183.90/184.43 [5308]~P65(x53081)+E(f333(f78(x53081),f333(f333(f22(x53081),x53082),x53083)),f333(f333(f22(x53081),x53083),x53082)) % 183.90/184.43 [5369]E(x53691,f116(x53692))+E(f117(x53692,f333(f333(f152(x53692),x53693),x53691)),f333(f333(f152(x53692),x53693),f117(x53692,x53691))) % 183.90/184.43 [5370]E(x53701,f116(x53702))+E(f117(x53702,f333(f333(f135(x53702),x53703),x53701)),f333(f333(f135(x53702),x53703),f117(x53702,x53701))) % 183.90/184.43 [5373]~P4(x53731)+E(f40(x53731,f333(f333(f311(x53731),x53732),x53733)),f333(f333(f104(x53731),x53732),f40(x53731,x53733))) % 183.90/184.43 [5374]~P4(x53741)+E(f39(x53741,f333(f333(f311(x53741),x53742),x53743)),f333(f333(f113(x53741),x53742),f39(x53741,x53743))) % 183.90/184.43 [5419]~P62(x54191)+E(f333(f333(f113(x54191),x54192),f333(f333(f113(x54191),x54192),x54193)),f333(f333(f113(x54191),x54192),x54193)) % 183.90/184.43 [5421]~P98(x54211)+E(f333(f333(f113(x54211),x54212),f333(f333(f113(x54211),x54212),x54213)),f333(f333(f113(x54211),x54212),x54213)) % 183.90/184.43 [5422]~P62(x54221)+E(f333(f333(f104(x54221),x54222),f333(f333(f104(x54221),x54222),x54223)),f333(f333(f104(x54221),x54222),x54223)) % 183.90/184.43 [5424]~P99(x54241)+E(f333(f333(f104(x54241),x54242),f333(f333(f104(x54241),x54242),x54243)),f333(f333(f104(x54241),x54242),x54243)) % 183.90/184.43 [5425]~P94(x54251)+E(f333(f333(f80(x54251),x54252),f333(f333(f80(x54251),x54252),x54253)),f333(f333(f80(x54251),x54252),x54253)) % 183.90/184.43 [5427]~P106(x54271)+E(f333(f333(f245(x54271),x54272),f333(f333(f245(x54271),x54272),x54273)),f333(f333(f245(x54271),x54272),x54273)) % 183.90/184.43 [5429]~P106(x54291)+E(f333(f333(f246(x54291),x54292),f333(f333(f246(x54291),x54292),x54293)),f333(f333(f246(x54291),x54292),x54293)) % 183.90/184.43 [5437]~P55(x54371)+E(f44(x54371,f333(f333(f79(x54371),x54372),x54373),x54373),f44(x54371,x54372,x54373)) % 183.90/184.43 [5438]~P55(x54381)+E(f44(x54381,f333(f333(f79(x54381),x54382),x54383),x54382),f44(x54381,x54383,x54382)) % 183.90/184.43 [5444]~P103(x54441)+E(f333(f333(f80(x54441),x54442),f333(f78(x54441),x54443)),f333(f78(x54441),f333(f333(f80(x54441),x54442),x54443))) % 183.90/184.43 [5445]~P58(x54451)+E(f333(f333(f291(x54451),x54452),f333(f78(x54451),x54453)),f333(f78(x54451),f333(f333(f291(x54451),x54452),x54453))) % 183.90/184.43 [5446]~P78(x54461)+E(f333(f333(f79(x54461),x54462),f333(f167(x54461),x54463)),f333(f167(x54461),f333(f333(f152(x54461),x54462),x54463))) % 183.90/184.43 [5476]~P103(x54761)+E(f333(f333(f80(x54761),f333(f78(x54761),x54762)),x54763),f333(f333(f80(x54761),x54762),f333(f78(x54761),x54763))) % 183.90/184.43 [5482]~P7(x54821,x54822,x54823)+E(f39(f882(x54821,a870),f333(f333(f60(x54821),x54822),x54823)),x54822) % 183.90/184.43 [5543]~P111(x55431)+E(f333(f333(f80(x55431),x55432),f333(f333(f258(x55431),x55432),x55433)),f333(f333(f258(x55431),x55432),f333(a115,x55433))) % 183.90/184.43 [5544]~P109(x55441)+E(f333(f333(f80(x55441),x55442),f333(f333(f258(x55441),x55442),x55443)),f333(f333(f258(x55441),x55442),f333(a115,x55443))) % 183.90/184.43 [5554]~P72(x55541)+E(f333(f333(f79(x55541),f333(f78(x55541),x55542)),f333(f333(f79(x55541),x55542),x55543)),x55543) % 183.90/184.43 [5577]~P141(x55771)+E(f333(f333(f258(x55771),f333(f103(x55771),x55772)),x55773),f333(f103(x55771),f333(f333(f258(a875),x55772),x55773))) % 183.90/184.43 [5578]~P138(x55781)+E(f333(f333(f258(x55781),f333(f105(x55781),x55782)),x55783),f333(f105(x55781),f333(f333(f258(a1),x55782),x55783))) % 183.90/184.43 [5584]~P83(x55841)+E(f333(f74(x55841),f333(f333(f22(x55841),x55842),x55843)),f333(f74(x55841),f333(f333(f22(x55841),x55843),x55842))) % 183.90/184.43 [5586]~P114(x55861)+E(f333(f333(f80(x55861),f81(x55861,x55862)),f81(x55861,x55863)),f81(x55861,f333(f333(f80(x55861),x55862),x55863))) % 183.90/184.43 [5590]E(x55901,f116(x55902))+E(f333(f333(f135(x55902),f333(f173(x55902),x55901)),x55903),f333(f173(x55902),f333(f333(f135(x55902),x55901),x55903))) % 183.90/184.43 [5595]~E(x55952,f333(a115,f333(f333(f79(a875),x55951),x55953)))+P1(f333(f333(f248(a875),x55951),x55952)) % 183.90/184.43 [5596]~P114(x55961)+E(f333(f333(f258(x55961),f333(f74(x55961),x55962)),x55963),f333(f74(x55961),f333(f333(f258(x55961),x55962),x55963))) % 183.90/184.43 [5597]~P103(x55971)+E(f333(f333(f80(x55971),f333(f78(x55971),x55972)),x55973),f333(f78(x55971),f333(f333(f80(x55971),x55972),x55973))) % 183.90/184.43 [5598]~P117(x55981)+E(f333(f333(f291(x55981),f333(f78(x55981),x55982)),x55983),f333(f78(x55981),f333(f333(f291(x55981),x55982),x55983))) % 183.90/184.43 [5696]E(f520(x56961,x56962,x56963),f556(x56961,x56962,x56963))+E(f333(f333(f104(f882(x56963,a870)),x56962),x56961),f196(f882(x56963,a870))) % 183.90/184.43 [5711]~P66(x57112)+E(f333(f333(f6(x57111,x57112),f333(f16(x57112,x57111),f2(x57112))),x57113),f2(x57112)) % 183.90/184.43 [5712]~P73(x57122)+E(f333(f333(f9(x57121,x57122),f333(f16(x57122,x57121),f77(x57122))),x57123),f77(x57122)) % 183.90/184.43 [5714]~P141(x57141)+E(f333(f333(f79(x57141),f333(f103(x57141),x57142)),f333(f103(x57141),x57143)),f333(f103(x57141),f333(f333(f79(a875),x57142),x57143))) % 183.90/184.43 [5715]~P141(x57151)+E(f333(f333(f80(x57151),f333(f103(x57151),x57152)),f333(f103(x57151),x57153)),f333(f103(x57151),f333(f333(f80(a875),x57152),x57153))) % 183.90/184.43 [5716]~P138(x57161)+E(f333(f333(f22(x57161),f333(f105(x57161),x57162)),f333(f105(x57161),x57163)),f333(f105(x57161),f333(f333(f22(a1),x57162),x57163))) % 183.90/184.43 [5717]~P138(x57171)+E(f333(f333(f79(x57171),f333(f105(x57171),x57172)),f333(f105(x57171),x57173)),f333(f105(x57171),f333(f333(f79(a1),x57172),x57173))) % 183.90/184.43 [5718]~P138(x57181)+E(f333(f333(f80(x57181),f333(f105(x57181),x57182)),f333(f105(x57181),x57183)),f333(f105(x57181),f333(f333(f80(a1),x57182),x57183))) % 183.90/184.43 [5719]~P90(x57191)+E(f333(f333(f22(x57191),f333(f106(x57191),x57192)),f333(f106(x57191),x57193)),f333(f106(x57191),f333(f333(f22(a1),x57192),x57193))) % 183.90/184.43 [5722]~P90(x57221)+E(f333(f333(f79(x57221),f333(f106(x57221),x57222)),f333(f106(x57221),x57223)),f333(f106(x57221),f333(f333(f79(a1),x57222),x57223))) % 183.90/184.43 [5723]~P90(x57231)+E(f333(f333(f80(x57231),f333(f106(x57231),x57232)),f333(f106(x57231),x57233)),f333(f106(x57231),f333(f333(f80(a1),x57232),x57233))) % 183.90/184.43 [5770]~E(x57703,x57702)+P1(f333(f333(f247(f882(x57701,a870)),x57702),x57703)) % 183.90/184.43 [5776]~E(x57762,x57763)+P1(f333(f333(f247(f882(x57761,a870)),x57762),x57763)) % 183.90/184.43 [5781]~P114(x57811)+E(f333(f333(f80(x57811),f333(f74(x57811),x57812)),f333(f74(x57811),x57813)),f333(f74(x57811),f333(f333(f80(x57811),x57812),x57813))) % 183.90/184.43 [5782]~P60(x57821)+E(f333(f333(f291(x57821),f333(f74(x57821),x57822)),f333(f74(x57821),x57823)),f333(f74(x57821),f333(f333(f291(x57821),x57822),x57823))) % 183.90/184.43 [5783]~P93(x57831)+E(f333(f333(f104(x57831),f333(f78(x57831),x57832)),f333(f78(x57831),x57833)),f333(f78(x57831),f333(f333(f113(x57831),x57832),x57833))) % 183.90/184.43 [5784]~P93(x57841)+E(f333(f333(f113(x57841),f333(f78(x57841),x57842)),f333(f78(x57841),x57843)),f333(f78(x57841),f333(f333(f104(x57841),x57842),x57843))) % 183.90/184.43 [5785]~P72(x57851)+E(f333(f333(f79(x57851),f333(f78(x57851),x57852)),f333(f78(x57851),x57853)),f333(f78(x57851),f333(f333(f79(x57851),x57853),x57852))) % 183.90/184.43 [5786]~P65(x57861)+E(f333(f333(f79(x57861),f333(f78(x57861),x57862)),f333(f78(x57861),x57863)),f333(f78(x57861),f333(f333(f79(x57861),x57862),x57863))) % 183.90/184.43 [5787]~P74(x57871)+E(f333(f333(f246(x57871),f333(f78(x57871),x57872)),f333(f78(x57871),x57873)),f333(f78(x57871),f333(f333(f245(x57871),x57872),x57873))) % 183.90/184.43 [5788]~P74(x57881)+E(f333(f333(f245(x57881),f333(f78(x57881),x57882)),f333(f78(x57881),x57883)),f333(f78(x57881),f333(f333(f246(x57881),x57882),x57883))) % 183.90/184.43 [5789]~P78(x57891)+E(f333(f333(f79(x57891),f333(f167(x57891),x57892)),f333(f167(x57891),x57893)),f333(f167(x57891),f333(f333(f135(x57891),x57892),x57893))) % 183.90/184.43 [5790]E(x57901,f196(f882(x57902,a870)))+~E(f333(f333(f113(f882(x57902,a870)),x57903),x57901),f196(f882(x57902,a870))) % 183.90/184.43 [5791]E(x57911,f196(f882(x57912,a870)))+~E(f333(f333(f113(f882(x57912,a870)),x57911),x57913),f196(f882(x57912,a870))) % 183.90/184.43 [5792]~P144(x57921,x57923,x57922)+P1(f333(x57921,f333(f333(f38(a1),x57922),x57923))) % 183.90/184.43 [5842]~P1(f333(f61(x58421),x58423))+P1(f333(f61(x58421),f333(f333(f311(x58421),x58422),x58423))) % 183.90/184.43 [5843]~P1(f333(f138(x58431),x58433))+P1(f333(f138(x58431),f333(f333(f177(x58431),x58432),x58433))) % 183.90/184.43 [5844]~P1(f333(f138(x58441),x58443))+P1(f333(f138(x58441),f333(f333(f139(x58441),x58442),x58443))) % 183.90/184.43 [5873]~P62(x58731)+P1(f333(f333(f247(x58731),x58732),f333(f333(f113(x58731),x58733),x58732))) % 183.90/184.43 [5874]~P98(x58741)+P1(f333(f333(f247(x58741),x58742),f333(f333(f113(x58741),x58743),x58742))) % 183.90/184.43 [5875]~P62(x58751)+P1(f333(f333(f247(x58751),x58752),f333(f333(f113(x58751),x58752),x58753))) % 183.90/184.43 [5876]~P98(x58761)+P1(f333(f333(f247(x58761),x58762),f333(f333(f113(x58761),x58762),x58763))) % 183.90/184.43 [5877]~P106(x58771)+P1(f333(f333(f247(x58771),x58772),f333(f333(f246(x58771),x58773),x58772))) % 183.90/184.43 [5878]~P106(x58781)+P1(f333(f333(f247(x58781),x58782),f333(f333(f246(x58781),x58782),x58783))) % 183.90/184.43 [5892]~E(x58921,f2(a875))+E(f333(f333(f38(a875),f333(f333(f80(a875),x58921),x58922)),f333(f333(f80(a875),x58921),x58923)),f2(a875)) % 183.90/184.43 [5959]P1(f333(x59591,x59592))+P1(f333(f333(f202(f31(x59591,x59593)),x59592),x59592)) % 183.90/184.43 [5974]~P90(x59741)+E(f333(f333(f22(x59741),f333(f106(x59741),x59742)),f333(f106(x59741),x59743)),f333(f106(x59741),f333(f333(f79(a1),x59742),f333(f78(a1),x59743)))) % 183.90/184.43 [6028]E(x60281,f2(a875))+E(f333(f333(f38(a875),f333(f333(f80(a875),x60281),x60282)),f333(f333(f80(a875),x60281),x60283)),f333(f333(f38(a875),x60282),x60283)) % 183.90/184.43 [6062]E(f153(x60621,f333(f333(f152(x60621),x60622),x60623)),f333(f333(f152(x60621),x60622),f153(x60621,x60623)))+P1(f333(f333(f335(x60621),x60622),f333(f174(x60621),x60623))) % 183.90/184.43 [6096]P144(x60961,x60962,x60963)+~P1(f333(x60961,f333(f333(f38(a1),x60963),x60962))) % 183.90/184.43 [6165]E(x61651,f116(x61652))+E(f333(f333(f152(x61652),f333(f142(x61652),x61651)),f333(f333(f177(x61652),x61653),f333(f173(x61652),x61651))),f333(f333(f177(x61652),f333(a115,x61653)),x61651)) % 183.90/184.43 [6172]E(f333(f333(f22(f882(x61721,a870)),x61722),x61723),x61722)+~E(f333(f333(f104(f882(x61721,a870)),x61722),x61723),f196(f882(x61721,a870))) % 183.90/184.43 [6186]E(f153(x61861,f333(f333(f152(x61861),x61862),x61863)),f153(x61861,x61863))+~P1(f333(f333(f335(x61861),x61862),f333(f174(x61861),x61863))) % 183.90/184.43 [6218]~P1(f333(f333(f248(a875),x62181),x62183))+P1(f333(f333(f248(a875),x62181),f333(f333(f79(a875),x62182),x62183))) % 183.90/184.43 [6220]~P1(f333(f333(f248(a875),x62201),x62202))+P1(f333(f333(f248(a875),x62201),f333(f333(f79(a875),x62202),x62203))) % 183.90/184.43 [6222]~P1(f333(f333(f247(a875),x62221),x62223))+P1(f333(f333(f247(a875),x62221),f333(f333(f79(a875),x62222),x62223))) % 183.90/184.43 [6224]~P1(f333(f333(f247(a875),x62241),x62242))+P1(f333(f333(f247(a875),x62241),f333(f333(f79(a875),x62242),x62243))) % 183.90/184.43 [6263]P1(f333(f61(x62631),x62632))+~P1(f333(f61(x62631),f333(f333(f311(x62631),x62633),x62632))) % 183.90/184.43 [6264]P1(f333(f138(x62641),x62642))+~P1(f333(f138(x62641),f333(f333(f152(x62641),x62643),x62642))) % 183.90/184.43 [6265]P1(f333(f138(x62651),x62652))+~P1(f333(f138(x62651),f333(f333(f135(x62651),x62653),x62652))) % 183.90/184.43 [6266]P1(f333(f138(x62661),x62662))+~P1(f333(f138(x62661),f333(f333(f135(x62661),x62662),x62663))) % 183.90/184.43 [6312]~P109(x63121)+E(f333(f333(f79(x63121),x63122),f333(f333(f80(x63121),x63123),x63122)),f333(f333(f80(x63121),f333(f333(f79(x63121),x63123),f77(x63121))),x63122)) % 183.90/184.43 [6359]~E(x63591,x63592)+~P1(f333(f333(f248(f882(x63593,a870)),x63591),x63592)) % 183.90/184.43 [6403]P1(f333(f333(f335(x64031),x64032),x64033))+P1(f333(f333(f335(x64031),x64032),f333(f78(f882(x64031,a870)),x64033))) % 183.90/184.43 [6409]E(f145(x64091,f333(f333(f139(x64091),x64092),x64093)),f145(x64091,x64093))+~P1(f333(f333(f248(a875),x64092),f333(f197(f876(x64091)),x64093))) % 183.90/184.43 [6410]E(f333(f333(f177(x64101),x64102),f117(x64101,x64103)),f333(f333(f177(x64101),x64102),x64103))+~P1(f333(f333(f248(a875),x64102),f333(f197(f876(x64101)),x64103))) % 183.90/184.43 [6464]E(f333(f333(f333(f191(f876(x64641),f876(x64641)),x64642),f169(x64641)),x64643),x64643)+~E(f44(a875,x64642,f333(f197(f876(x64641)),x64643)),f2(a875)) % 183.90/184.43 [6471]~P7(x64711,x64713,x64712)+E(f333(f333(f290(x64711,x64711,x64711),f333(f288(x64711,x64711),x64712)),x64712),x64712) % 183.90/184.43 [6513]~E(f333(f333(f113(f882(x65131,a870)),x65132),x65133),x65133)+P1(f333(f333(f247(f882(x65131,a870)),x65132),x65133)) % 183.90/184.43 [6518]~P49(x65181,x65181,x65183)+P49(x65181,x65181,f333(f333(f191(f881(x65181,x65181),a870),x65182),x65183)) % 183.90/184.43 [6520]~P1(f333(f333(f335(x65201),x65203),f333(f174(x65201),x65202)))+P1(f333(f333(f248(a875),f2(a875)),f333(f197(f876(x65201)),x65202))) % 183.90/184.43 [6546]~P83(x65461)+E(f333(f74(x65461),f333(f333(f79(x65461),f333(f74(x65461),x65462)),f333(f74(x65461),x65463))),f333(f333(f79(x65461),f333(f74(x65461),x65462)),f333(f74(x65461),x65463))) % 183.90/184.43 [6557]E(f333(f333(f38(a875),f333(f333(f80(a875),x65571),x65572)),f333(f333(f80(a875),x65571),x65573)),f333(f333(f38(a875),x65572),x65573))+~P1(f333(f333(f248(a875),f2(a875)),x65571)) % 183.90/184.43 [6605]E(x66051,x66052)+~P1(f333(f333(f333(f333(a204,a24),x66051),x66053),x66052)) % 183.90/184.43 [6694]~P1(f333(f61(x66941),x66943))+E(f333(f333(f64(x66941,f882(x66941,a870),f311(x66941)),x66942),x66943),f333(f333(f113(f882(x66941,a870)),x66943),x66942)) % 183.90/184.43 [6753]E(f333(f333(f113(f882(x67531,a870)),x67532),x67533),x67532)+~P1(f333(f333(f247(f882(x67531,a870)),x67533),x67532)) % 183.90/184.43 [6755]E(f333(f333(f113(f882(x67551,a870)),x67552),x67553),x67553)+~P1(f333(f333(f247(f882(x67551,a870)),x67552),x67553)) % 183.90/184.43 [6756]E(f333(f333(f104(f882(x67561,a870)),x67562),x67563),x67563)+~P1(f333(f333(f247(f882(x67561,a870)),x67563),x67562)) % 183.90/184.43 [6757]E(f333(f333(f104(f882(x67571,a870)),x67572),x67573),x67572)+~P1(f333(f333(f247(f882(x67571,a870)),x67572),x67573)) % 183.90/184.43 [6809]~P1(f333(f138(x68091),x68092))+E(f333(f333(f22(f882(x68091,a870)),f333(f174(x68091),x68092)),f333(f333(f311(x68091),x68093),f196(f882(x68091,a870)))),f333(f174(x68091),f172(x68091,x68093,x68092))) % 183.90/184.43 [6862]P37(x68621,x68622)+~P37(x68621,f333(f333(f191(f881(x68621,x68621),a870),x68623),x68622)) % 183.90/184.43 [6928]P1(f333(f48(x69281,x69282),f333(a50,x69283)))+~P1(f333(f48(f333(f78(a1),x69281),f333(f78(a1),x69282)),x69283)) % 183.90/184.43 [6933]E(f333(f333(f22(f882(x69331,a870)),f333(f333(f311(x69331),x69332),x69333)),f333(f333(f311(x69331),x69332),f196(f882(x69331,a870)))),x69333)+P1(f333(f333(f335(x69331),x69332),x69333)) % 183.90/184.43 [6954]E(f333(f333(f104(f882(x69541,a870)),f333(f174(x69541),x69542)),f333(f174(x69541),x69543)),f196(f882(x69541,a870)))+~P1(f333(f138(x69541),f333(f333(f135(x69541),x69542),x69543))) % 183.90/184.43 [6970]~P1(f333(f333(f335(x69701),x69702),f333(f174(x69701),x69703)))+~P1(f333(f138(x69701),f333(f333(f152(x69701),x69702),x69703))) % 183.90/184.43 [7042]P31(x70421,x70422,x70423)+P1(f333(f333(f248(a875),f795(x70423,x70422,x70421)),f333(f197(f876(x70421)),x70423))) % 183.90/184.43 [7052]E(f333(f333(f104(f882(x70521,a870)),x70522),x70523),f196(f882(x70521,a870)))+P1(f333(f333(f335(x70521),f520(x70523,x70522,x70521)),x70522)) % 183.90/184.43 [7053]E(f333(f333(f104(f882(x70531,a870)),x70532),x70533),f196(f882(x70531,a870)))+P1(f333(f333(f335(x70531),f556(x70533,x70532,x70531)),x70533)) % 183.90/184.43 [7057]E(f117(x70571,f333(f333(f177(x70571),x70572),x70573)),f333(f333(f177(x70571),f333(f333(f22(a875),x70572),f77(a875))),x70573))+~P1(f333(f333(f247(a875),x70572),f333(f197(f876(x70571)),x70573))) % 183.90/184.43 [7116]~P33(x71163,x71162,x71161)+P1(f333(f333(f248(a875),f790(x71161,x71162,x71163)),f333(f197(f876(x71163)),x71161))) % 183.90/184.43 [7134]P1(f333(f333(f248(a875),f2(a875)),x71341))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x71342),x71341)),f333(f333(f80(a875),x71343),x71341))) % 183.90/184.43 [7135]P1(f333(f333(f248(a875),f2(a875)),x71351))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x71351),x71352)),f333(f333(f80(a875),x71351),x71353))) % 183.90/184.43 [7138]~P1(f333(f333(f335(x71381),x71382),x71383))+~P1(f333(f333(f335(x71381),x71382),f333(f78(f882(x71381,a870)),x71383))) % 183.90/184.43 [7145]~P1(f333(f333(f248(f882(x71451,a870)),x71452),x71453))+P1(f333(f333(f247(f882(x71451,a870)),x71452),x71453)) % 183.90/184.43 [7244]~P1(f333(f333(f248(a875),x72442),x72443))+P1(f333(f333(f248(a875),f333(f333(f79(a875),x72441),x72442)),f333(f333(f79(a875),x72441),x72443))) % 183.90/184.43 [7245]~P1(f333(f333(f248(a875),x72451),x72453))+P1(f333(f333(f248(a875),f333(f333(f79(a875),x72451),x72452)),f333(f333(f79(a875),x72453),x72452))) % 183.90/184.43 [7246]~P1(f333(f333(f248(a1),x72461),x72463))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x72461),x72462)),f333(f333(f79(a1),x72463),x72462))) % 183.90/184.43 [7249]~P1(f333(f333(f247(a875),x72493),x72492))+P1(f333(f333(f247(a875),f333(f333(f22(a875),x72491),x72492)),f333(f333(f22(a875),x72491),x72493))) % 183.90/184.43 [7250]~P1(f333(f333(f247(a875),x72501),x72503))+P1(f333(f333(f247(a875),f333(f333(f22(a875),x72501),x72502)),f333(f333(f22(a875),x72503),x72502))) % 183.90/184.43 [7251]~P1(f333(f333(f247(a875),x72512),x72513))+P1(f333(f333(f247(a875),f333(f333(f79(a875),x72511),x72512)),f333(f333(f79(a875),x72511),x72513))) % 183.90/184.43 [7252]~P1(f333(f333(f247(a875),x72521),x72523))+P1(f333(f333(f247(a875),f333(f333(f79(a875),x72521),x72522)),f333(f333(f79(a875),x72523),x72522))) % 183.90/184.43 [7254]~P1(f333(f333(f247(a875),x72542),x72543))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x72541),x72542)),f333(f333(f80(a875),x72541),x72543))) % 183.90/184.43 [7256]~P1(f333(f333(f247(a875),x72561),x72563))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x72561),x72562)),f333(f333(f80(a875),x72563),x72562))) % 183.90/184.43 [7257]~P1(f333(f333(f247(a875),x72571),x72573))+P1(f333(f333(f247(a875),f333(f333(f38(a875),x72571),x72572)),f333(f333(f38(a875),x72573),x72572))) % 183.90/184.43 [7258]~P1(f333(f333(f247(a1),x72582),x72583))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x72581),x72582)),f333(f333(f79(a1),x72581),x72583))) % 183.90/184.43 [7338]E(x73381,x73382)+~P1(f333(f333(f335(x73383),x73381),f333(f333(f311(x73383),x73382),f196(f882(x73383,a870))))) % 183.90/184.43 [7340]~E(f333(f333(f104(f882(x73401,a870)),x73402),x73403),f196(f882(x73401,a870)))+P1(f333(f333(f247(f882(x73401,a870)),x73402),f333(f78(f882(x73401,a870)),x73403))) % 183.90/184.43 [7348]P1(f333(f333(f335(f882(x73481,a870)),x73482),f333(f310(x73481),x73483)))+~P1(f333(f333(f247(f882(x73481,a870)),x73482),x73483)) % 183.90/184.43 [7401]E(f333(f333(f152(x74011),f333(f333(f166(x74011),x74012),x74013)),f333(f333(f139(x74011),f333(a115,x74013)),x74012)),f333(f333(f139(x74011),x74013),x74012))+~P1(f333(f333(f248(a875),x74013),f333(f197(f876(x74011)),x74012))) % 183.90/184.43 [7428]P1(f333(f333(f335(f881(x74281,x74281)),x74282),f309(x74281,x74283)))+~P1(f333(f333(f335(f881(x74281,x74281)),x74282),x74283)) % 183.90/184.43 [7439]~P1(f333(f333(f335(f882(x74391,a870)),x74392),f333(f310(x74391),x74393)))+P1(f333(f333(f247(f882(x74391,a870)),x74392),x74393)) % 183.90/184.43 [7485]P1(f333(f333(f247(f882(x74851,a870)),x74852),f39(f882(x74851,a870),x74853)))+~P1(f333(f333(f335(f882(x74851,a870)),x74852),x74853)) % 183.90/184.43 [7510]~P138(x75101)+E(f333(f333(f80(x75101),f333(f333(f258(x75101),f333(f78(x75101),f77(x75101))),x75102)),f333(f333(f258(x75101),x75103),x75102)),f333(f333(f258(x75101),f333(f78(x75101),x75103)),x75102)) % 183.90/184.43 [7532]E(f333(f333(f166(x75321),x75322),f333(f333(f22(a875),f333(f197(f876(x75321)),x75322)),f333(a115,x75323))),f333(f333(f166(x75321),f333(f170(x75321),x75322)),x75323))+~P1(f333(f333(f248(a875),x75323),f333(f197(f876(x75321)),x75322))) % 183.90/184.43 [7549]~E(f333(f333(f104(f882(x75491,a870)),f824(x75493,x75492,x75491)),x75493),f196(f882(x75491,a870)))+E(f333(f333(f104(f882(x75491,a870)),f39(f882(x75491,a870),x75492)),x75493),f196(f882(x75491,a870))) % 183.90/184.43 [7610]~P1(f333(f333(f335(x76103),x76102),f333(f174(x76103),x76101)))+P1(f333(f333(f248(a875),f653(x76101,x76102,x76103)),f333(f197(f876(x76103)),x76101))) % 183.90/184.43 [7618]P1(f333(f333(f335(x76181),f333(f333(f166(x76181),x76182),x76183)),f333(f174(x76181),x76182)))+~P1(f333(f333(f248(a875),x76183),f333(f197(f876(x76181)),x76182))) % 183.90/184.43 [7720]~P1(f333(x77202,f753(x77203,x77202,x77201)))+E(f333(f333(f139(x77201),f333(f197(f876(x77201)),f179(x77201,x77202,x77203))),x77203),f116(x77201)) % 183.90/184.43 [7731]P1(f333(f333(f247(f882(f876(x77311),a870)),f162(x77311,x77312)),f162(x77311,x77313)))+~P1(f333(f333(f247(f882(x77311,a870)),x77312),x77313)) % 183.90/184.43 [7732]P1(f333(f333(f247(f882(f876(x77321),a870)),f161(x77321,x77322)),f161(x77321,x77323)))+~P1(f333(f333(f247(f882(x77321,a870)),x77322),x77323)) % 183.90/184.43 [7761]E(f333(f333(f104(f882(x77611,a870)),f39(f882(x77611,a870),x77612)),x77613),f196(f882(x77611,a870)))+P1(f333(f333(f335(f882(x77611,a870)),f824(x77613,x77612,x77611)),x77612)) % 183.90/184.43 [7764]~P1(f333(f333(f335(f882(x77641,a870)),x77643),x77642))+P1(f333(f333(f247(f882(x77641,a870)),f40(f882(x77641,a870),x77642)),x77643)) % 183.90/184.43 [7766]E(f333(f333(f104(f882(x77661,a870)),x77662),x77663),f196(f882(x77661,a870)))+~P1(f333(f333(f247(f882(x77661,a870)),x77662),f333(f78(f882(x77661,a870)),x77663))) % 183.90/184.43 [7815]E(f333(f333(f22(a875),f333(f333(f79(a875),f333(f167(a875),x78151)),x78152)),f333(f333(f166(a875),x78151),x78153)),f333(f167(a875),f333(f333(f160(a875,x78151),x78153),x78152)))+~P1(f333(f333(f248(a875),x78153),f333(f197(f876(a875)),x78151))) % 183.90/184.43 [7865]P1(f333(f333(f248(a875),x78651),x78652))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),x78653),x78651)),f333(f333(f79(a875),x78653),x78652))) % 183.90/184.43 [7866]P1(f333(f333(f248(a875),x78661),x78662))+~P1(f333(f333(f248(a875),f333(f333(f80(a875),x78663),x78661)),f333(f333(f80(a875),x78663),x78662))) % 183.90/184.43 [7867]P1(f333(f333(f248(a875),x78671),x78672))+~P1(f333(f333(f248(a875),f333(f333(f80(a875),x78671),x78673)),f333(f333(f80(a875),x78672),x78673))) % 183.90/184.43 [7870]P1(f333(f333(f247(a875),x78701),x78702))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x78703),x78701)),f333(f333(f79(a875),x78703),x78702))) % 183.90/184.43 [7900]P1(f333(f333(f248(a875),f2(a875)),x79001))+~P1(f333(f333(f248(a875),f333(f333(f80(a875),x79002),x79001)),f333(f333(f80(a875),x79003),x79001))) % 183.90/184.43 [7901]P1(f333(f333(f248(a875),f2(a875)),x79011))+~P1(f333(f333(f248(a875),f333(f333(f80(a875),x79011),x79012)),f333(f333(f80(a875),x79011),x79013))) % 183.90/184.43 [7975]E(f260(x79751,x79752,x79753),x79752)+~P1(f333(f333(f247(f882(x79751,a870)),x79753),f333(f333(f311(x79751),x79752),f196(f882(x79751,a870))))) % 183.90/184.43 [8033]~P1(f333(f138(x80331),x80333))+E(f333(f137(x80331,f333(f333(f8(a870,a870,x80331),a328),f333(a330,x80332))),x80333),f172(x80331,x80332,x80333)) % 183.90/184.43 [8056]E(f333(f333(f139(x80561),f333(f197(f876(x80561)),f179(x80561,x80562,x80563))),x80563),f116(x80561))+P1(f333(f333(f335(x80561),f753(x80563,x80562,x80561)),f333(f174(x80561),x80563))) % 183.90/184.43 [8060]E(f333(f333(f135(x80601),f333(f333(f177(x80601),x80602),x80603)),f333(f333(f152(x80601),f333(f333(f166(x80601),x80603),x80602)),f116(x80601))),f333(f333(f177(x80601),f333(a115,x80602)),x80603))+~P1(f333(f333(f248(a875),x80602),f333(f197(f876(x80601)),x80603))) % 183.90/184.43 [8122]E(f333(f137(x81221,f333(f333(f8(a870,a870,x81221),a328),f333(a330,x81222))),x81223),x81223)+P1(f333(f333(f335(x81221),x81222),f333(f174(x81221),x81223))) % 183.90/184.43 [8130]P1(f333(f333(f247(f882(f882(x81301,a870),a870)),f261(x81301,x81302)),f261(x81301,x81303)))+~P1(f333(f333(f247(f882(x81301,a870)),x81302),x81303)) % 183.90/184.43 [8175]~P1(f333(f138(x81751),x81753))+P1(f333(f138(x81751),f333(f333(f333(f191(f876(x81751),f876(x81751)),x81752),f169(x81751)),x81753))) % 183.90/184.43 [8180]~P1(f333(f333(f248(a875),x81802),x81803))+P1(f333(f333(f248(a875),f333(f333(f80(a875),f333(a115,x81801)),x81802)),f333(f333(f80(a875),f333(a115,x81801)),x81803))) % 183.90/184.43 [8203]P1(f333(f333(f247(f882(f882(x82031,a870),a870)),f333(f310(x82031),x82032)),f333(f310(x82031),x82033)))+~P1(f333(f333(f247(f882(x82031,a870)),x82032),x82033)) % 183.90/184.43 [8365]~P1(f333(f333(f247(f882(x83651,a870)),x83653),x83652))+P1(f333(f333(f247(f882(x83651,a870)),f333(f78(f882(x83651,a870)),x83652)),f333(f78(f882(x83651,a870)),x83653))) % 183.90/184.43 [8398]E(f333(f312(a875,a875,f333(f333(f7(a875,a875,a875),f22(a875)),x83981)),f333(f303(a875,x83982),x83983)),f333(f303(a875,f333(f333(f22(a875),x83982),x83981)),f333(f333(f22(a875),x83983),x83981)))+~P1(f333(f333(f248(a875),x83981),x83983)) % 183.90/184.43 [8427]~P78(x84271)+E(f333(f333(f79(x84271),x84272),f333(f143(x84271,x84271,f79(x84271),f2(x84271)),x84273)),f333(f143(x84271,x84271,f79(x84271),x84272),x84273)) % 183.90/184.43 [8509]~P83(x85091)+P1(f333(f333(f247(x85091),f333(f74(x85091),f333(f333(f22(x85091),x85092),x85093))),f333(f333(f79(x85091),f333(f74(x85091),x85092)),f333(f74(x85091),x85093)))) % 183.90/184.43 [8510]~P83(x85101)+P1(f333(f333(f247(x85101),f333(f74(x85101),f333(f333(f79(x85101),x85102),x85103))),f333(f333(f79(x85101),f333(f74(x85101),x85102)),f333(f74(x85101),x85103)))) % 183.90/184.43 [8520]E(f333(f333(f79(a1),f333(f333(f80(a1),x85201),f44(a1,f333(f333(f38(a1),x85202),x85201),x85203))),f44(a1,x85202,x85201)),f44(a1,x85202,f333(f333(f80(a1),x85201),x85203)))+~P1(f333(f333(f248(a1),f2(a1)),x85203)) % 183.90/184.43 [8526]E(f333(f333(f135(x85261),f333(f333(f177(x85261),x85262),x85263)),f333(f333(f152(x85261),f333(f142(x85261),f333(f333(f139(x85261),x85262),x85263))),f116(x85261))),f333(f333(f177(x85261),f333(a115,x85262)),x85263))+~P1(f333(f333(f248(a875),x85262),f333(f197(f876(x85261)),x85263))) % 183.90/184.43 [8545]E(f333(f279(x85451,f333(f333(f155(x85451,f881(a102,x85451)),f333(f268(a102,x85451),f77(a102))),x85452)),f333(a3,x85453)),f333(f333(f166(x85451),x85452),x85453))+~P1(f333(f333(f248(a875),x85453),f333(f197(f876(x85451)),x85452))) % 183.90/184.43 [8609]P1(f333(f333(f335(f881(x86091,x86091)),x86092),f333(f333(f290(x86091,x86091,x86091),x86093),f309(x86091,x86093))))+~P1(f333(f333(f335(f881(x86091,x86091)),x86092),x86093)) % 183.90/184.43 [8629]P1(f333(f333(f247(a875),x86291),x86292))+~P1(f333(f333(f247(a875),f333(f333(f80(a875),f333(a115,x86293)),x86291)),f333(f333(f80(a875),f333(a115,x86293)),x86292))) % 183.90/184.43 [8643]P1(f333(f333(f247(f882(x86431,a870)),x86432),x86433))+~P1(f333(f333(f247(f882(x86431,a870)),f333(f78(f882(x86431,a870)),x86433)),f333(f78(f882(x86431,a870)),x86432))) % 183.90/184.43 [8661]P1(f333(f138(x86611),x86612))+~P1(f333(f138(x86611),f333(f333(f333(f191(f876(x86611),f876(x86611)),x86613),f169(x86611)),x86612))) % 183.90/184.43 [8721]E(f333(f312(f881(x87211,x87212),x87212,f271(x87211,x87212)),f333(f174(f881(x87211,x87212)),x87213)),f188(x87211,x87212,f333(f180(x87211,x87212),x87213)))+~P1(f333(f138(x87211),f333(f333(f155(f881(x87211,x87212),x87211),f267(x87211,x87212)),x87213))) % 183.90/184.43 [8730]E(f333(f287(x87301,x87301,f309(x87301,x87302)),x87303),x87303)+~P1(f333(f333(f247(f882(x87301,a870)),f333(f287(x87301,x87301,x87302),x87303)),x87303)) % 183.90/184.43 [8772]~P106(x87721)+P14(x87721,f333(f137(x87721,f333(f333(f7(x87721,x87721,a870),a330),f333(x87722,x87723))),x87723)) % 183.90/184.43 [8778]~P1(f333(f333(f247(a875),x87781),x87782))+P1(f333(f333(f247(a875),x87781),f333(f143(a875,a875,f79(a875),x87782),x87783))) % 183.90/184.43 [8856]~P1(f333(f333(f335(f881(x88561,x88561)),x88562),f309(x88561,x88563)))+P1(f333(f333(f335(f881(x88561,x88561)),x88562),f333(f333(f191(f881(x88561,x88561),a870),f633(x88563,x88562,x88561)),x88563))) % 183.90/184.43 [8951]~P78(x89511)+E(f333(f333(f79(x89511),x89512),f333(f143(x89511,x89511,f333(f7(x89511,x89511,x89511),f79(x89511)),f2(x89511)),f333(f170(x89511),x89513))),f333(f143(x89511,x89511,f79(x89511),x89512),x89513)) % 183.90/184.43 [9219]P49(x92191,x92192,x92193)+P1(f333(f333(f335(f881(x92191,x92192)),f333(f333(f268(x92191,x92192),f625(x92193,x92192,x92191)),f614(x92193,x92192,x92191))),x92193)) % 183.90/184.43 [9220]P49(x92201,x92202,x92203)+P1(f333(f333(f335(f881(x92201,x92202)),f333(f333(f268(x92201,x92202),f625(x92203,x92202,x92201)),f613(x92203,x92202,x92201))),x92203)) % 183.90/184.43 [9290]~P1(f333(f333(f335(f881(x92901,x92901)),x92902),f333(f333(f290(x92901,x92901,x92901),x92903),f309(x92901,x92903))))+P1(f333(f333(f335(f881(x92901,x92901)),x92902),f333(f333(f191(f881(x92901,x92901),a870),f635(x92903,x92902,x92901)),x92903))) % 183.90/184.43 [9291]~P1(f333(x92911,f333(f333(f166(x92912),x92913),f333(f197(f876(x92912)),f179(x92912,x92911,x92913)))))+~P1(f333(f333(f248(a875),f333(f197(f876(x92912)),f179(x92912,x92911,x92913))),f333(f197(f876(x92912)),x92913))) % 183.90/184.43 [9380]~P1(f333(f333(f247(f882(x93801,a870)),x93802),x93803))+P1(f333(f333(f247(f882(x93801,a870)),f333(f333(f7(x93801,f882(x93801,a870),a870),f335(x93801)),x93802)),f333(f333(f7(x93801,f882(x93801,a870),a870),f335(x93801)),x93803))) % 183.90/184.43 [9433]~P1(f333(f333(f335(f881(f882(x94331,a870),f882(x94331,a870))),f333(f333(f268(f882(x94331,a870),f882(x94331,a870)),x94332),x94333)),f308(x94331)))+P1(f333(f333(f248(f882(x94331,a870)),x94332),x94333)) % 183.90/184.43 [9458]P50(x94581,x94582,x94583)+~P1(f333(f333(f335(f881(x94581,x94581)),f333(f333(f268(x94581,x94581),f628(x94583,x94582,x94581)),f627(x94583,x94582,x94581))),x94583)) % 183.90/184.43 [9459]P50(x94591,x94592,x94593)+~P1(f333(f333(f335(f881(x94591,x94591)),f333(f333(f268(x94591,x94591),f627(x94593,x94592,x94591)),f628(x94593,x94592,x94591))),x94593)) % 183.90/184.43 [9495]~P1(f333(f333(f335(f881(f876(x94951),f876(x94951))),f333(f333(f268(f876(x94951),f876(x94951)),x94952),x94952)),f148(x94951,x94953)))+P1(f333(f333(f335(f881(x94951,x94951)),f333(f333(f268(x94951,x94951),f668(x94952,x94953,x94951)),f668(x94952,x94953,x94951))),x94953)) % 183.90/184.43 [9546]P1(f333(f333(f247(f882(x95461,a870)),x95462),x95463))+~P1(f333(f333(f247(f882(x95461,a870)),f333(f333(f7(x95461,f882(x95461,a870),a870),f335(x95461)),x95462)),f333(f333(f7(x95461,f882(x95461,a870),a870),f335(x95461)),x95463))) % 183.90/184.43 [9627]E(f333(f333(f22(a875),f333(f333(f6(a875,a875),x96271),f333(f254(a875),x96272))),f333(f333(f6(a875,a875),x96273),f333(f254(a875),x96272))),f333(f333(f6(a875,a875),f333(f333(f18(a875,a875,a875),f333(f333(f8(a875,f882(a875,a875),a875),f22(a875)),x96271)),x96273)),f333(f254(a875),x96272)))+~P1(f333(f333(f247(a875),f333(x96273,f405(x96272,x96271,x96273))),f333(x96271,f405(x96272,x96271,x96273)))) % 183.90/184.43 [9930]E(f333(f253(f881(x99301,x99302)),f333(f272(x99301,x99302,a870),f333(f333(f7(x99301,f882(x99302,f879(x99302)),f882(x99302,a870)),f333(f333(f8(f882(f879(x99302),a870),f882(f882(x99302,f879(x99302)),f882(x99302,a870)),x99301),f8(f879(x99302),a870,x99302)),f333(f333(f8(f879(x99302),f882(f879(x99302),a870),x99301),a330),f333(f180(x99301,x99302),x99303)))),f240(x99302)))),f333(f174(f881(x99301,x99302)),x99303))+~P1(f333(f138(x99301),f333(f333(f155(f881(x99301,x99302),x99301),f267(x99301,x99302)),x99303))) % 183.90/184.43 [5630]~P72(x56301)+E(f333(f333(f22(x56301),f333(f333(f79(x56301),x56302),x56303)),x56303),x56302) % 183.90/184.43 [5631]~P72(x56311)+E(f333(f333(f79(x56311),f333(f333(f22(x56311),x56312),x56313)),x56313),x56312) % 183.90/184.43 [5850]~P72(x58501)+E(f333(f333(f79(x58501),x58502),f333(f333(f79(x58501),f333(f78(x58501),x58502)),x58503)),x58503) % 183.90/184.43 [5933]~P77(x59331)+E(f333(f333(f80(x59331),f333(f333(f258(x59331),x59332),x59333)),x59332),f333(f333(f258(x59331),x59332),f333(a115,x59333))) % 183.90/184.43 [5934]~P109(x59341)+E(f333(f333(f80(x59341),f333(f333(f258(x59341),x59342),x59343)),x59342),f333(f333(f258(x59341),x59342),f333(a115,x59343))) % 183.90/184.43 [6146]~P114(x61461)+E(f333(f74(x61461),f333(f333(f258(x61461),f333(f78(x61461),x61462)),x61463)),f333(f74(x61461),f333(f333(f258(x61461),x61462),x61463))) % 183.90/184.43 [6200]~P77(x62001)+E(f333(f333(f80(x62001),f333(f333(f258(x62001),x62002),x62003)),x62002),f333(f333(f80(x62001),x62002),f333(f333(f258(x62001),x62002),x62003))) % 183.90/184.43 [6254]E(f333(f333(f22(a102),f333(f333(f79(a102),x62541),x62542)),x62543),f283(x62541,x62542,x62543))+~P1(f333(f333(f248(a102),x62542),x62543)) % 183.90/184.43 [6275]~E(f333(f333(f139(x62751),x62753),x62752),f116(x62751))+P1(f333(f333(f247(a875),f333(f197(f876(x62751)),x62752)),x62753)) % 183.90/184.43 [6408]E(f333(f333(f80(a875),f333(f106(a875),x64081)),f333(f333(f80(a875),f333(f106(a875),x64082)),x64083)),f2(a875))+~P1(f333(f333(f248(a1),x64081),a82)) % 183.90/184.43 [6424]~P58(x64241)+E(f333(f333(f258(x64241),f333(f333(f291(x64241),f77(x64241)),x64242)),x64243),f333(f333(f291(x64241),f77(x64241)),f333(f333(f258(x64241),x64242),x64243))) % 183.90/184.43 [6500]E(f333(f333(f22(a875),f333(f333(f79(a875),x65001),x65002)),x65003),f333(f333(f22(a875),x65001),f333(f333(f22(a875),x65003),x65002)))+~P1(f333(f333(f247(a875),x65002),x65003)) % 183.90/184.43 [6502]E(f333(f333(f22(a875),f333(f333(f79(a875),x65021),x65022)),x65023),f333(f333(f79(a875),x65021),f333(f333(f22(a875),x65022),x65023)))+~P1(f333(f333(f247(a875),x65023),x65022)) % 183.90/184.43 [6537]~P62(x65371)+P1(f333(f333(f247(x65371),f333(f333(f104(x65371),x65372),x65373)),x65373)) % 183.90/184.43 [6538]~P99(x65381)+P1(f333(f333(f247(x65381),f333(f333(f104(x65381),x65382),x65383)),x65383)) % 183.90/184.43 [6539]~P62(x65391)+P1(f333(f333(f247(x65391),f333(f333(f104(x65391),x65392),x65393)),x65392)) % 183.90/184.43 [6540]~P99(x65401)+P1(f333(f333(f247(x65401),f333(f333(f104(x65401),x65402),x65403)),x65402)) % 183.90/184.43 [6541]~P106(x65411)+P1(f333(f333(f247(x65411),f333(f333(f245(x65411),x65412),x65413)),x65413)) % 183.90/184.43 [6542]~P106(x65421)+P1(f333(f333(f247(x65421),f333(f333(f245(x65421),x65422),x65423)),x65422)) % 183.90/184.43 [6556]E(f333(f333(f38(a1),f333(f333(f38(a1),x65561),x65562)),x65563),f333(f333(f38(a1),x65561),f333(f333(f80(a1),x65562),x65563)))+~P1(f333(f333(f248(a1),f2(a1)),x65563)) % 183.90/184.43 [6608]~P109(x66081)+E(f333(f333(f79(x66081),f333(f333(f80(x66081),x66082),x66083)),x66083),f333(f333(f80(x66081),f333(f333(f79(x66081),x66082),f77(x66081))),x66083)) % 183.90/184.43 [6609]~P90(x66091)+E(f333(f333(f80(x66091),f333(f78(x66091),f333(f106(x66091),x66092))),x66093),f333(f333(f80(x66091),f333(f106(x66091),f333(f78(a1),x66092))),x66093)) % 183.90/184.43 [6681]~P78(x66811)+E(f333(f167(x66811),f333(f333(f155(x66812,x66811),f333(f16(x66811,x66812),f2(x66811))),x66813)),f2(x66811)) % 183.90/184.43 [6697]E(f333(f333(f79(a875),f333(f106(a875),x66971)),f333(f333(f79(a875),f333(f106(a875),x66972)),x66973)),f333(f333(f79(a875),f333(f106(a875),x66972)),x66973))+~P1(f333(a201,f333(f106(a1),x66971))) % 183.90/184.43 [6711]~P4(x67111)+E(f40(x67111,f333(f333(f311(x67111),x67112),f333(f333(f311(x67111),x67113),f196(f882(x67111,a870))))),f333(f333(f104(x67111),x67112),x67113)) % 183.90/184.43 [6712]~P4(x67121)+E(f39(x67121,f333(f333(f311(x67121),x67122),f333(f333(f311(x67121),x67123),f196(f882(x67121,a870))))),f333(f333(f113(x67121),x67122),x67123)) % 183.90/184.43 [6735]E(f333(f333(f177(x67351),x67352),x67353),x67353)+~P1(f333(f333(f247(a875),f333(f197(f876(x67351)),x67353)),x67352)) % 183.90/184.43 [6748]E(f333(f333(f139(x67481),x67482),x67483),f116(x67481))+~P1(f333(f333(f247(a875),f333(f197(f876(x67481)),x67483)),x67482)) % 183.90/184.43 [6759]E(f333(f333(f79(a875),f333(f333(f22(a875),x67591),x67592)),x67593),f333(f333(f22(a875),f333(f333(f79(a875),x67591),x67593)),x67592))+~P1(f333(f333(f247(a875),x67592),x67591)) % 183.90/184.43 [6773]~P1(f333(f333(f248(a875),x67731),x67733))+P1(f333(f333(f248(a875),f333(f333(f22(a875),x67731),x67732)),x67733)) % 183.90/184.43 [6801]~P106(x68011)+E(f172(x68011,x68012,f333(f333(f149(x68011,x68011,f5(x68011)),x68012),x68013)),x68013) % 183.90/184.43 [6890]E(f333(f333(f22(a875),f333(f333(f79(a875),x68901),x68902)),f333(a115,x68903)),f333(f333(f22(a875),x68901),f333(a115,f333(f333(f22(a875),x68903),x68902))))+~P1(f333(f333(f247(a875),x68902),x68903)) % 183.90/184.43 [6891]~P114(x68911)+P1(f333(f333(f247(x68911),f2(x68911)),f333(f333(f258(x68911),f333(f74(x68911),x68912)),x68913))) % 183.90/184.43 [6938]P24(x69381,x69382,x69383)+~P1(f333(f333(f247(f882(f874(x69381),a870)),x69383),x69382)) % 183.90/184.43 [6981]~P1(f333(f61(x69811),x69812))+P1(f333(f61(x69811),f333(f333(f22(f882(x69811,a870)),x69812),x69813))) % 183.90/184.43 [6982]~P1(f333(f61(x69821),x69823))+P1(f333(f61(x69821),f333(f333(f104(f882(x69821,a870)),x69822),x69823))) % 183.90/184.43 [6983]~P1(f333(f61(x69831),x69832))+P1(f333(f61(x69831),f333(f333(f104(f882(x69831,a870)),x69832),x69833))) % 183.90/184.43 [7124]~P37(x71241,x71243)+P37(x71241,f333(f333(f104(f882(f881(x71241,x71241),a870)),x71242),x71243)) % 183.90/184.43 [7125]~P37(x71251,x71252)+P37(x71251,f333(f333(f104(f882(f881(x71251,x71251),a870)),x71252),x71253)) % 183.90/184.43 [7240]~P62(x72401)+E(f13(x72401,f333(f174(x72401),f333(f333(f152(x72401),x72402),x72403))),f333(f143(x72401,x72401,f113(x72401),x72402),x72403)) % 183.90/184.43 [7241]~P62(x72411)+E(f10(x72411,f333(f174(x72411),f333(f333(f152(x72411),x72412),x72413))),f333(f143(x72411,x72411,f104(x72411),x72412),x72413)) % 183.90/184.43 [7242]~P106(x72421)+E(f14(x72421,f333(f174(x72421),f333(f333(f152(x72421),x72422),x72423))),f333(f143(x72421,x72421,f245(x72421),x72422),x72423)) % 183.90/184.43 [7243]~P106(x72431)+E(f15(x72431,f333(f174(x72431),f333(f333(f152(x72431),x72432),x72433))),f333(f143(x72431,x72431,f246(x72431),x72432),x72433)) % 183.90/184.43 [7303]~P1(f333(f61(x73031),x73032))+P1(f333(f333(f247(a875),f333(f37(x73031),x73032)),f333(f37(x73031),f333(f333(f311(x73031),x73033),x73032)))) % 183.90/184.43 [7311]E(f333(f333(f113(f882(a875,a870)),f333(f303(a875,x73111),x73112)),f333(f303(a875,x73112),f333(f333(f79(a875),x73112),x73113))),f333(f303(a875,x73111),f333(f333(f79(a875),x73112),x73113)))+~P1(f333(f333(f247(a875),x73111),x73112)) % 183.90/184.43 [7319]P1(f333(f333(f248(a875),x73191),x73192))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),x73191),x73193)),x73192)) % 183.90/184.43 [7322]P1(f333(f333(f247(a875),x73221),x73222))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x73223),x73221)),x73222)) % 183.90/184.43 [7323]P1(f333(f333(f247(a875),x73231),x73232))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x73231),x73233)),x73232)) % 183.90/184.43 [7365]~P106(x73651)+E(f11(x73651,f245(x73651),f333(f174(x73651),f333(f333(f152(x73651),x73652),x73653))),f333(f143(x73651,x73651,f245(x73651),x73652),x73653)) % 183.90/184.43 [7366]~P106(x73661)+E(f12(x73661,f246(x73661),f333(f174(x73661),f333(f333(f152(x73661),x73662),x73663))),f333(f143(x73661,x73661,f246(x73661),x73662),x73663)) % 183.90/184.43 [7370]~E(x73702,f196(f882(f881(x73701,x73701),a870)))+P1(f333(f333(f247(f882(f881(x73701,x73701),a870)),x73702),x73703)) % 183.90/184.43 [7480]E(f333(f333(f113(f882(x74801,a870)),x74802),f333(f333(f22(f882(x74801,a870)),x74803),x74802)),x74803)+~P1(f333(f333(f247(f882(x74801,a870)),x74802),x74803)) % 183.90/184.43 [7481]~P1(f333(f333(f248(a875),x74811),f333(f333(f22(a875),x74813),x74812)))+P1(f333(f333(f248(a875),f333(f333(f79(a875),x74811),x74812)),x74813)) % 183.90/184.43 [7482]~P1(f333(f333(f247(a875),x74821),f333(f333(f79(a875),x74823),x74822)))+P1(f333(f333(f247(a875),f333(f333(f22(a875),x74821),x74822)),x74823)) % 183.90/184.43 [7539]E(x75391,f116(x75392))+E(f333(f142(x75392),f333(f333(f333(f191(f876(x75392),f876(x75392)),x75393),f169(x75392)),x75391)),f333(f333(f166(x75392),x75391),f44(a875,x75393,f333(f197(f876(x75392)),x75391)))) % 183.90/184.43 [7548]E(f333(f333(f311(x75481),x75482),f333(f333(f22(f882(x75481,a870)),x75483),f333(f333(f311(x75481),x75482),f196(f882(x75481,a870))))),x75483)+~P1(f333(f333(f335(x75481),x75482),x75483)) % 183.90/184.43 [7711]P1(f333(f333(f248(a875),x77111),f333(f333(f22(a875),x77112),x77113)))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),x77111),x77113)),x77112)) % 183.90/184.43 [7712]P1(f333(f333(f247(a875),x77121),f333(f333(f79(a875),x77122),x77123)))+~P1(f333(f333(f247(a875),f333(f333(f22(a875),x77121),x77123)),x77122)) % 183.90/184.44 [7735]P1(f333(f61(x77351),x77352))+~P1(f333(f61(x77351),f333(f333(f113(f882(x77351,a870)),x77353),x77352))) % 183.90/184.44 [7736]P1(f333(f61(x77361),x77362))+~P1(f333(f61(x77361),f333(f333(f113(f882(x77361,a870)),x77362),x77363))) % 183.90/184.44 [7814]~P45(x78141,x78143)+P1(f333(f333(f335(f881(x78141,x78141)),f333(f333(f268(x78141,x78141),x78142),x78142)),x78143)) % 183.90/184.44 [7948]E(f333(f333(f166(a875),f140(a875,f333(f303(a875,x79481),x79482))),x79483),f333(f333(f79(a875),x79481),x79483))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),x79481),x79483)),x79482)) % 183.90/184.44 [8017]~P1(f333(f333(f202(f333(a25,x80171)),x80172),x80173))+P1(f333(f333(f202(f333(f244(a871),f333(a27,x80171))),x80172),x80173)) % 183.90/184.44 [8022]E(f333(f333(f177(a875),x80221),f140(a875,f333(f303(a875,x80222),x80223))),f140(a875,f333(f303(a875,x80222),f333(f333(f79(a875),x80222),x80221))))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x80222),x80221)),x80223)) % 183.90/184.44 [8075]~P90(x80751)+E(f333(f333(f258(x80751),x80752),f333(f106(a875),f333(f333(f79(a1),x80753),x80753))),f333(f333(f85(x80751,x80751),f333(f333(f258(x80751),x80752),f333(f106(a875),x80753))),f333(f333(f18(x80751,x80751,x80751),f80(x80751)),f5(x80751)))) % 183.90/184.44 [8285]P1(f333(f333(f202(f333(a25,x82851)),x82852),x82853))+~P1(f333(f333(f202(f333(f244(a871),f333(a27,x82851))),x82852),x82853)) % 183.90/184.44 [8345]E(f333(f333(f135(x83451),f333(f333(f177(x83451),x83452),x83453)),f333(f333(f152(x83451),f333(f333(f166(x83451),x83453),x83452)),f333(f333(f139(x83451),f333(a115,x83452)),x83453))),x83453)+~P1(f333(f333(f248(a875),x83452),f333(f197(f876(x83451)),x83453))) % 183.90/184.44 [8352]P1(f333(f333(f247(f882(x83521,a870)),f321(x83521,x83522)),f321(x83521,x83523)))+~P1(f333(f333(f247(f882(x83521,f882(x83521,a870))),x83523),x83522)) % 183.90/184.44 [8354]~P50(x83541,x83542,x83543)+P50(x83541,x83542,f333(f333(f22(f882(f881(x83541,x83541),a870)),x83543),f309(x83541,f196(f882(f881(x83541,x83541),a870))))) % 183.90/184.44 [8371]P1(f333(f333(f247(f882(x83711,a870)),f322(x83711,x83712)),f322(x83711,x83713)))+~P1(f333(f333(f247(f882(f881(x83711,x83711),a870)),x83713),x83712)) % 183.90/184.44 [8378]~P121(x83781)+P1(f333(f333(f247(x83781),f2(x83781)),f333(f333(f79(x83781),f333(f333(f80(x83781),x83782),x83782)),f333(f333(f80(x83781),x83783),x83783)))) % 183.90/184.44 [8414]P1(f333(f333(f247(f882(x84141,a870)),f333(f286(x84141),x84142)),f333(f286(x84141),x84143)))+~P1(f333(f333(f247(f882(f881(x84141,x84141),a870)),x84142),x84143)) % 183.90/184.44 [8448]~P41(x84481,x84482)+~P1(f333(f333(f335(f881(x84481,x84481)),f333(f333(f268(x84481,x84481),x84483),x84483)),x84482)) % 183.90/184.44 [8450]~P37(x84501,x84502)+~P1(f333(f333(f335(f881(x84501,x84501)),f333(f333(f268(x84501,x84501),x84503),x84503)),x84502)) % 183.90/184.44 [8511]P1(f333(f333(f247(f882(x85111,a870)),f40(f882(x85111,a870),x85112)),f40(f882(x85111,a870),x85113)))+~P1(f333(f333(f247(f882(f882(x85111,a870),a870)),x85113),x85112)) % 183.90/184.44 [8512]P1(f333(f333(f247(f882(x85121,a870)),f39(f882(x85121,a870),x85122)),f39(f882(x85121,a870),x85123)))+~P1(f333(f333(f247(f882(f882(x85121,a870),a870)),x85122),x85123)) % 183.90/184.44 [8564]~P7(x85641,x85643,x85642)+P1(f333(f333(f247(f882(f881(x85641,x85641),a870)),x85642),f333(f333(f270(x85641,x85641),x85643),f333(f16(f882(x85641,a870),x85641),x85643)))) % 183.90/184.44 [8565]~P39(x85651,x85653,x85652)+P1(f333(f333(f247(f882(f881(x85651,x85651),a870)),x85652),f333(f333(f270(x85651,x85651),x85653),f333(f16(f882(x85651,a870),x85651),x85653)))) % 183.90/184.44 [8610]~P83(x86101)+P1(f333(f333(f247(x86101),f333(f333(f22(x86101),f333(f74(x86101),x86102)),f333(f74(x86101),x86103))),f333(f74(x86101),f333(f333(f22(x86101),x86103),x86102)))) % 183.90/184.44 [8611]~P83(x86111)+P1(f333(f333(f247(x86111),f333(f333(f22(x86111),f333(f74(x86111),x86112)),f333(f74(x86111),x86113))),f333(f74(x86111),f333(f333(f22(x86111),x86112),x86113)))) % 183.90/184.44 [8641]P1(f333(f333(f247(f882(f881(x86411,x86411),a870)),f309(x86411,x86412)),f309(x86411,x86413)))+~P1(f333(f333(f247(f882(f881(x86411,x86411),a870)),x86412),x86413)) % 183.90/184.44 [8796]P50(x87961,x87962,x87963)+~P50(x87961,x87962,f333(f333(f22(f882(f881(x87961,x87961),a870)),x87963),f309(x87961,f196(f882(f881(x87961,x87961),a870))))) % 183.90/184.44 [8815]P1(f333(f333(f247(f882(f881(f876(x88151),f876(x88151)),a870)),f158(x88151,x88152)),f158(x88151,x88153)))+~P1(f333(f333(f247(f882(f881(x88151,x88151),a870)),x88152),x88153)) % 183.90/184.44 [8816]P1(f333(f333(f247(f882(f881(f876(x88161),f876(x88161)),a870)),f159(x88161,x88162)),f159(x88161,x88163)))+~P1(f333(f333(f247(f882(f881(x88161,x88161),a870)),x88162),x88163)) % 183.90/184.44 [8835]~P39(x88351,x88353,x88352)+P1(f333(f333(f247(f882(f881(x88351,x88351),a870)),x88352),f333(f333(f290(x88351,x88351,x88351),f333(f288(x88351,x88351),x88352)),x88352))) % 183.90/184.44 [8884]~P1(f333(f138(x88841),x88842))+E(f333(f137(x88841,f333(f333(f7(x88841,f882(x88841,a870),a870),f335(x88841)),f333(f174(x88841),f178(x88841,x88842,x88843)))),x88842),f178(x88841,x88842,x88843)) % 183.90/184.44 [8949]E(x89491,x89492)+~P1(f333(f333(f335(f881(x89493,x89493)),f333(f333(f268(x89493,x89493),x89491),x89492)),f309(x89493,f196(f882(f881(x89493,x89493),a870))))) % 183.90/184.44 [9034]P1(f333(f333(f335(x90341),x90342),f322(x90341,x90343)))+P1(f333(f333(f335(f881(x90341,x90341)),f333(f333(f268(x90341,x90341),f557(x90343,x90342,x90341)),x90342)),x90343)) % 183.90/184.44 [9035]P1(f333(f333(f335(x90351),x90352),f322(x90351,x90353)))+P1(f333(f333(f335(f881(x90351,x90351)),f333(f333(f268(x90351,x90351),f617(x90353,x90352,x90351)),x90352)),x90353)) % 183.90/184.44 [9036]P1(f333(f333(f335(x90361),x90362),f322(x90361,x90363)))+P1(f333(f333(f335(f881(x90361,x90361)),f333(f333(f268(x90361,x90361),f619(x90363,x90362,x90361)),x90362)),x90363)) % 183.90/184.44 [9122]~P1(f333(f333(f335(f876(x91221)),x91223),f162(x91221,x91222)))+P1(f333(f161(x91221,f333(f333(f7(x91221,f882(x91221,a870),a870),f335(x91221)),x91222)),x91223)) % 183.90/184.44 [9143]P1(f333(x91433,x91432))+E(f333(f253(x91431),f333(f333(f18(x91431,a870,a870),f333(f333(f8(a870,f882(a870,a870),x91431),a331),f333(a330,x91432))),x91433)),f196(f882(x91431,a870))) % 183.90/184.44 [9164]~P83(x91641)+P1(f333(f333(f247(x91641),f333(f74(x91641),f333(f333(f22(x91641),f333(f74(x91641),x91642)),f333(f74(x91641),x91643)))),f333(f74(x91641),f333(f333(f22(x91641),x91642),x91643)))) % 183.90/184.44 [9178]~P1(f333(x91783,x91782))+E(f333(f253(x91781),f333(f333(f18(x91781,a870,a870),f333(f333(f8(a870,f882(a870,a870),x91781),a331),f333(a330,x91782))),x91783)),f333(f333(f311(x91781),x91782),f196(f882(x91781,a870)))) % 183.90/184.44 [9185]~P1(f333(f333(f335(f882(x91851,a870)),x91853),f333(f310(x91851),x91852)))+P1(f333(f261(x91851,f333(f333(f7(x91851,f882(x91851,a870),a870),f335(x91851)),x91852)),x91853)) % 183.90/184.44 [9218]P37(x92181,x92182)+P1(f333(f333(f335(f881(x92181,x92181)),f333(f333(f268(x92181,x92181),f333(f566(x92182,x92181),f333(a115,x92183))),f333(f566(x92182,x92181),x92183))),x92182)) % 183.90/184.44 [9359]P1(f333(f333(f335(f876(x93591)),x93592),f162(x93591,x93593)))+~P1(f333(f161(x93591,f333(f333(f7(x93591,f882(x93591,a870),a870),f335(x93591)),x93593)),x93592)) % 183.90/184.44 [9372]P1(f333(f333(f335(f882(x93721,a870)),x93722),f333(f310(x93721),x93723)))+~P1(f333(f261(x93721,f333(f333(f7(x93721,f882(x93721,a870),a870),f335(x93721)),x93723)),x93722)) % 183.90/184.44 [9429]P1(f333(f333(f335(x94291),f333(f279(x94291,x94292),x94293)),f333(f174(x94291),f333(f333(f155(f881(a102,x94291),x94291),f271(a102,x94291)),x94292))))+~P1(f333(f333(f248(a102),x94293),f333(f167(a102),f333(f333(f155(f881(a102,x94291),a102),f267(a102,x94291)),x94292)))) % 183.90/184.44 [9477]P1(f333(f333(f247(f882(f881(f876(x94771),f876(x94771)),a870)),f159(x94771,x94772)),f333(f333(f270(f876(x94771),f876(x94771)),f162(x94771,x94773)),f333(f16(f882(f876(x94771),a870),f876(x94771)),f162(x94771,x94773)))))+~P1(f333(f333(f247(f882(f881(x94771,x94771),a870)),x94772),f333(f333(f270(x94771,x94771),x94773),f333(f16(f882(x94771,a870),x94771),x94773)))) % 183.90/184.44 [9498]P1(f333(f333(f335(x94981),f333(f267(x94981,f881(a102,a102)),f333(f277(x94981,x94982),x94983))),f333(f174(x94981),f333(f333(f155(f881(a102,x94981),x94981),f271(a102,x94981)),x94982))))+~P1(f333(f333(f248(a102),f2(a102)),f333(f167(a102),f333(f333(f155(f881(a102,x94981),a102),f267(a102,x94981)),x94982)))) % 183.90/184.44 [9515]~P1(f333(f333(f247(f882(f881(x95151,x95151),a870)),x95152),f333(f333(f270(x95151,x95151),x95153),f333(f16(f882(x95151,a870),x95151),x95153))))+P1(f333(f333(f247(f882(f881(x95151,x95151),a870)),f333(f333(f290(x95151,x95151,x95151),x95152),f309(x95151,x95152))),f333(f333(f270(x95151,x95151),x95153),f333(f16(f882(x95151,a870),x95151),x95153)))) % 183.90/184.44 [9817]~P37(x98171,x98172)+~P1(f333(f333(f335(f881(x98171,x98171)),f333(f333(f268(x98171,x98171),f333(x98173,f333(a115,f567(x98172,x98171,x98173)))),f333(x98173,f567(x98172,x98171,x98173)))),x98172)) % 183.90/184.44 [9818]~P37(x98181,x98182)+~P1(f333(f333(f335(f881(x98181,x98181)),f333(f333(f268(x98181,x98181),f333(x98183,f333(a115,f623(x98183,x98182,x98181)))),f333(x98183,f623(x98183,x98182,x98181)))),x98182)) % 183.90/184.44 [10071]P1(f333(f333(f247(f882(f881(f882(x100711,a870),f882(x100711,a870)),a870)),f333(f333(f290(f882(x100711,a870),f882(x100711,a870),f882(x100711,a870)),f324(x100711,x100712)),f333(f333(f113(f882(f881(f882(x100711,a870),f882(x100711,a870)),a870)),f324(x100711,x100713)),f333(f333(f311(f881(f882(x100711,a870),f882(x100711,a870))),f333(f333(f268(f882(x100711,a870),f882(x100711,a870)),f196(f882(x100711,a870))),f196(f882(x100711,a870)))),f196(f882(f881(f882(x100711,a870),f882(x100711,a870)),a870)))))),f324(x100711,x100712)))+~P1(f333(f333(f247(f882(f881(x100711,x100711),a870)),f333(f333(f290(x100711,x100711,x100711),x100712),x100713)),x100712)) % 183.90/184.44 [10072]P1(f333(f333(f247(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)),f333(f333(f290(f882(x100721,a870),f882(x100721,a870),f882(x100721,a870)),f325(x100721,x100722)),f333(f333(f113(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)),f325(x100721,x100723)),f333(f333(f311(f881(f882(x100721,a870),f882(x100721,a870))),f333(f333(f268(f882(x100721,a870),f882(x100721,a870)),f196(f882(x100721,a870))),f196(f882(x100721,a870)))),f196(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)))))),f325(x100721,x100722)))+~P1(f333(f333(f247(f882(f881(x100721,x100721),a870)),f333(f333(f290(x100721,x100721,x100721),x100722),x100723)),x100722)) % 183.90/184.44 [7239]~P1(f333(f333(f247(a875),x72392),x72391))+E(f333(f333(f22(a875),f333(a115,f333(f333(f22(a875),x72391),x72392))),x72393),f333(f333(f22(a875),f333(a115,x72391)),f333(f333(f79(a875),x72392),x72393))) % 183.90/184.44 [7278]~P55(x72781)+E(f333(f333(f79(x72781),f44(x72781,x72782,x72783)),f333(f333(f80(x72781),f333(f333(f38(x72781),x72782),x72783)),x72783)),x72782) % 183.90/184.44 [7486]E(f333(f333(f80(a875),f333(f106(a875),x74861)),f333(f333(f80(a875),f333(f106(a875),x74862)),x74863)),f333(f333(f80(a875),f333(f106(a875),f333(f333(f80(a1),x74861),x74862))),x74863))+P1(f333(f333(f248(a1),x74861),a82)) % 183.90/184.44 [7957]~P1(f333(f333(f247(a875),x79573),x79572))+P1(f333(f333(f247(a875),x79571),f333(f333(f22(a875),f333(f333(f79(a875),x79572),x79571)),x79573))) % 183.90/184.44 [8165]~P1(f333(f333(f247(a875),x81651),x81652))+E(f333(f333(f135(a875),f140(a875,f333(f303(a875,x81651),x81652))),f140(a875,f333(f303(a875,x81652),f333(f333(f79(a875),x81652),x81653)))),f140(a875,f333(f303(a875,x81651),f333(f333(f79(a875),x81652),x81653)))) % 183.90/184.44 [8424]~P1(f333(f61(x84241),x84242))+E(f333(a115,f333(f37(x84241),f333(f333(f22(f882(x84241,a870)),x84242),f333(f333(f311(x84241),x84243),f196(f882(x84241,a870)))))),f333(f37(x84241),f333(f333(f311(x84241),x84243),x84242))) % 183.90/184.44 [8471]~P1(f333(f61(x84711),x84712))+E(f333(f333(f79(a875),f77(a875)),f333(f37(x84711),f333(f333(f22(f882(x84711,a870)),x84712),f333(f333(f311(x84711),x84713),f196(f882(x84711,a870)))))),f333(f37(x84711),f333(f333(f311(x84711),x84713),x84712))) % 183.90/184.44 [8650]E(f333(f333(f22(a875),f333(f37(x86501),x86502)),f333(f37(x86501),f333(f333(f104(f882(x86501,a870)),x86502),x86503))),f333(f37(x86501),f333(f333(f22(f882(x86501,a870)),x86502),x86503)))+~P1(f333(f61(x86501),f333(f333(f104(f882(x86501,a870)),x86502),x86503))) % 183.90/184.44 [8880]~P5(f333(x88802,f415(x88802,x88803,x88801)))+E(f333(f103(a1),f333(f333(f6(x88801,a875),f333(f333(f8(a1,a875,x88801),a107),x88802)),x88803)),f333(f333(f6(x88801,a1),x88802),x88803)) % 183.90/184.44 [8881]~P5(f333(x88812,f416(x88812,x88813,x88811)))+E(f333(f103(a1),f333(f333(f9(x88811,a875),f333(f333(f8(a1,a875,x88811),a107),x88812)),x88813)),f333(f333(f9(x88811,a1),x88812),x88813)) % 183.90/184.44 [8931]~P1(f333(f61(x89311),x89313))+P1(f333(f333(f247(a875),f333(f333(f22(a875),f333(f37(x89311),x89312)),f333(f37(x89311),x89313))),f333(f37(x89311),f333(f333(f22(f882(x89311,a870)),x89312),x89313)))) % 183.90/184.44 [8957]P1(f333(f333(f335(x89571),f415(x89572,x89573,x89571)),x89573))+E(f333(f103(a1),f333(f333(f6(x89571,a875),f333(f333(f8(a1,a875,x89571),a107),x89572)),x89573)),f333(f333(f6(x89571,a1),x89572),x89573)) % 183.90/184.44 [8958]P1(f333(f333(f335(x89581),f416(x89582,x89583,x89581)),x89583))+E(f333(f103(a1),f333(f333(f9(x89581,a875),f333(f333(f8(a1,a875,x89581),a107),x89582)),x89583)),f333(f333(f9(x89581,a1),x89582),x89583)) % 183.90/184.44 [9026]E(f84(x90261,f333(f333(f7(x90261,f882(x90261,a870),a870),f335(x90261)),f333(f333(f22(f882(x90261,a870)),x90262),f333(f333(f311(x90261),x90263),f196(f882(x90261,a870)))))),f260(x90261,x90263,x90262))+P1(f333(f333(f247(f882(x90261,a870)),x90262),f333(f333(f311(x90261),x90263),f196(f882(x90261,a870))))) % 183.90/184.44 [9373]E(f333(f333(f155(f876(x93731),x93731),f333(f333(f7(f876(x93731),a875,x93731),f166(x93731)),x93732)),f333(f137(f876(x93731),f333(f333(f8(a875,a870,f876(x93731)),f333(f248(a875),x93732)),f197(f876(x93731)))),x93733)),f333(f333(f166(f876(x93731)),f182(x93731,x93733)),x93732))+~P1(f333(f333(f248(a875),x93732),f333(f197(f876(f876(x93731))),f182(x93731,x93733)))) % 183.90/184.44 [9446]E(f333(f137(x94461,x94462),x94463),f179(x94461,x94462,x94463))+P1(f333(f333(f335(x94461),f756(x94463,x94462,x94461)),f333(f174(x94461),f333(f333(f139(x94461),f333(f197(f876(x94461)),f179(x94461,x94462,x94463))),x94463)))) % 183.90/184.44 [9586]E(f333(f333(f139(x95861),f333(f197(f876(x95861)),f179(x95861,x95862,x95863))),x95863),f116(x95861))+~P1(f333(x95862,f333(f142(x95861),f333(f333(f139(x95861),f333(f197(f876(x95861)),f179(x95861,x95862,x95863))),x95863)))) % 183.90/184.44 [9679]~P1(f333(f333(f335(f881(x96791,x96791)),x96792),f309(x96791,x96793)))+P1(f333(f333(f335(f881(x96791,x96791)),x96792),f333(f333(f41(a875,f882(f881(x96791,x96791),a870)),f256(f882(a875,a870))),f333(f333(f7(a875,f882(f881(x96791,x96791),a870),f882(f881(x96791,x96791),a870)),f191(f881(x96791,x96791),a870)),x96793)))) % 183.90/184.44 [9735]~P1(f333(f333(f247(f882(x97351,a870)),f333(f333(f41(a875,f882(x97351,a870)),f333(f303(a875,f2(a875)),f393(x97353,x97352,x97351))),x97352)),x97353))+P1(f333(f333(f247(f882(x97351,a870)),f333(f333(f41(a875,f882(x97351,a870)),f256(f882(a875,a870))),x97352)),x97353)) % 183.90/184.44 [9793]~P1(f333(f333(f248(a1),f2(a1)),x97933))+P1(f333(f333(f248(a1),x97931),f333(f333(f79(a1),x97932),f333(f333(f80(a1),f333(f333(f79(a1),f333(f74(a1),f333(f333(f22(a1),x97932),x97931))),f77(a1))),x97933)))) % 183.90/184.44 [9804]~P37(x98041,f333(f333(f113(f882(f881(x98041,x98041),a870)),x98042),x98043))+P37(x98041,f333(f333(f113(f882(f881(x98041,x98041),a870)),f333(f333(f113(f882(f881(x98041,x98041),a870)),f333(f333(f290(x98041,x98041,x98041),x98042),x98042)),f333(f333(f290(x98041,x98041,x98041),x98043),x98042))),x98043)) % 183.90/184.44 [9886]P37(x98861,f333(f333(f113(f882(f881(x98861,x98861),a870)),x98862),x98863))+~P37(x98861,f333(f333(f113(f882(f881(x98861,x98861),a870)),f333(f333(f113(f882(f881(x98861,x98861),a870)),f333(f333(f290(x98861,x98861,x98861),x98862),x98862)),f333(f333(f290(x98861,x98861,x98861),x98863),x98862))),x98863)) % 183.90/184.44 [9450]~P138(x94501)+E(f333(f105(x94501),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x94502),x94503)),f196(f882(f881(a875,a875),a870)))))),f333(f333(f22(x94501),f333(f103(x94501),x94502)),f333(f103(x94501),x94503))) % 183.90/184.44 [9533]P1(f333(x95333,x95332))+E(f333(f253(x95331),f333(f333(f18(x95331,a870,a870),f333(f333(f8(a870,f882(a870,a870),x95331),a331),f333(f333(f7(x95331,x95331,a870),a330),x95332))),x95333)),f196(f882(x95331,a870))) % 183.90/184.44 [9535]~P1(f333(x95353,x95352))+E(f333(f253(x95351),f333(f333(f18(x95351,a870,a870),f333(f333(f8(a870,f882(a870,a870),x95351),a331),f333(f333(f7(x95351,x95351,a870),a330),x95352))),x95353)),f333(f333(f311(x95351),x95352),f196(f882(x95351,a870)))) % 183.90/184.44 [9771]E(x97711,x97712)+P1(f333(f333(f257(x97713,x97713,f333(f333(f8(f882(x97713,a870),f882(x97713,a870),x97713),f333(f8(a870,a870,x97713),a328)),a330)),x97711),x97712)) % 183.90/184.44 [9864]~E(x98641,x98642)+~P1(f333(f333(f257(x98643,x98643,f333(f333(f8(f882(x98643,a870),f882(x98643,a870),x98643),f333(f8(a870,a870,x98643),a328)),a330)),x98641),x98642)) % 183.90/184.44 [9878]~P1(f333(f61(x98781),x98783))+E(f333(f333(f64(x98781,f882(x98781,a870),f333(f333(f8(f882(x98781,a870),f882(f882(x98781,a870),f882(x98781,a870)),x98781),f333(f7(f882(x98781,a870),f882(x98781,a870),f882(x98781,a870)),f22(f882(x98781,a870)))),f333(f333(f7(x98781,f882(x98781,a870),f882(x98781,a870)),f311(x98781)),f196(f882(x98781,a870))))),x98782),x98783),f333(f333(f22(f882(x98781,a870)),x98782),x98783)) % 183.90/184.44 [9910]~P1(f333(f333(f248(a1),f2(a1)),x99103))+P1(f333(f333(f248(a1),f333(f333(f22(a1),x99101),f333(f333(f80(a1),f333(f333(f79(a1),f333(f74(a1),f333(f333(f22(a1),x99101),x99102))),f77(a1))),x99103))),x99102)) % 183.90/184.44 [10133]~P1(f333(f333(f335(x101331),x101333),f322(x101331,x101332)))+P1(f333(f321(x101331,f333(f333(f7(x101331,f882(f881(x101331,x101331),a870),f882(x101331,a870)),f333(f333(f8(f882(x101331,f882(f882(f881(x101331,x101331),a870),a870)),f882(f882(f881(x101331,x101331),a870),f882(x101331,a870)),x101331),f7(x101331,f882(f881(x101331,x101331),a870),a870)),f333(f333(f8(f882(x101331,f881(x101331,x101331)),f882(x101331,f882(f882(f881(x101331,x101331),a870),a870)),x101331),f333(f8(f881(x101331,x101331),f882(f882(f881(x101331,x101331),a870),a870),x101331),f335(f881(x101331,x101331)))),f268(x101331,x101331)))),x101332)),x101333)) % 183.90/184.44 [10145]P1(f333(f333(f335(x101451),x101452),f322(x101451,x101453)))+~P1(f333(f321(x101451,f333(f333(f7(x101451,f882(f881(x101451,x101451),a870),f882(x101451,a870)),f333(f333(f8(f882(x101451,f882(f882(f881(x101451,x101451),a870),a870)),f882(f882(f881(x101451,x101451),a870),f882(x101451,a870)),x101451),f7(x101451,f882(f881(x101451,x101451),a870),a870)),f333(f333(f8(f882(x101451,f881(x101451,x101451)),f882(x101451,f882(f882(f881(x101451,x101451),a870),a870)),x101451),f333(f8(f881(x101451,x101451),f882(f882(f881(x101451,x101451),a870),a870),x101451),f335(f881(x101451,x101451)))),f268(x101451,x101451)))),x101453)),x101452)) % 183.90/184.44 [9733]~P1(f333(f61(x97331),f333(f253(x97331),x97333)))+P1(f333(f61(x97331),f333(f253(x97331),f333(f333(f18(x97331,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97331),a331),x97332)),x97333)))) % 183.90/184.44 [9734]~P1(f333(f61(x97341),f333(f253(x97341),x97342)))+P1(f333(f61(x97341),f333(f253(x97341),f333(f333(f18(x97341,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97341),a331),x97342)),x97343)))) % 183.90/184.44 [9836]P1(f333(f61(x98361),f333(f253(x98361),x98362)))+~P1(f333(f61(x98361),f333(f253(x98361),f333(f333(f18(x98361,a870,a870),f333(f333(f8(a870,f882(a870,a870),x98361),a332),x98363)),x98362)))) % 183.90/184.44 [9837]P1(f333(f61(x98371),f333(f253(x98371),x98372)))+~P1(f333(f61(x98371),f333(f253(x98371),f333(f333(f18(x98371,a870,a870),f333(f333(f8(a870,f882(a870,a870),x98371),a332),x98372)),x98373)))) % 183.90/184.44 [10120]~P1(f333(f61(x101201),x101202))+P1(f333(f61(f876(x101201)),f333(f253(f876(x101201)),f333(f333(f18(f876(x101201),a870,a870),f333(f333(f8(a870,f882(a870,a870),f876(x101201)),a331),f333(f333(f7(f876(x101201),f882(x101201,a870),a870),f333(f333(f8(f882(x101201,a870),f882(f882(x101201,a870),a870),f876(x101201)),f247(f882(x101201,a870))),f174(x101201))),x101202))),f333(f333(f7(f876(x101201),a875,a870),f333(f333(f8(a875,f882(a875,a870),f876(x101201)),a330),f197(f876(x101201)))),x101203))))) % 183.90/184.44 [10121]~P1(f333(f61(x101211),x101212))+P1(f333(f61(f876(x101211)),f333(f253(f876(x101211)),f333(f333(f18(f876(x101211),a870,a870),f333(f333(f8(a870,f882(a870,a870),f876(x101211)),a331),f333(f333(f7(f876(x101211),f882(x101211,a870),a870),f333(f333(f8(f882(x101211,a870),f882(f882(x101211,a870),a870),f876(x101211)),f247(f882(x101211,a870))),f174(x101211))),x101212))),f333(f333(f7(f876(x101211),a875,a870),f333(f333(f8(a875,f882(a875,a870),f876(x101211)),f247(a875)),f197(f876(x101211)))),x101213))))) % 183.90/184.44 [9851]~P109(x98511)+E(f333(f333(f258(x98511),x98512),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x98513)),f333(f333(f80(x98511),f333(f333(f258(x98511),x98512),x98513)),f333(f333(f258(x98511),x98512),x98513))) % 183.90/184.44 [9891]~P77(x98911)+E(f333(f333(f258(x98911),f333(f333(f258(x98911),x98912),x98913)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f258(x98911),x98912),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x98913))) % 183.90/184.44 [9937]~P138(x99371)+E(f333(f333(f258(x99371),f333(f78(x99371),x99372)),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99373)),f333(f333(f258(x99371),x99372),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99373))) % 183.90/184.44 [10078]~P114(x100781)+P1(f333(f333(f247(x100781),f2(x100781)),f333(f333(f79(x100781),f333(f333(f258(x100781),x100782),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x100781),x100783),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))) % 183.90/184.44 [9947]~P109(x99471)+E(f333(f333(f258(x99471),x99472),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99473))),f333(f333(f80(x99471),x99472),f333(f333(f80(x99471),f333(f333(f258(x99471),x99472),x99473)),f333(f333(f258(x99471),x99472),x99473)))) % 183.90/184.44 [9996]~P77(x99961)+E(f333(f333(f80(x99961),x99962),f333(f333(f258(x99961),f333(f333(f258(x99961),x99962),x99963)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x99961),x99962),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99963)))) % 183.90/184.44 [10035]~P114(x100351)+P1(f333(f333(f247(x100351),f2(x100351)),f333(f333(f258(x100351),x100352),f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x100353)))) % 183.90/184.44 [10101]~P90(x101011)+E(f333(f333(f22(x101011),f333(f333(f79(x101011),f333(f333(f258(x101011),x101012),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101011),x101013),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f333(f333(f80(x101011),f333(f333(f80(x101011),f333(f106(x101011),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x101012)),x101013)),f333(f333(f258(x101011),f333(f333(f22(x101011),x101012),x101013)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.44 [10102]~P90(x101021)+E(f333(f333(f79(x101021),f333(f333(f79(x101021),f333(f333(f258(x101021),x101022),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101021),x101023),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f333(f333(f80(x101021),f333(f333(f80(x101021),f333(f106(x101021),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x101022)),x101023)),f333(f333(f258(x101021),f333(f333(f79(x101021),x101022),x101023)),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.44 [10200]~P27(x102001,x102002,x102003)+P1(f98(x102001,a870,f333(f333(f8(f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,a870))),f882(a871,f882(f882(x102001,f882(a872,a870)),a870)),f882(x102001,f882(a872,a870))),f333(f8(f882(f882(x102001,f882(a872,a870)),f882(x102001,a870)),f882(f882(x102001,f882(a872,a870)),a870),a871),f333(f8(f882(x102001,a870),a870,f882(x102001,f882(a872,a870))),f87(x102001)))),f333(f333(f8(f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,a870))),f882(x102001,f882(a872,a870))),f333(f8(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,a870)),a871),f333(f8(f882(x102001,f882(a872,a870)),f882(x102001,a870),f882(x102001,f882(a872,a870))),f333(f8(f882(a872,a870),a870,x102001),f87(a872))))),f333(f333(f7(f882(x102001,f882(a872,a870)),f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))))),f333(f333(f8(f882(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f882(f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f882(a871,f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))))),f882(x102001,f882(a872,a870))),f8(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),a871)),f333(f333(f8(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f882(x102001,f882(a872,a870))),f8(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870)))),f333(f333(f8(f882(x102001,f882(f882(a872,a870),f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f882(x102001,f882(a872,a870))),f18(x102001,f882(a872,a870),f882(a872,a870))),f333(f333(f8(f882(x102001,f882(a872,f882(a870,a870))),f882(x102001,f882(f882(a872,a870),f882(a872,a870))),f882(x102001,f882(a872,a870))),f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x102001),f18(a872,a870,a870))),f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x102001),f333(f8(a870,f882(a870,a870),a872),a336))))))),f333(f333(f8(f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,f882(a872,a870)))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),a871),f333(f8(f882(x102001,f882(a872,f882(a872,a870))),f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,a870))),f333(f8(f882(a872,f882(a872,a870)),f882(a872,a870),x102001),f333(f8(f882(a872,a870),a870,a872),f87(a872))))),f333(f333(f8(f882(f882(a872,a870),f882(a872,f882(a872,a870))),f882(f882(x102001,f882(a872,a870)),f882(x102001,f882(a872,f882(a872,a870)))),a871),f8(f882(a872,a870),f882(a872,f882(a872,a870)),x102001)),f333(f333(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))),f333(f333(f8(f882(a872,f882(a872,f882(a870,a870))),f882(a872,f882(f882(a872,a870),f882(a872,a870))),a871),f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870))),f333(f333(f8(f882(a872,f882(a872,a870)),f882(a872,f882(a872,f882(a870,a870))),a871),f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f333(f8(a870,f882(a870,a870),a872),a336))),f333(f333(f7(a871,a875,f882(a872,f882(a872,a870))),f333(f333(f8(f882(a872,f882(a875,f882(a872,a870))),f882(a875,f882(a872,f882(a872,a870))),a871),f7(a872,a875,f882(a872,a870))),a204)),x102002))))))))),x102003)) % 183.90/184.44 [10202]P27(x102021,x102022,x102023)+~P1(f98(x102021,a870,f333(f333(f8(f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,a870))),f882(a871,f882(f882(x102021,f882(a872,a870)),a870)),f882(x102021,f882(a872,a870))),f333(f8(f882(f882(x102021,f882(a872,a870)),f882(x102021,a870)),f882(f882(x102021,f882(a872,a870)),a870),a871),f333(f8(f882(x102021,a870),a870,f882(x102021,f882(a872,a870))),f87(x102021)))),f333(f333(f8(f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,a870))),f882(x102021,f882(a872,a870))),f333(f8(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,a870)),a871),f333(f8(f882(x102021,f882(a872,a870)),f882(x102021,a870),f882(x102021,f882(a872,a870))),f333(f8(f882(a872,a870),a870,x102021),f87(a872))))),f333(f333(f7(f882(x102021,f882(a872,a870)),f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))))),f333(f333(f8(f882(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f882(f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f882(a871,f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))))),f882(x102021,f882(a872,a870))),f8(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),a871)),f333(f333(f8(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f882(x102021,f882(a872,a870))),f8(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870)))),f333(f333(f8(f882(x102021,f882(f882(a872,a870),f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f882(x102021,f882(a872,a870))),f18(x102021,f882(a872,a870),f882(a872,a870))),f333(f333(f8(f882(x102021,f882(a872,f882(a870,a870))),f882(x102021,f882(f882(a872,a870),f882(a872,a870))),f882(x102021,f882(a872,a870))),f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x102021),f18(a872,a870,a870))),f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x102021),f333(f8(a870,f882(a870,a870),a872),a336))))))),f333(f333(f8(f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,f882(a872,a870)))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),a871),f333(f8(f882(x102021,f882(a872,f882(a872,a870))),f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,a870))),f333(f8(f882(a872,f882(a872,a870)),f882(a872,a870),x102021),f333(f8(f882(a872,a870),a870,a872),f87(a872))))),f333(f333(f8(f882(f882(a872,a870),f882(a872,f882(a872,a870))),f882(f882(x102021,f882(a872,a870)),f882(x102021,f882(a872,f882(a872,a870)))),a871),f8(f882(a872,a870),f882(a872,f882(a872,a870)),x102021)),f333(f333(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))),f333(f333(f8(f882(a872,f882(a872,f882(a870,a870))),f882(a872,f882(f882(a872,a870),f882(a872,a870))),a871),f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870))),f333(f333(f8(f882(a872,f882(a872,a870)),f882(a872,f882(a872,f882(a870,a870))),a871),f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f333(f8(a870,f882(a870,a870),a872),a336))),f333(f333(f7(a871,a875,f882(a872,f882(a872,a870))),f333(f333(f8(f882(a872,f882(a875,f882(a872,a870))),f882(a875,f882(a872,f882(a872,a870))),a871),f7(a872,a875,f882(a872,a870))),a204)),x102022))))))))),x102023)) % 183.90/184.44 [4683]E(x46831,x46832)+~E(f32(x46833,x46831),f32(x46834,x46832)) % 183.90/184.44 [4684]E(x46841,x46842)+~E(f32(x46841,x46843),f32(x46842,x46844)) % 183.90/184.44 [4685]E(x46851,x46852)+~E(f31(x46853,x46851),f31(x46854,x46852)) % 183.90/184.44 [4686]E(x46861,x46862)+~E(f31(x46861,x46863),f31(x46862,x46864)) % 183.90/184.44 [7755]P25(x77551,x77552,x77553,x77554)+~E(f692(x77554,x77553,x77552,x77551),f693(x77554,x77553,x77552,x77551)) % 183.90/184.44 [8054]P34(x80541,x80542,x80543,x80544,f116(x80542))+~E(x80544,f116(x80541)) % 183.90/184.44 [8055]P34(x80551,x80552,x80553,f116(x80551),x80554)+~E(x80554,f116(x80552)) % 183.90/184.44 [8270]~P25(x82701,f879(x82702),x82704,f186(x82701,x82702,x82704))+P25(x82701,f879(x82702),f187(x82701,x82702,x82703,x82704),f186(x82701,x82702,x82704)) % 183.90/184.44 [8485]~P25(x84851,f879(x84852),f187(x84851,x84852,x84854,x84853),f186(x84851,x84852,x84853))+P25(x84851,f879(x84852),x84853,f186(x84851,x84852,x84853)) % 183.90/184.44 [8600]~P34(x86002,x86003,x86004,x86001,f116(x86003))+E(x86001,f116(x86002)) % 183.90/184.44 [8601]~P34(x86013,x86012,x86014,f116(x86013),x86011)+E(x86011,f116(x86012)) % 183.90/184.44 [5058]~P17(x50583,x50581,x50584)+E(f333(f333(x50581,x50582),x50582),x50582) % 183.90/184.44 [5306]P1(f333(x53062,x53064))+E(f333(f137(x53061,x53062),f171(x53061,x53063,x53064)),f116(x53061)) % 183.90/184.44 [5342]~E(x53424,f196(f882(x53421,a870)))+E(f333(f312(x53421,x53422,x53423),x53424),f196(f882(x53422,a870))) % 183.90/184.44 [5582]~P1(f333(x55822,x55824))+E(f333(f137(x55821,x55822),f171(x55821,x55823,x55824)),f171(x55821,x55823,x55824)) % 183.90/184.44 [5611]~E(f333(f312(x56112,x56113,x56114),x56111),f196(f882(x56113,a870)))+E(x56111,f196(f882(x56112,a870))) % 183.90/184.44 [5893]~P106(x58932)+E(f333(f333(f149(x58931,x58932,x58933),x58934),f116(x58931)),f333(f333(f152(x58931),x58934),f116(x58931))) % 183.90/184.44 [5929]E(f333(x59291,x59292),f209(x59293))+P1(f333(f333(f335(x59294),x59292),f186(x59294,x59293,x59291))) % 183.90/184.44 [6247]~E(x62471,f196(f882(x62472,a870)))+~P1(f333(f62(x62472,x62473,x62471),x62474)) % 183.90/184.44 [6269]~P53(x62691,x62693,x62694,x62692)+P1(f333(f61(x62691),x62692)) % 183.90/184.44 [6270]~P53(x62701,x62703,x62702,x62704)+P1(f333(f61(x62701),x62702)) % 183.90/184.44 [6276]~P53(x62762,x62763,x62764,x62761)+~E(x62761,f196(f882(x62762,a870))) % 183.90/184.44 [6307]~P108(x63071)+E(f333(f333(f104(f882(x63071,a870)),f333(f303(x63071,x63072),x63073)),f304(x63071,x63073,x63074)),f196(f882(x63071,a870))) % 183.90/184.44 [6334]~P1(f333(f333(x63343,x63344),x63342))+P1(f333(f333(f335(x63341),x63342),f294(x63341,x63343,x63344))) % 183.90/184.44 [6335]~P1(f333(f333(x63353,x63354),x63352))+P1(f333(f333(f335(x63351),x63352),f295(x63351,x63353,x63354))) % 183.90/184.44 [6336]~P1(f333(f333(x63363,x63362),x63364))+P1(f333(f333(f335(x63361),x63362),f296(x63361,x63363,x63364))) % 183.90/184.44 [6337]~P1(f333(f333(x63373,x63372),x63374))+P1(f333(f333(f335(x63371),x63372),f299(x63371,x63373,x63374))) % 183.90/184.44 [6475]~P108(x64751)+E(f333(f333(f104(f882(x64751,a870)),f307(x64751,x64752,x64753)),f304(x64751,x64753,x64754)),f196(f882(x64751,a870))) % 183.90/184.44 [6476]~P108(x64761)+E(f333(f333(f104(f882(x64761,a870)),f306(x64761,x64762,x64763)),f307(x64761,x64763,x64764)),f196(f882(x64761,a870))) % 183.90/184.44 [6477]~P108(x64771)+E(f333(f333(f104(f882(x64771,a870)),f306(x64771,x64772,x64773)),f306(x64771,x64773,x64774)),f196(f882(x64771,a870))) % 183.90/184.44 [6478]~P108(x64781)+E(f333(f333(f104(f882(x64781,a870)),f304(x64781,x64782,x64783)),f307(x64781,x64783,x64784)),f196(f882(x64781,a870))) % 183.90/184.44 [6479]~P108(x64791)+E(f333(f333(f104(f882(x64791,a870)),f304(x64791,x64792,x64793)),f306(x64791,x64793,x64794)),f196(f882(x64791,a870))) % 183.90/184.44 [6516]P1(f333(f333(x65161,x65162),f563(x65162,x65161)))+~P1(f333(f262(x65163,x65164,x65161),x65162)) % 183.90/184.44 [6565]~E(f333(x65651,x65652),f209(x65653))+~P1(f333(f333(f335(x65654),x65652),f186(x65654,x65653,x65651))) % 183.90/184.44 [6594]~P106(x65942)+E(f333(f174(x65941),f151(x65941,x65942,x65943,x65944)),f333(f174(x65941),x65944)) % 183.90/184.44 [6646]~P141(x66461)+E(f198(x66461,x66462,f333(a115,x66463),x66464),f198(x66461,x66462,x66463,f333(x66462,x66464))) % 183.90/184.44 [6706]~P1(f333(f333(f335(x67064),x67063),f294(x67064,x67061,x67062)))+P1(f333(f333(x67061,x67062),x67063)) % 183.90/184.44 [6707]~P1(f333(f333(f335(x67074),x67073),f295(x67074,x67071,x67072)))+P1(f333(f333(x67071,x67072),x67073)) % 183.90/184.44 [6708]~P1(f333(f333(f335(x67084),x67082),f296(x67084,x67081,x67083)))+P1(f333(f333(x67081,x67082),x67083)) % 183.90/184.44 [6709]~P1(f333(f333(f335(x67094),x67092),f299(x67094,x67091,x67093)))+P1(f333(f333(x67091,x67092),x67093)) % 183.90/184.44 [6786]E(f333(f37(f880(x67861,x67862)),f320(x67861,x67862,x67863,x67864)),f2(a875))+P1(f333(f61(x67862),x67864)) % 183.90/184.44 [6787]E(f333(f37(f880(x67871,x67872)),f320(x67871,x67872,x67873,x67874)),f2(a875))+P1(f333(f61(x67871),x67873)) % 183.90/184.44 [6990]~P15(x69904,x69901,x69902)+E(f333(f72(x69901,x69901,x69901,f333(x69902,x69903)),f333(x69902,x69903)),f333(x69902,x69903)) % 183.90/184.44 [7794]~P1(f333(x77941,x77944))+P1(f333(x77941,f95(x77942,a875,x77943,x77941))) % 183.90/184.44 [7878]~E(x78782,x78783)+P1(f333(f333(f335(f881(x78781,x78781)),f333(f333(f268(x78781,x78781),x78782),x78783)),f309(x78781,x78784))) % 183.90/184.44 [7907]~P25(x79071,x79072,x79073,f256(f882(x79071,a870)))+E(f333(f76(x79071,x79072,f256(f882(x79071,a870)),x79073),f333(x79073,x79074)),x79074) % 183.90/184.44 [8000]~P1(f333(f333(f335(f876(x80001)),f333(f333(f152(x80001),x80004),x80002)),f162(x80001,x80003)))+P1(f333(f333(f335(f876(x80001)),x80002),f162(x80001,x80003))) % 183.90/184.44 [8001]~P1(f333(f333(f335(f876(x80011)),f333(f333(f135(x80011),x80014),x80012)),f162(x80011,x80013)))+P1(f333(f333(f335(f876(x80011)),x80012),f162(x80011,x80013))) % 183.90/184.44 [8002]~P1(f333(f333(f335(f876(x80021)),f333(f333(f135(x80021),x80022),x80024)),f162(x80021,x80023)))+P1(f333(f333(f335(f876(x80021)),x80022),f162(x80021,x80023))) % 183.90/184.44 [8018]~P106(x80181)+P14(x80181,f333(f333(f155(x80182,x80181),x80183),f151(x80182,x80181,x80183,x80184))) % 183.90/184.44 [8116]P25(x81164,x81163,x81161,x81162)+E(f333(x81161,f692(x81162,x81161,x81163,x81164)),f333(x81161,f693(x81162,x81161,x81163,x81164))) % 183.90/184.44 [8129]E(f187(x81291,x81292,x81293,x81294),f187(x81291,x81292,x81294,x81293))+~E(f333(f333(f104(f882(x81291,a870)),f186(x81291,x81292,x81293)),f186(x81291,x81292,x81294)),f196(f882(x81291,a870))) % 183.90/184.44 [8233]~P25(x82332,x82331,x82334,x82333)+P25(x82331,x82332,f76(x82332,x82331,x82333,x82334),f333(f312(x82332,x82331,x82334),x82333)) % 183.90/184.44 [8369]P37(f881(x83692,x83694),f285(x83692,x83694,x83691,x83693))+P1(f333(x83691,f565(x83692,x83693,x83694,x83691))) % 183.90/184.44 [8492]E(x84921,x84922)+~P1(f333(f333(f335(f881(x84923,x84923)),f333(f333(f268(x84923,x84923),x84921),x84922)),f265(x84923,x84924))) % 183.90/184.44 [8556]~P1(f333(f61(f880(x85563,x85561)),f320(x85563,x85561,x85564,x85562)))+P1(f333(f61(x85561),x85562)) % 183.90/184.44 [8557]~P1(f333(f61(f880(x85571,x85573)),f320(x85571,x85573,x85572,x85574)))+P1(f333(f61(x85571),x85572)) % 183.90/184.44 [8733]P37(f881(x87331,x87332),f285(x87331,x87332,x87333,x87334))+~P37(x87332,f333(x87334,f565(x87331,x87334,x87332,x87333))) % 183.90/184.44 [9295]E(f333(f333(f160(x92951,x92952),f688(x92953,x92954,x92952,x92951)),f689(x92953,x92954,x92952,x92951)),x92954)+~P1(f333(f333(f335(f881(f876(x92951),f876(x92951))),f333(f333(f268(f876(x92951),f876(x92951)),x92952),x92954)),f158(x92951,x92953))) % 183.90/184.44 [9296]~P1(f333(x92963,x92964))+P1(f333(f333(f247(a875),f333(x92961,f95(x92962,a875,x92961,x92963))),f333(x92961,x92964))) % 183.90/184.44 [9302]~P1(f333(f333(f335(f881(f876(x93021),f876(x93021))),f333(f333(f268(f876(x93021),f876(x93021)),x93022),x93023)),f146(x93021,x93024)))+P1(f333(f333(f335(f881(f876(x93021),f876(x93021))),f333(f333(f268(f876(x93021),f876(x93021)),x93022),x93023)),f148(x93021,x93024))) % 183.90/184.44 [9408]P1(f333(f61(x94081),x94082))+~P1(f333(f333(f335(f881(f882(x94081,a870),f882(x94081,a870))),f333(f333(f268(f882(x94081,a870),f882(x94081,a870)),x94083),x94082)),f325(x94081,x94084))) % 183.90/184.44 [9409]P1(f333(f61(x94091),x94092))+~P1(f333(f333(f335(f881(f882(x94091,a870),f882(x94091,a870))),f333(f333(f268(f882(x94091,a870),f882(x94091,a870)),x94092),x94093)),f325(x94091,x94094))) % 183.90/184.44 [9412]~E(x94121,f196(f882(x94122,a870)))+~P1(f333(f333(f335(f881(f882(x94122,a870),f882(x94122,a870))),f333(f333(f268(f882(x94122,a870),f882(x94122,a870)),x94123),x94121)),f325(x94122,x94124))) % 183.90/184.44 [10047]P12(x100471,x100472,x100473,x100474)+~P1(f333(f333(f272(x100471,x100471,a870),f333(f333(f7(x100471,f882(x100471,x100472),f882(x100471,a870)),f333(f333(f8(f882(x100472,a870),f882(f882(x100471,x100472),f882(x100471,a870)),x100471),f8(x100472,a870,x100471)),f333(f333(f8(x100472,f882(x100472,a870),x100471),a330),x100474))),x100474)),f597(x100474,x100473,x100472,x100471))) % 183.90/184.44 [4960]~E(x49602,f116(x49601))+E(f333(f333(f160(x49601,x49602),x49603),x49604),f116(x49601)) % 183.90/184.44 [4961]~E(x49614,f116(x49611))+E(f333(f333(f155(x49611,x49612),x49613),x49614),f116(x49612)) % 183.90/184.44 [4962]~E(x49624,f209(x49621))+E(f333(f333(f210(x49621,x49622),x49623),x49624),f209(x49622)) % 183.90/184.44 [5190]E(x51901,f116(x51902))+~E(f333(f333(f155(x51902,x51903),x51904),x51901),f116(x51903)) % 183.90/184.44 [5191]E(x51911,f209(x51912))+~E(f333(f333(f210(x51912,x51913),x51914),x51911),f209(x51913)) % 183.90/184.44 [5192]E(x51921,f116(x51922))+~E(f333(f333(f160(x51922,x51921),x51923),x51924),f116(x51922)) % 183.90/184.44 [5224]E(x52241,x52242)+~E(f333(f333(f135(x52243),x52244),x52241),f333(f333(f135(x52243),x52244),x52242)) % 183.90/184.44 [5225]E(x52251,x52252)+~E(f333(f333(f135(x52253),x52251),x52254),f333(f333(f135(x52253),x52252),x52254)) % 183.90/184.44 [5379]P1(f333(x53793,x53792))+E(f172(x53791,x53792,f333(f137(x53791,x53793),x53794)),f333(f137(x53791,x53793),x53794)) % 183.90/184.44 [5382]~P1(f333(x53822,x53823))+P33(x53821,x53822,f333(f333(f152(x53821),x53823),x53824)) % 183.90/184.44 [5391]E(x53911,x53912)+~E(f140(a875,f333(f303(a875,x53911),x53913)),f333(f333(f152(a875),x53912),x53914)) % 183.90/184.44 [5439]~P26(x54392,x54393)+P26(x54391,f333(f333(f73(x54392,x54391),x54393),x54394)) % 183.90/184.44 [5440]~P37(x54402,x54403)+P37(x54401,f333(f333(f289(x54402,x54401),x54403),x54404)) % 183.90/184.44 [5566]~P33(x55661,x55662,x55664)+P33(x55661,x55662,f333(f333(f152(x55661),x55663),x55664)) % 183.90/184.44 [5567]~P33(x55671,x55672,x55674)+P33(x55671,x55672,f333(f333(f135(x55671),x55673),x55674)) % 183.90/184.44 [5568]~P33(x55681,x55682,x55683)+P33(x55681,x55682,f333(f333(f135(x55681),x55683),x55684)) % 183.90/184.44 [5654]~E(x56541,f116(x56542))+~E(f333(f333(f135(x56542),x56543),f333(f333(f152(x56542),x56544),f116(x56542))),x56541) % 183.90/184.44 [5679]~P31(x56793,x56791,f333(f333(f152(x56793),x56792),x56794))+P1(f333(x56791,x56792)) % 183.90/184.44 [5689]E(f117(x56891,x56892),x56893)+~E(f333(f333(f135(x56891),x56893),f333(f333(f152(x56891),x56894),f116(x56891))),x56892) % 183.90/184.44 [5690]E(f145(x56901,x56902),x56903)+~E(f333(f333(f135(x56901),x56904),f333(f333(f152(x56901),x56903),f116(x56901))),x56902) % 183.90/184.44 [5798]~E(f140(a875,f333(f303(a875,x57981),x57982)),f333(f333(f152(a875),x57983),x57984))+P1(f333(f333(f248(a875),x57981),x57982)) % 183.90/184.44 [5806]P31(x58061,x58062,x58063)+~P31(x58061,x58062,f333(f333(f152(x58061),x58064),x58063)) % 183.90/184.44 [5807]P31(x58071,x58072,x58073)+~P31(x58071,x58072,f333(f333(f135(x58071),x58074),x58073)) % 183.90/184.44 [5808]P31(x58081,x58082,x58083)+~P31(x58081,x58082,f333(f333(f135(x58081),x58083),x58084)) % 183.90/184.44 [5996]E(x59961,f333(f333(f135(x59962),f333(f170(x59962),x59963)),f333(f333(f152(x59962),x59964),f116(x59962))))+~E(f333(f170(x59962),x59961),f333(f333(f152(x59962),x59964),x59963)) % 183.90/184.44 [6167]~P108(x61671)+E(f333(f333(f104(f882(x61671,a870)),f333(f303(x61671,x61672),x61673)),f333(f303(x61671,x61673),x61674)),f196(f882(x61671,a870))) % 183.90/184.44 [6178]E(f333(f333(f166(x61781),f171(x61781,x61782,x61783)),x61784),x61783)+~P1(f333(f333(f248(a875),x61784),x61782)) % 183.90/184.44 [6205]~P66(x62051)+E(f333(f167(x62051),f333(f333(f155(a1,x62051),x62052),f181(x62053,x62054))),f333(f333(f6(a1,x62051),x62052),f333(f174(a1),f181(x62053,x62054)))) % 183.90/184.44 [6206]~P66(x62061)+E(f333(f333(f6(a1,x62061),x62062),f333(f174(a1),f181(x62063,x62064))),f333(f167(x62061),f333(f333(f155(a1,x62061),x62062),f181(x62063,x62064)))) % 183.90/184.44 [6347]~E(x63472,f333(f333(f135(x63471),f333(f170(x63471),x63474)),f333(f333(f152(x63471),x63473),f116(x63471))))+E(f333(f170(x63471),x63472),f333(f333(f152(x63471),x63473),x63474)) % 183.90/184.44 [6363]~P19(x63632,x63633,x63634,x63631)+E(f333(x63631,f196(f882(x63632,a870))),f33(x63633)) % 183.90/184.44 [6389]~P108(x63891)+E(f333(f333(f104(f882(x63891,a870)),f307(x63891,x63892,x63893)),f333(f303(x63891,x63893),x63894)),f196(f882(x63891,a870))) % 183.90/184.44 [6595]E(x65951,f196(f882(x65952,a870)))+~E(f320(x65953,x65952,x65954,x65951),f196(f882(f880(x65953,x65952),a870))) % 183.90/184.44 [6596]E(x65961,f196(f882(x65962,a870)))+~E(f320(x65962,x65963,x65961,x65964),f196(f882(f880(x65962,x65963),a870))) % 183.90/184.44 [6665]~P106(x66652)+E(f333(f197(f876(x66651)),f151(x66651,x66652,x66653,x66654)),f333(f197(f876(x66651)),x66654)) % 183.90/184.44 [6677]~P1(f333(f263(x66773,x66774,x66771),x66772))+P1(f333(f333(x66771,f564(x66772,x66771)),x66772)) % 183.90/184.44 [6717]~P1(f333(f61(x67172),x67174))+P1(f333(f61(x67171),f333(f312(x67172,x67171,x67173),x67174))) % 183.90/184.44 [6950]~P25(x69502,x69501,x69503,x69504)+E(f333(f37(x69501),f333(f312(x69502,x69501,x69503),x69504)),f333(f37(x69502),x69504)) % 183.90/184.44 [6969]E(f333(f312(x69691,x69692,x69693),f333(f313(x69691,x69692,x69693),x69694)),x69694)+~E(f333(f312(x69691,x69692,x69693),f256(f882(x69691,a870))),f256(f882(x69692,a870))) % 183.90/184.44 [7379]~P25(x73791,x73792,x73793,f256(f882(x73791,a870)))+E(f333(f313(x73791,x73792,x73793),f333(f312(x73791,x73792,x73793),x73794)),x73794) % 183.90/184.44 [7667]E(x76671,x76672)+~P1(f333(f333(f335(x76673),x76671),f333(f174(x76673),f171(x76673,x76674,x76672)))) % 183.90/184.44 [7677]~E(x76771,f2(a875))+~P1(f333(f333(f335(x76772),x76773),f333(f174(x76772),f171(x76772,x76771,x76774)))) % 183.90/184.44 [7714]P1(f333(x77141,x77142))+~P1(f333(f333(f335(x77143),x77142),f333(f174(x77143),f179(x77143,x77141,x77144)))) % 183.90/184.44 [7825]~P1(f333(f333(f335(f876(x78251)),f333(f333(f152(x78251),x78252),x78254)),f162(x78251,x78253)))+P1(f333(f333(f335(x78251),x78252),x78253)) % 183.90/184.44 [7954]~P1(f333(f333(f335(x79541),x79542),f333(f174(x79541),f178(x79541,x79543,x79544))))+P1(f333(f333(f335(x79541),x79542),f333(f174(x79541),x79543))) % 183.90/184.44 [7955]~P1(f333(f333(f335(x79551),x79552),f333(f174(x79551),f172(x79551,x79554,x79553))))+P1(f333(f333(f335(x79551),x79552),f333(f174(x79551),x79553))) % 183.90/184.44 [7956]~P1(f333(f333(f335(x79561),x79562),f333(f174(x79561),f179(x79561,x79564,x79563))))+P1(f333(f333(f335(x79561),x79562),f333(f174(x79561),x79563))) % 183.90/184.44 [7966]E(f333(f197(f876(x79661)),x79662),x79663)+~P1(f333(f333(f335(f876(x79661)),x79662),f333(f174(f876(x79661)),f54(x79661,x79663,x79664)))) % 183.90/184.44 [8066]P1(f333(x80663,x80662))+E(f333(f137(x80661,f333(f333(f8(a870,a870,x80661),a328),f333(a330,x80662))),f333(f137(x80661,x80663),x80664)),f333(f137(x80661,x80663),x80664)) % 183.90/184.44 [8182]E(f333(f333(f166(x81821),f179(x81821,x81822,x81823)),x81824),f333(f333(f166(x81821),x81823),x81824))+~P1(f333(f333(f248(a875),x81824),f333(f197(f876(x81821)),f179(x81821,x81822,x81823)))) % 183.90/184.44 [8268]~P66(x82681)+E(f333(f333(f6(a875,x82681),f333(f333(f8(a875,x82681,a875),x82682),a115)),f333(f303(a875,x82683),x82684)),f333(f333(f6(a875,x82681),x82682),f333(f303(a875,f333(a115,x82683)),f333(a115,x82684)))) % 183.90/184.44 [8277]~P66(x82771)+E(f333(f333(f6(a875,x82771),f333(f333(f8(a875,x82771,a875),x82772),a115)),f304(a875,x82773,x82774)),f333(f333(f6(a875,x82771),x82772),f304(a875,f333(a115,x82773),f333(a115,x82774)))) % 183.90/184.44 [8407]~P25(x84071,x84073,x84074,f256(f882(x84071,a870)))+P25(x84071,f882(x84072,x84073),f333(f333(f8(x84073,f882(x84072,x84073),x84071),f16(x84073,x84072)),x84074),f256(f882(x84071,a870))) % 183.90/184.44 [8500]~P25(x85002,x85001,x85004,x85003)+E(f333(f312(x85001,x85002,f76(x85002,x85001,x85003,x85004)),f333(f312(x85002,x85001,x85004),x85003)),x85003) % 183.90/184.44 [8558]~P1(f333(f333(f335(f881(x85581,x85581)),f333(f333(f268(x85581,x85581),x85582),x85584)),f265(x85581,x85583)))+P1(f333(f333(f335(x85581),x85582),x85583)) % 183.90/184.44 [8646]E(f333(f333(f333(f71(x86461,f879(x86462)),f333(f16(f879(x86462),x86461),f209(x86462))),x86463),f333(f240(x86462),f721(x86463,x86464,x86462,x86461))),x86464)+~E(f186(x86461,x86462,x86464),f333(f333(f311(x86461),x86463),f196(f882(x86461,a870)))) % 183.90/184.44 [8768]~E(f333(f333(f6(x87681,a875),x87684),x87683),f333(a115,x87682))+P1(f333(f333(f335(x87681),f519(x87682,x87683,x87684,x87681)),x87683)) % 183.90/184.44 [8788]~E(f333(f333(f6(x87884,a875),x87881),x87883),f333(a115,x87882))+P1(f333(f333(f248(a875),f2(a875)),f333(x87881,f519(x87882,x87883,x87881,x87884)))) % 183.90/184.44 [8799]~P1(f333(f61(x87992),x87994))+P1(f333(f333(f247(a875),f333(f37(x87991),f333(f312(x87992,x87991,x87993),x87994))),f333(f37(x87992),x87994))) % 183.90/184.44 [8800]E(f333(f333(f268(x88001,x88002),f659(x88003,x88004,x88002,x88001)),f660(x88003,x88004,x88002,x88001)),x88004)+~P1(f333(f333(f335(f881(x88001,x88002)),x88004),f333(f288(x88002,x88001),x88003))) % 183.90/184.44 [8809]P25(x88091,x88092,x88093,x88094)+P1(f333(f333(f335(x88091),f692(x88094,x88093,x88092,x88091)),x88094)) % 183.90/184.44 [8810]P25(x88101,x88102,x88103,x88104)+P1(f333(f333(f335(x88101),f693(x88104,x88103,x88102,x88101)),x88104)) % 183.90/184.44 [8871]P12(x88711,x88712,x88713,x88714)+P1(f333(f333(f335(f881(x88711,x88711)),f597(x88714,x88713,x88712,x88711)),x88713)) % 183.90/184.44 [8935]P1(f333(x89351,x89352))+~P1(f333(x89351,f333(f333(f268(x89353,x89354),f539(x89354,x89353,x89351)),f540(x89354,x89353,x89351)))) % 183.90/184.44 [8952]E(f333(f197(f876(x89521)),x89522),f333(f197(f876(x89521)),x89523))+~P1(f333(f333(f335(f881(f876(x89521),f876(x89521))),f333(f333(f268(f876(x89521),f876(x89521)),x89522),x89523)),f146(x89521,x89524))) % 183.90/184.44 [8953]E(f333(f197(f876(x89531)),x89532),f333(f197(f876(x89531)),x89533))+~P1(f333(f333(f335(f881(f876(x89531),f876(x89531))),f333(f333(f268(f876(x89531),f876(x89531)),x89532),x89533)),f158(x89531,x89534))) % 183.90/184.44 [8956]E(f333(f197(f876(x89561)),x89562),f333(f197(f876(x89561)),x89563))+~P1(f333(f333(f335(f881(f876(x89561),f876(x89561))),f333(f333(f268(f876(x89561),f876(x89561)),x89562),x89563)),f159(x89561,x89564))) % 183.90/184.44 [9030]P1(f333(f333(f247(a875),f156(x90301,x90302,x90303)),f156(x90301,x90304,x90303)))+P1(f333(f333(f335(x90301),f687(x90304,x90302,x90303,x90301)),f333(f174(x90301),x90303))) % 183.90/184.44 [9033]E(f333(f197(f876(x90331)),x90332),f333(f197(f876(x90331)),x90333))+~P1(f333(f333(f335(f881(f876(x90331),f876(x90331))),f333(f333(f268(f876(x90331),f876(x90331)),x90332),x90333)),f309(f876(x90331),f158(x90331,x90334)))) % 183.90/184.44 [9267]~P25(x92671,x92672,x92673,x92674)+~P1(f333(f333(f248(a875),f333(f37(x92672),f333(f312(x92671,x92672,x92673),x92674))),f333(f37(x92671),x92674))) % 183.90/184.44 [9313]~P1(f333(f333(f335(f881(f876(x93131),f876(x93131))),f333(f333(f268(f876(x93131),f876(x93131)),x93132),x93133)),f158(x93131,x93134)))+P1(f333(f333(f335(f881(f876(x93131),f876(x93131))),f333(f333(f268(f876(x93131),f876(x93131)),x93132),x93133)),f159(x93131,f309(x93131,x93134)))) % 183.90/184.44 [9317]~P1(f333(f333(f335(f881(f876(x93171),f876(x93171))),f333(f333(f268(f876(x93171),f876(x93171)),x93172),x93173)),f159(x93171,x93174)))+P1(f333(f333(f335(f881(f876(x93171),f876(x93171))),f333(f333(f268(f876(x93171),f876(x93171)),x93172),x93173)),f309(f876(x93171),f158(x93171,x93174)))) % 183.90/184.44 [9334]P1(f333(f333(f335(f881(x93341,x93341)),f333(f333(f268(x93341,x93341),x93342),x93343)),f309(x93341,x93344)))+~P1(f333(f333(f335(f881(x93341,x93341)),f333(f333(f268(x93341,x93341),x93342),x93343)),f333(f333(f290(x93341,x93341,x93341),x93344),f309(x93341,x93344)))) % 183.90/184.44 [9516]E(f333(f333(f135(x95161),f701(x95162,x95163,x95164,x95161)),f333(f333(f152(x95161),f702(x95162,x95163,x95164,x95161)),f704(x95162,x95163,x95164,x95161))),x95164)+~P1(f333(f333(f335(f881(f876(x95161),f876(x95161))),f333(f333(f268(f876(x95161),f876(x95161)),x95164),x95163)),f158(x95161,x95162))) % 183.90/184.44 [9517]E(f333(f333(f135(x95171),f701(x95172,x95173,x95174,x95171)),f333(f333(f152(x95171),f703(x95172,x95173,x95174,x95171)),f704(x95172,x95173,x95174,x95171))),x95173)+~P1(f333(f333(f335(f881(f876(x95171),f876(x95171))),f333(f333(f268(f876(x95171),f876(x95171)),x95174),x95173)),f158(x95171,x95172))) % 183.90/184.44 [9593]P1(f333(f333(f335(f881(x95931,x95931)),f333(f333(f268(x95931,x95931),x95932),f650(x95933,x95934,x95932,x95931))),f309(x95931,x95933)))+~P1(f333(f333(f335(f881(x95931,x95931)),f333(f333(f268(x95931,x95931),x95932),x95934)),f333(f333(f290(x95931,x95931,x95931),x95933),f309(x95931,x95933)))) % 183.90/184.44 [9662]P1(f333(f333(f247(a875),f156(x96621,x96622,x96623)),f156(x96621,x96624,x96623)))+~P1(f333(f333(f248(a875),f333(x96622,f687(x96624,x96622,x96623,x96621))),f333(x96624,f687(x96624,x96622,x96623,x96621)))) % 183.90/184.44 [9729]P1(f333(f333(f335(f881(x97291,x97291)),f333(f333(f268(x97291,x97291),f642(x97292,x97293,x97294,x97291)),x97293)),f309(x97291,x97292)))+~P1(f333(f333(f335(f881(x97291,x97291)),f333(f333(f268(x97291,x97291),x97294),x97293)),f333(f333(f290(x97291,x97291,x97291),x97292),f309(x97291,x97292)))) % 183.90/184.44 [5207]~E(x52072,x52073)+E(f172(x52071,x52072,f333(f333(f152(x52071),x52073),x52074)),x52074) % 183.90/184.44 [5334]P1(f333(x53342,x53343))+E(f179(x53341,x53342,f333(f333(f152(x53341),x53343),x53344)),f116(x53341)) % 183.90/184.44 [5403]~P86(x54032)+E(f333(f333(f78(f882(x54031,x54032)),x54033),x54034),f333(f78(x54032),f333(x54033,x54034))) % 183.90/184.44 [5415]~E(x54152,f2(a875))+E(f333(f333(f139(x54151),x54152),f333(f333(f152(x54151),x54153),x54154)),f333(f333(f152(x54151),x54153),x54154)) % 183.90/184.44 [5416]P1(f333(x54162,x54163))+E(f333(f137(x54161,x54162),f333(f333(f152(x54161),x54163),x54164)),f333(f137(x54161,x54162),x54164)) % 183.90/184.44 [5549]~E(x55492,x55494)+P1(f333(f333(f333(f311(x55491),x55492),x55493),x55494)) % 183.90/184.44 [5557]E(x55571,f116(x55572))+E(f145(x55573,f333(f333(f155(x55572,x55573),x55574),x55571)),f333(x55574,f145(x55572,x55571))) % 183.90/184.44 [5571]~E(x55711,f63(x55712,x55714))+E(f333(x55711,f333(f333(f311(x55712),x55713),f196(f882(x55712,a870)))),x55713) % 183.90/184.44 [5606]E(x56061,f116(x56062))+E(f333(f142(x56063),f333(f333(f155(x56062,x56063),x56064),x56061)),f333(x56064,f333(f142(x56062),x56061))) % 183.90/184.44 [5709]~P1(f333(x57093,x57094))+P1(f333(f333(f333(f311(x57091),x57092),x57093),x57094)) % 183.90/184.44 [5823]~P18(x58232,x58234,x58231)+E(f333(x58231,f333(f333(f311(x58232),x58233),f196(f882(x58232,a870)))),x58233) % 183.90/184.44 [5847]~E(x58472,x58473)+P1(f333(f333(f335(x58471),x58472),f333(f333(f311(x58471),x58473),x58474))) % 183.90/184.44 [5851]~P62(x58511)+E(f333(f333(f113(x58511),x58512),f333(f333(f113(x58511),x58513),x58514)),f333(f333(f113(x58511),x58513),f333(f333(f113(x58511),x58512),x58514))) % 183.90/184.44 [5853]~P98(x58531)+E(f333(f333(f113(x58531),x58532),f333(f333(f113(x58531),x58533),x58534)),f333(f333(f113(x58531),x58533),f333(f333(f113(x58531),x58532),x58534))) % 183.90/184.44 [5854]~P62(x58541)+E(f333(f333(f104(x58541),x58542),f333(f333(f104(x58541),x58543),x58544)),f333(f333(f104(x58541),x58543),f333(f333(f104(x58541),x58542),x58544))) % 183.90/184.44 [5856]~P99(x58561)+E(f333(f333(f104(x58561),x58562),f333(f333(f104(x58561),x58563),x58564)),f333(f333(f104(x58561),x58563),f333(f333(f104(x58561),x58562),x58564))) % 183.90/184.44 [5857]~P109(x58571)+E(f333(f333(f79(x58571),x58572),f333(f333(f79(x58571),x58573),x58574)),f333(f333(f79(x58571),x58573),f333(f333(f79(x58571),x58572),x58574))) % 183.90/184.44 [5858]~P109(x58581)+E(f333(f333(f80(x58581),x58582),f333(f333(f80(x58581),x58583),x58584)),f333(f333(f80(x58581),x58583),f333(f333(f80(x58581),x58582),x58584))) % 183.90/184.44 [5860]~P106(x58601)+E(f333(f333(f245(x58601),x58602),f333(f333(f245(x58601),x58603),x58604)),f333(f333(f245(x58601),x58603),f333(f333(f245(x58601),x58602),x58604))) % 183.90/184.44 [5862]~P106(x58621)+E(f333(f333(f246(x58621),x58622),f333(f333(f246(x58621),x58623),x58624)),f333(f333(f246(x58621),x58623),f333(f333(f246(x58621),x58622),x58624))) % 183.90/184.44 [5867]E(x58671,x58672)+E(f172(x58673,x58671,f333(f333(f152(x58673),x58672),x58674)),f333(f333(f152(x58673),x58672),f172(x58673,x58671,x58674))) % 183.90/184.44 [5880]~P1(f333(x58802,x58803))+E(f333(f137(x58801,x58802),f333(f333(f152(x58801),x58803),x58804)),f333(f333(f152(x58801),x58803),f333(f137(x58801,x58802),x58804))) % 183.90/184.44 [6016]~P1(f333(x60162,x60163))+E(f179(x60161,x60162,f333(f333(f152(x60161),x60163),x60164)),f333(f333(f152(x60161),x60163),f179(x60161,x60162,x60164))) % 183.90/184.44 [6067]P24(x60671,x60672,x60673)+~P24(x60671,x60672,f333(f333(f311(f874(x60671)),x60674),x60673)) % 183.90/184.44 [6080]E(x60801,f196(f882(x60802,a870)))+E(f333(f333(f41(x60802,f882(x60803,a870)),x60801),f333(f16(f882(x60803,a870),x60802),x60804)),x60804) % 183.90/184.44 [6081]E(x60811,f196(f882(x60812,a870)))+E(f333(f333(f42(x60812,f882(x60813,a870)),x60811),f333(f16(f882(x60813,a870),x60812),x60814)),x60814) % 183.90/184.44 [6090]~E(x60904,f196(f882(x60902,a870)))+E(f333(f333(f270(x60901,x60902),x60903),f333(f16(f882(x60902,a870),x60901),x60904)),f196(f882(f881(x60901,x60902),a870))) % 183.90/184.44 [6091]~E(x60913,f196(f882(x60911,a870)))+E(f333(f333(f270(x60911,x60912),x60913),f333(f16(f882(x60912,a870),x60911),x60914)),f196(f882(f881(x60911,x60912),a870))) % 183.90/184.44 [6137]E(x61371,f2(a875))+E(f333(f333(f139(x61372),x61371),f333(f333(f152(x61372),x61373),x61374)),f333(f333(f139(x61372),f333(f333(f22(a875),x61371),f77(a875))),x61374)) % 183.90/184.44 [6161]E(x61611,f196(f882(x61612,a870)))+E(f333(f312(x61612,x61613,f333(f16(x61613,x61612),x61614)),x61611),f333(f333(f311(x61613),x61614),f196(f882(x61613,a870)))) % 183.90/184.44 [6164]E(f333(f313(x61641,x61642,f333(f16(x61642,x61641),x61643)),x61644),f196(f882(x61641,a870)))+P1(f333(f333(f335(x61642),x61643),x61644)) % 183.90/184.44 [6231]~E(x62313,f196(f882(x62311,a870)))+E(f333(f333(f41(x62311,f882(x62312,a870)),x62313),f333(f16(f882(x62312,a870),x62311),x62314)),f196(f882(x62312,a870))) % 183.90/184.44 [6232]~E(x62323,f196(f882(x62321,a870)))+E(f333(f333(f42(x62321,f882(x62322,a870)),x62323),f333(f16(f882(x62322,a870),x62321),x62324)),f256(f882(x62322,a870))) % 183.90/184.44 [6234]~P55(x62341)+E(f44(x62341,f333(f333(f80(x62341),x62342),x62343),f333(f333(f80(x62341),x62342),x62344)),f333(f333(f80(x62341),x62342),f44(x62341,x62343,x62344))) % 183.90/184.44 [6399]E(f333(f313(x63991,x63992,f333(f16(x63992,x63991),x63993)),x63994),f256(f882(x63991,a870)))+~P1(f333(f333(f335(x63992),x63993),x63994)) % 183.90/184.44 [6422]~P1(f333(f333(f335(x64221),x64222),x64224))+P1(f333(f333(f335(x64221),x64222),f333(f333(f311(x64221),x64223),x64224))) % 183.90/184.44 [6427]P1(f333(x64271,x64272))+~P1(f333(f161(x64273,x64271),f333(f333(f152(x64273),x64272),x64274))) % 183.90/184.44 [6436]~E(x64363,f333(f333(f22(a875),f333(f197(f876(x64361)),x64362)),f77(a875)))+E(f117(x64361,f333(f333(f160(x64361,x64362),x64363),x64364)),f117(x64361,x64362)) % 183.90/184.44 [6454]~P106(x64541)+E(f333(f333(f104(f882(x64541,a870)),f333(f302(x64541),x64542)),f304(x64541,x64543,x64544)),f304(x64541,x64543,f333(f333(f245(x64541),x64542),x64544))) % 183.90/184.44 [6455]~P106(x64551)+E(f333(f333(f104(f882(x64551,a870)),f333(f255(x64551),x64552)),f304(x64551,x64553,x64554)),f304(x64551,f333(f333(f246(x64551),x64552),x64553),x64554)) % 183.90/184.44 [6470]E(f333(f333(f104(f882(x64701,a870)),x64702),f333(f333(f311(x64701),x64703),x64704)),f333(f333(f104(f882(x64701,a870)),x64702),x64704))+P1(f333(f333(f335(x64701),x64703),x64702)) % 183.90/184.44 [6482]E(f172(x64821,x64822,f333(f333(f135(x64821),x64823),x64824)),f333(f333(f135(x64821),x64823),f172(x64821,x64822,x64824)))+P1(f333(f333(f335(x64821),x64822),f333(f174(x64821),x64823))) % 183.90/184.44 [6486]~P77(x64861)+E(f333(f333(f80(x64861),f333(f333(f258(x64861),x64862),x64863)),f333(f333(f258(x64861),x64862),x64864)),f333(f333(f258(x64861),x64862),f333(f333(f79(a875),x64863),x64864))) % 183.90/184.44 [6487]~P109(x64871)+E(f333(f333(f80(x64871),f333(f333(f258(x64871),x64872),x64873)),f333(f333(f258(x64871),x64872),x64874)),f333(f333(f258(x64871),x64872),f333(f333(f79(a875),x64873),x64874))) % 183.90/184.44 [6523]~P96(x65231)+E(f333(f333(f104(x65231),f333(f333(f113(x65231),x65232),x65233)),f333(f333(f113(x65231),x65232),x65234)),f333(f333(f113(x65231),x65232),f333(f333(f104(x65231),x65233),x65234))) % 183.90/184.44 [6524]~P96(x65241)+E(f333(f333(f113(x65241),f333(f333(f104(x65241),x65242),x65243)),f333(f333(f104(x65241),x65242),x65244)),f333(f333(f104(x65241),x65242),f333(f333(f113(x65241),x65243),x65244))) % 183.90/184.44 [6525]~P109(x65251)+E(f333(f333(f79(x65251),f333(f333(f80(x65251),x65252),x65253)),f333(f333(f80(x65251),x65252),x65254)),f333(f333(f80(x65251),x65252),f333(f333(f79(x65251),x65253),x65254))) % 183.90/184.44 [6526]~P106(x65261)+E(f333(f333(f246(x65261),f333(f333(f245(x65261),x65262),x65263)),f333(f333(f245(x65261),x65262),x65264)),f333(f333(f245(x65261),x65262),f333(f333(f246(x65261),x65263),x65264))) % 183.90/184.44 [6527]~P106(x65271)+E(f333(f333(f245(x65271),f333(f333(f246(x65271),x65272),x65273)),f333(f333(f246(x65271),x65272),x65274)),f333(f333(f246(x65271),x65272),f333(f333(f245(x65271),x65273),x65274))) % 183.90/184.44 [6559]~P55(x65591)+E(f44(x65591,f333(f333(f80(x65591),x65592),x65593),f333(f333(f80(x65591),x65594),x65593)),f333(f333(f80(x65591),f44(x65591,x65592,x65594)),x65593)) % 183.90/184.44 [6562]~E(f333(f197(f876(x65621)),x65623),f333(f197(f876(x65622)),x65624))+E(f333(f333(f155(f881(x65621,x65622),x65622),f271(x65621,x65622)),f333(f333(f184(x65621,x65622),x65623),x65624)),x65624) % 183.90/184.44 [6563]~E(f333(f197(f876(x65631)),x65633),f333(f197(f876(x65632)),x65634))+E(f333(f333(f155(f881(x65631,x65632),x65631),f267(x65631,x65632)),f333(f333(f184(x65631,x65632),x65633),x65634)),x65633) % 183.90/184.44 [6569]P1(f333(f161(x65691,x65692),x65693))+~P1(f333(f161(x65691,x65692),f333(f333(f152(x65691),x65694),x65693))) % 183.90/184.44 [6570]P1(f333(f161(x65701,x65702),x65703))+~P1(f333(f161(x65701,x65702),f333(f333(f135(x65701),x65704),x65703))) % 183.90/184.44 [6571]P1(f333(f161(x65711,x65712),x65713))+~P1(f333(f161(x65711,x65712),f333(f333(f135(x65711),x65713),x65714))) % 183.90/184.44 [6576]~P56(x65761)+E(f44(x65761,f333(f333(f22(x65761),x65762),f44(x65761,x65763,x65764)),x65764),f44(x65761,f333(f333(f22(x65761),x65762),x65763),x65764)) % 183.90/184.44 [6578]~P55(x65781)+E(f44(x65781,f333(f333(f80(x65781),x65782),f44(x65781,x65783,x65784)),x65784),f44(x65781,f333(f333(f80(x65781),x65782),x65783),x65784)) % 183.90/184.44 [6579]~P55(x65791)+E(f44(x65791,f333(f333(f79(x65791),x65792),f44(x65791,x65793,x65794)),x65794),f44(x65791,f333(f333(f79(x65791),x65792),x65793),x65794)) % 183.90/184.44 [6659]~P106(x66591)+E(f333(f333(f104(f882(x66591,a870)),f304(x66591,x66592,x66593)),f333(f302(x66591),x66594)),f304(x66591,x66592,f333(f333(f245(x66591),x66593),x66594))) % 183.90/184.44 [6660]~P106(x66601)+E(f333(f333(f104(f882(x66601,a870)),f304(x66601,x66602,x66603)),f333(f255(x66601),x66604)),f304(x66601,f333(f333(f246(x66601),x66602),x66604),x66603)) % 183.90/184.44 [6663]~E(f333(f197(f876(x66631)),x66633),f333(f197(f876(x66632)),x66634))+E(f333(f333(f184(x66631,x66632),f333(f170(x66631),x66633)),f333(f170(x66632),x66634)),f333(f170(f881(x66631,x66632)),f333(f333(f184(x66631,x66632),x66633),x66634))) % 183.90/184.44 [6673]E(x66731,f333(f333(f22(a875),f333(f197(f876(x66732)),x66733)),f77(a875)))+E(f117(x66732,f333(f333(f160(x66732,x66733),x66731),x66734)),f333(f333(f160(x66732,f117(x66732,x66733)),x66731),x66734)) % 183.90/184.44 [6688]~P1(f333(f138(x66882),x66884))+P1(f333(f138(f881(x66881,x66882)),f333(f333(f184(x66881,x66882),x66883),x66884))) % 183.90/184.44 [6689]~P1(f333(f138(x66891),x66893))+P1(f333(f138(f881(x66891,x66892)),f333(f333(f184(x66891,x66892),x66893),x66894))) % 183.90/184.44 [6953]E(f333(f333(f38(a875),x69531),x69532),x69533)+~P1(f333(f47(x69531,x69532),f333(f333(f268(a875,a875),x69533),x69534))) % 183.90/184.44 [6977]E(f44(a875,x69771,x69772),x69773)+~P1(f333(f47(x69771,x69772),f333(f333(f268(a875,a875),x69774),x69773))) % 183.90/184.44 [6980]P1(f333(f138(x69801),x69802))+~P1(f333(f138(x69803),f333(f333(f155(x69801,x69803),x69804),x69802))) % 183.90/184.44 [6988]~P24(x69881,x69882,f333(f333(f311(f874(x69881)),x69883),x69884))+P24(x69881,x69882,f333(f333(f311(f874(x69881)),x69883),f196(f882(f874(x69881),a870)))) % 183.90/184.44 [6994]P1(f333(f333(f202(x69941),x69942),x69943))+~P1(f333(f333(f333(f333(a204,x69941),x69942),x69944),x69943)) % 183.90/184.44 [7066]E(f172(x70661,x70662,f333(f333(f135(x70661),x70663),x70664)),f333(f333(f135(x70661),f172(x70661,x70662,x70663)),x70664))+~P1(f333(f333(f335(x70661),x70662),f333(f174(x70661),x70663))) % 183.90/184.44 [7156]~P56(x71561)+E(f44(x71561,f333(f333(f22(x71561),f44(x71561,x71562,x71563)),x71564),x71563),f44(x71561,f333(f333(f22(x71561),x71562),x71564),x71563)) % 183.90/184.44 [7159]~P55(x71591)+E(f44(x71591,f333(f333(f79(x71591),f44(x71591,x71592,x71593)),x71594),x71593),f44(x71591,f333(f333(f79(x71591),x71592),x71594),x71593)) % 183.90/184.44 [7160]~P55(x71601)+E(f44(x71601,f333(f333(f80(x71601),f44(x71601,x71602,x71603)),x71604),x71603),f44(x71601,f333(f333(f80(x71601),x71602),x71604),x71603)) % 183.90/184.44 [7350]~E(x73501,f333(f333(f152(x73502),x73503),x73504))+~P1(f333(f333(f247(a875),f333(f197(f876(x73502)),x73501)),f333(f197(f876(x73502)),x73504))) % 183.90/184.44 [7425]~E(f333(f180(x74251,x74252),x74253),f333(f180(x74251,x74252),x74254))+E(f333(f312(f881(x74251,x74252),x74251,f267(x74251,x74252)),f333(f174(f881(x74251,x74252)),x74253)),f333(f312(f881(x74251,x74252),x74251,f267(x74251,x74252)),f333(f174(f881(x74251,x74252)),x74254))) % 183.90/184.44 [7560]P25(x75601,x75602,x75603,f333(f174(x75601),x75604))+~P1(f333(f138(x75602),f333(f333(f155(x75601,x75602),x75603),x75604))) % 183.90/184.44 [7634]~P1(f333(f333(f247(f882(x76341,a870)),x76342),x76344))+P1(f333(f333(f247(f882(x76341,a870)),x76342),f333(f333(f311(x76341),x76343),x76344))) % 183.90/184.44 [7668]~P56(x76681)+E(f44(x76681,f333(f333(f22(x76681),f44(x76681,x76682,x76683)),f44(x76681,x76684,x76683)),x76683),f44(x76681,f333(f333(f22(x76681),x76682),x76684),x76683)) % 183.90/184.44 [7669]~P55(x76691)+E(f44(x76691,f333(f333(f79(x76691),f44(x76691,x76692,x76693)),f44(x76691,x76694,x76693)),x76693),f44(x76691,f333(f333(f79(x76691),x76692),x76694),x76693)) % 183.90/184.44 [7670]~P55(x76701)+E(f44(x76701,f333(f333(f80(x76701),f44(x76701,x76702,x76703)),f44(x76701,x76704,x76703)),x76703),f44(x76701,f333(f333(f80(x76701),x76702),x76704),x76703)) % 183.90/184.44 [7773]P1(f333(f333(f333(f333(a204,x77731),x77732),f333(a115,x77733)),x77734))+~P1(f333(f333(f333(f333(a204,x77731),x77732),x77733),x77734)) % 183.90/184.44 [7780]~E(f333(x77804,f825(x77804,x77803,x77801,x77802)),f196(f882(x77802,a870)))+E(f333(f333(f41(x77801,f882(x77802,a870)),x77803),x77804),f196(f882(x77802,a870))) % 183.90/184.44 [7781]~E(f333(x77814,f832(x77814,x77813,x77811,x77812)),f256(f882(x77812,a870)))+E(f333(f333(f42(x77811,f882(x77812,a870)),x77813),x77814),f256(f882(x77812,a870))) % 183.90/184.44 [7782]~E(f333(x77824,f826(x77824,x77823,x77822,x77821)),f196(f882(x77822,a870)))+E(f333(f333(f41(x77821,f882(x77822,a870)),x77823),x77824),f196(f882(x77822,a870))) % 183.90/184.44 [7783]~E(f333(x77834,f834(x77834,x77833,x77832,x77831)),f256(f882(x77832,a870)))+E(f333(f333(f42(x77831,f882(x77832,a870)),x77833),x77834),f256(f882(x77832,a870))) % 183.90/184.44 [8183]P1(f333(x81831,x81832))+~P1(f333(f333(f335(x81833),x81832),f333(f333(f104(f882(x81833,a870)),x81834),f333(f253(x81833),x81831)))) % 183.90/184.44 [8222]~P1(f333(f333(f247(f882(x82221,a870)),x82223),x82224))+P1(f333(f333(f247(f882(x82221,a870)),f333(f333(f311(x82221),x82222),x82223)),f333(f333(f311(x82221),x82222),x82224))) % 183.90/184.44 [8389]P1(f333(f333(f202(x83891),x83892),f356(x83893,x83892,x83894,x83891)))+~P1(f333(f333(f202(f32(x83891,x83894)),x83892),x83893)) % 183.90/184.44 [8390]P1(f333(f333(f202(x83901),x83902),f365(x83903,x83902,x83904,x83901)))+~P1(f333(f333(f202(f32(x83901,x83904)),x83902),x83903)) % 183.90/184.44 [8399]P1(f333(x83992,x83993))+E(f333(f333(f139(x83991),f333(f197(f876(x83991)),f179(x83991,x83992,f333(f333(f152(x83991),x83993),x83994)))),f333(f333(f152(x83991),x83993),x83994)),f333(f333(f152(x83991),x83993),x83994)) % 183.90/184.44 [8514]~P1(f333(f333(f248(a875),f333(x85144,x85142)),f333(x85144,x85143)))+P1(f333(f333(f335(f881(x85141,x85141)),f333(f333(f268(x85141,x85141),x85142),x85143)),f333(f333(f289(a875,x85141),a252),x85144))) % 183.90/184.44 [8603]~P1(f333(x86032,f779(x86034,x86032,x86033,x86031)))+E(f179(x86031,x86032,f333(f333(f135(x86031),x86033),x86034)),f333(f333(f135(x86031),x86033),f179(x86031,x86032,x86034))) % 183.90/184.44 [8673]P25(f876(x86731),f876(x86732),f333(f155(x86731,x86732),x86733),x86734)+~P25(x86731,x86732,x86733,f39(f882(x86731,a870),f333(f312(f876(x86731),f882(x86731,a870),f174(x86731)),x86734))) % 183.90/184.44 [8740]~P1(f333(x87402,x87403))+E(f333(f333(f139(x87401),f333(f197(f876(x87401)),f179(x87401,x87402,f333(f333(f152(x87401),x87403),x87404)))),f333(f333(f152(x87401),x87403),x87404)),f333(f333(f139(x87401),f333(f197(f876(x87401)),f179(x87401,x87402,x87404))),x87404)) % 183.90/184.44 [8779]~E(x87792,x87793)+E(f333(f137(x87791,f333(f333(f8(a870,a870,x87791),a328),f333(a330,x87792))),f333(f333(f152(x87791),x87793),x87794)),f333(f137(x87791,f333(f333(f8(a870,a870,x87791),a328),f333(a330,x87792))),x87794)) % 183.90/184.44 [8789]E(f333(f333(f41(x87891,f882(x87892,a870)),x87893),x87894),f196(f882(x87892,a870)))+P1(f333(f333(f335(x87891),f825(x87894,x87893,x87891,x87892)),x87893)) % 183.90/184.44 [8790]E(f333(f333(f42(x87901,f882(x87902,a870)),x87903),x87904),f256(f882(x87902,a870)))+P1(f333(f333(f335(x87901),f832(x87904,x87903,x87901,x87902)),x87903)) % 183.90/184.44 [8791]E(f333(f333(f41(x87911,f882(x87912,a870)),x87913),x87914),f196(f882(x87912,a870)))+P1(f333(f333(f335(x87911),f826(x87914,x87913,x87912,x87911)),x87913)) % 183.90/184.44 [8792]E(f333(f333(f42(x87921,f882(x87922,a870)),x87923),x87924),f256(f882(x87922,a870)))+P1(f333(f333(f335(x87921),f834(x87924,x87923,x87922,x87921)),x87923)) % 183.90/184.44 [8829]P1(f333(f333(f248(a875),f333(x88291,x88292)),f333(x88291,x88293)))+~P1(f333(f333(f335(f881(x88294,x88294)),f333(f333(f268(x88294,x88294),x88292),x88293)),f333(f333(f289(a875,x88294),a252),x88291))) % 183.90/184.44 [8850]E(f179(x88501,x88502,f333(f333(f135(x88501),x88503),x88504)),f333(f333(f135(x88501),x88503),f179(x88501,x88502,x88504)))+P1(f333(f333(f335(x88501),f779(x88504,x88502,x88503,x88501)),f333(f174(x88501),x88503))) % 183.90/184.44 [8887]P1(f333(f333(f202(x88871),f356(x88872,x88873,x88871,x88874)),x88872))+~P1(f333(f333(f202(f32(x88874,x88871)),x88873),x88872)) % 183.90/184.44 [8888]P1(f333(f333(f202(x88881),f365(x88882,x88883,x88881,x88884)),x88882))+~P1(f333(f333(f202(f32(x88884,x88881)),x88883),x88882)) % 183.90/184.44 [9019]P1(f333(f333(f335(x90191),f501(x90192,x90193,x90194,x90191)),x90193))+~P1(f333(f333(f335(f882(x90191,a870)),x90194),f333(f333(f60(x90191),x90193),x90192))) % 183.90/184.44 [9022]E(x90221,x90222)+~P1(f333(f333(f335(f881(x90223,x90223)),f333(f333(f268(x90223,x90223),x90221),x90222)),f333(f333(f191(f881(x90223,x90223),a870),f2(a875)),x90224))) % 183.90/184.44 [9101]E(f333(f287(x91011,x91011,x91012),f333(f333(f311(x91011),f501(x91012,x91013,x91014,x91011)),f196(f882(x91011,a870)))),x91014)+~P1(f333(f333(f335(f882(x91011,a870)),x91014),f333(f333(f60(x91011),x91013),x91012))) % 183.90/184.44 [9106]~P1(f333(f333(f335(f881(x91061,x91061)),f333(f333(f268(x91061,x91061),x91063),x91062)),f309(x91061,x91064)))+P1(f333(f333(f335(f881(x91061,x91061)),f333(f333(f268(x91061,x91061),x91062),x91063)),f309(x91061,f333(f288(x91061,x91061),x91064)))) % 183.90/184.44 [9118]~P55(x91181)+E(f333(f333(f79(x91181),f333(f333(f79(x91181),f333(f333(f80(x91181),x91182),f333(f333(f38(x91181),x91183),x91182))),f44(x91181,x91183,x91182))),x91184),f333(f333(f79(x91181),x91183),x91184)) % 183.90/184.44 [9128]~P1(f333(f333(f335(x91281),x91283),x91284))+P1(f333(f333(f335(f882(x91281,a870)),f333(f287(x91281,x91281,x91282),f333(f333(f311(x91281),x91283),f196(f882(x91281,a870))))),f333(f333(f60(x91281),x91284),x91282))) % 183.90/184.44 [9139]P1(f333(f333(f335(f881(x91391,x91391)),f333(f333(f268(x91391,x91391),x91392),x91393)),f309(x91391,x91394)))+~P1(f333(f333(f335(f881(x91391,x91391)),f333(f333(f268(x91391,x91391),x91393),x91392)),f309(x91391,f333(f288(x91391,x91391),x91394)))) % 183.90/184.44 [9231]E(f333(f333(f160(x92311,f333(f170(x92311),x92312)),f333(f333(f22(a875),f333(f333(f22(a875),f333(f197(f876(x92311)),x92312)),x92313)),f77(a875))),x92314),f333(f170(x92311),f333(f333(f160(x92311,x92312),x92313),x92314)))+~P1(f333(f333(f248(a875),x92313),f333(f197(f876(x92311)),x92312))) % 183.90/184.44 [9234]~P1(f333(x92342,f773(x92344,x92342,x92343,x92341)))+E(f333(f333(f139(x92341),f333(f197(f876(x92341)),f179(x92341,x92342,f333(f333(f135(x92341),x92343),x92344)))),f333(f333(f135(x92341),x92343),x92344)),f333(f333(f139(x92341),f333(f197(f876(x92341)),f179(x92341,x92342,x92344))),x92344)) % 183.90/184.44 [9273]~P25(x92732,x92731,x92733,f256(f882(x92732,a870)))+P1(f333(f333(f247(f882(x92731,a870)),f333(f312(x92732,x92731,x92733),f333(f78(f882(x92732,a870)),x92734))),f333(f78(f882(x92731,a870)),f333(f312(x92732,x92731,x92733),x92734)))) % 183.90/184.44 [9286]~P4(x92861)+E(f333(f143(x92861,x92862,f333(f7(x92862,x92861,x92861),f333(f333(f8(x92861,f882(x92861,x92861),x92862),f113(x92861)),x92863)),f196(x92861)),x92864),f333(f333(f41(x92862,x92861),f333(f174(x92862),x92864)),x92863)) % 183.90/184.44 [9287]~P4(x92871)+E(f333(f143(x92871,x92872,f333(f7(x92872,x92871,x92871),f333(f333(f8(x92871,f882(x92871,x92871),x92872),f104(x92871)),x92873)),f256(x92871)),x92874),f333(f333(f42(x92872,x92871),f333(f174(x92872),x92874)),x92873)) % 183.90/184.44 [9299]E(f333(f333(f139(x92991),f333(f197(f876(x92991)),f179(x92991,x92992,f333(f333(f135(x92991),x92993),x92994)))),f333(f333(f135(x92991),x92993),x92994)),f333(f333(f139(x92991),f333(f197(f876(x92991)),f179(x92991,x92992,x92994))),x92994))+P1(f333(f333(f335(x92991),f773(x92994,x92992,x92993,x92991)),f333(f174(x92991),x92993))) % 183.90/184.44 [9367]~P1(f333(f333(f335(f881(f876(x93674),f876(x93674))),f333(f333(f268(f876(x93674),f876(x93674)),x93673),x93672)),f158(x93674,x93671)))+P1(f333(f333(f248(a875),f688(x93671,x93672,x93673,x93674)),f333(f197(f876(x93674)),x93673))) % 183.90/184.44 [9368]~P55(x93681)+E(f333(f333(f79(x93681),f333(f333(f79(x93681),f333(f333(f80(x93681),f333(f333(f38(x93681),x93682),x93683)),x93683)),f44(x93681,x93682,x93683))),x93684),f333(f333(f79(x93681),x93682),x93684)) % 183.90/184.44 [9396]~P1(f333(f333(f335(f881(f876(x93961),f876(x93961))),f333(f333(f268(f876(x93961),f876(x93961)),x93962),x93963)),f333(f288(f876(x93961),f876(x93961)),f158(x93961,x93964))))+P1(f333(f333(f335(f881(f876(x93961),f876(x93961))),f333(f333(f268(f876(x93961),f876(x93961)),x93962),x93963)),f158(x93961,f333(f288(x93961,x93961),x93964)))) % 183.90/184.44 [9397]P1(f333(f333(f335(f881(f876(x93971),f876(x93971))),f333(f333(f268(f876(x93971),f876(x93971)),x93972),x93973)),f333(f288(f876(x93971),f876(x93971)),f158(x93971,x93974))))+~P1(f333(f333(f335(f881(f876(x93971),f876(x93971))),f333(f333(f268(f876(x93971),f876(x93971)),x93972),x93973)),f158(x93971,f333(f288(x93971,x93971),x93974)))) % 183.90/184.44 [9431]~P1(f333(f333(f335(x94311),x94313),f333(f266(x94311,x94312),x94314)))+P1(f333(f333(f335(f881(x94311,x94312)),f333(f333(f268(x94311,x94312),x94313),f572(x94314,x94312,x94313,x94311))),x94314)) % 183.90/184.44 [9432]~P1(f333(f333(f335(x94321),x94323),f333(f266(x94321,x94322),x94324)))+P1(f333(f333(f335(f881(x94321,x94322)),f333(f333(f268(x94321,x94322),x94323),f574(x94324,x94322,x94323,x94321))),x94324)) % 183.90/184.44 [9541]~P1(f333(f61(f879(x95411)),f333(f312(x95412,f879(x95411),x95413),f256(f882(x95412,a870)))))+P1(f333(f61(f879(x95411)),f333(f312(x95412,f879(x95411),f187(x95412,x95411,x95413,f333(f180(x95412,x95411),x95414))),f256(f882(x95412,a870))))) % 183.90/184.44 [9588]~P1(f333(f333(f335(f881(x95881,x95881)),f333(f333(f268(x95881,x95881),x95882),x95884)),f333(f333(f290(x95881,x95881,x95881),x95883),f309(x95881,x95883))))+P1(f333(f333(f335(f881(x95881,x95881)),f333(f333(f268(x95881,x95881),x95882),f642(x95883,x95884,x95882,x95881))),x95883)) % 183.90/184.44 [9756]~P1(f333(f333(f335(f881(x97562,x97561)),x97564),f333(f288(x97561,x97562),x97563)))+P1(f333(f333(f335(f881(x97561,x97562)),f333(f333(f268(x97561,x97562),f660(x97563,x97564,x97561,x97562)),f659(x97563,x97564,x97561,x97562))),x97563)) % 183.90/184.44 [9784]~P1(f333(f333(f335(f881(f876(x97841),f876(x97841))),f333(f333(f268(f876(x97841),f876(x97841)),x97844),x97843)),f158(x97841,x97842)))+P1(f333(f333(f335(f881(x97841,x97841)),f333(f333(f268(x97841,x97841),f702(x97842,x97843,x97844,x97841)),f703(x97842,x97843,x97844,x97841))),x97842)) % 183.90/184.44 [9880]~P1(f333(f333(f335(f881(f876(x98801),f876(x98801))),f333(f333(f268(f876(x98801),f876(x98801)),x98802),x98804)),f158(x98801,x98803)))+P1(f333(f333(f335(f881(x98801,x98801)),f333(f333(f268(x98801,x98801),f333(f333(f166(x98801),x98802),f688(x98803,x98804,x98802,x98801))),f689(x98803,x98804,x98802,x98801))),x98803)) % 183.90/184.44 [9902]~P1(f333(f61(x99022),x99024))+E(f333(f333(f333(f65(f882(x99021,a870),x99022,f113(f882(x99021,a870))),f333(f333(f7(x99022,f882(x99021,a870),f882(x99021,a870)),f333(f333(f8(x99021,f882(f882(x99021,a870),f882(x99021,a870)),x99022),f311(x99021)),x99023)),f196(f882(x99021,a870)))),f196(f882(x99021,a870))),x99024),f333(f312(x99022,x99021,x99023),x99024)) % 183.90/184.44 [9997]~P25(x99971,x99972,x99973,f256(f882(x99971,a870)))+P1(f333(f333(f247(f882(x99971,a870)),f333(f313(x99971,x99972,x99973),f333(f333(f311(x99972),x99974),f196(f882(x99972,a870))))),f333(f333(f311(x99971),f84(x99971,f333(f333(f7(x99971,x99972,a870),f333(f333(f8(x99972,f882(x99972,a870),x99971),a330),x99973)),x99974))),f196(f882(x99971,a870))))) % 183.90/184.44 [5615]~E(f333(f333(f135(x56151),x56152),x56154),x56153)+E(f333(f333(f177(x56151),f333(f197(f876(x56151)),x56152)),x56153),x56152) % 183.90/184.44 [5616]~E(f333(f333(f135(x56162),x56163),x56161),x56164)+E(x56161,f333(f333(f139(x56162),f333(f197(f876(x56162)),x56163)),x56164)) % 183.90/184.44 [5627]~E(x56274,f2(a875))+E(f333(f333(f166(x56271),f333(f333(f152(x56271),x56272),x56273)),x56274),x56272) % 183.90/184.44 [6150]~P109(x61501)+E(f333(f333(f258(x61501),f333(f333(f258(x61501),x61502),x61503)),x61504),f333(f333(f258(x61501),x61502),f333(f333(f80(a875),x61503),x61504))) % 183.90/184.44 [6151]~P77(x61511)+E(f333(f333(f258(x61511),f333(f333(f258(x61511),x61512),x61513)),x61514),f333(f333(f258(x61511),x61512),f333(f333(f80(a875),x61513),x61514))) % 183.90/184.44 [6162]E(x61621,f2(a875))+E(f333(f333(f166(x61622),f333(f333(f152(x61622),x61623),x61624)),x61621),f333(f333(f166(x61622),x61624),f333(f333(f22(a875),x61621),f77(a875)))) % 183.90/184.44 [6189]~P117(x61891)+E(f333(f333(f291(x61891),f333(f333(f80(x61891),x61892),x61893)),x61894),f333(f333(f80(x61891),x61892),f333(f333(f291(x61891),x61893),x61894))) % 183.90/184.44 [6190]~P62(x61901)+E(f333(f333(f113(x61901),f333(f333(f113(x61901),x61902),x61903)),x61904),f333(f333(f113(x61901),x61902),f333(f333(f113(x61901),x61903),x61904))) % 183.90/184.44 [6192]~P98(x61921)+E(f333(f333(f113(x61921),f333(f333(f113(x61921),x61922),x61923)),x61924),f333(f333(f113(x61921),x61922),f333(f333(f113(x61921),x61923),x61924))) % 183.90/184.44 [6193]~P62(x61931)+E(f333(f333(f104(x61931),f333(f333(f104(x61931),x61932),x61933)),x61934),f333(f333(f104(x61931),x61932),f333(f333(f104(x61931),x61933),x61934))) % 183.90/184.44 [6195]~P99(x61951)+E(f333(f333(f104(x61951),f333(f333(f104(x61951),x61952),x61953)),x61954),f333(f333(f104(x61951),x61952),f333(f333(f104(x61951),x61953),x61954))) % 183.90/184.44 [6196]~P68(x61961)+E(f333(f333(f79(x61961),f333(f333(f79(x61961),x61962),x61963)),x61964),f333(f333(f79(x61961),x61962),f333(f333(f79(x61961),x61963),x61964))) % 183.90/184.44 [6197]~P109(x61971)+E(f333(f333(f79(x61971),f333(f333(f79(x61971),x61972),x61973)),x61974),f333(f333(f79(x61971),x61972),f333(f333(f79(x61971),x61973),x61974))) % 183.90/184.44 [6198]~P67(x61981)+E(f333(f333(f80(x61981),f333(f333(f80(x61981),x61982),x61983)),x61984),f333(f333(f80(x61981),x61982),f333(f333(f80(x61981),x61983),x61984))) % 183.90/184.44 [6199]~P109(x61991)+E(f333(f333(f80(x61991),f333(f333(f80(x61991),x61992),x61993)),x61994),f333(f333(f80(x61991),x61992),f333(f333(f80(x61991),x61993),x61994))) % 183.90/184.44 [6202]~P106(x62021)+E(f333(f333(f245(x62021),f333(f333(f245(x62021),x62022),x62023)),x62024),f333(f333(f245(x62021),x62022),f333(f333(f245(x62021),x62023),x62024))) % 183.90/184.44 [6204]~P106(x62041)+E(f333(f333(f246(x62041),f333(f333(f246(x62041),x62042),x62043)),x62044),f333(f333(f246(x62041),x62042),f333(f333(f246(x62041),x62043),x62044))) % 183.90/184.44 [6215]~P55(x62151)+E(f44(x62151,f333(f333(f79(x62151),x62152),f333(f333(f80(x62151),x62153),x62154)),x62154),f44(x62151,x62152,x62154)) % 183.90/184.44 [6216]~P55(x62161)+E(f44(x62161,f333(f333(f79(x62161),x62162),f333(f333(f80(x62161),x62163),x62164)),x62163),f44(x62161,x62162,x62163)) % 183.90/184.44 [6348]E(f333(f333(f166(x63481),f333(f333(f177(x63481),x63482),x63483)),x63484),f333(f333(f166(x63481),x63483),x63484))+~P1(f333(f333(f248(a875),x63484),x63482)) % 183.90/184.44 [6521]~P109(x65211)+E(f333(f333(f79(x65211),f333(f333(f79(x65211),x65212),x65213)),x65214),f333(f333(f79(x65211),f333(f333(f79(x65211),x65212),x65214)),x65213)) % 183.90/184.44 [6522]~P109(x65221)+E(f333(f333(f80(x65221),f333(f333(f80(x65221),x65222),x65223)),x65224),f333(f333(f80(x65221),f333(f333(f80(x65221),x65222),x65224)),x65223)) % 183.90/184.44 [6582]~P141(x65822)+E(f333(f333(f6(x65821,x65822),f333(f16(x65822,x65821),x65823)),x65824),f333(f333(f80(x65822),f333(f103(x65822),f333(f37(x65821),x65824))),x65823)) % 183.90/184.44 [6751]E(f333(f333(f104(f882(x67511,a870)),f333(f333(f311(x67511),x67512),x67513)),x67514),f333(f333(f104(f882(x67511,a870)),x67513),x67514))+P1(f333(f333(f335(x67511),x67512),x67514)) % 183.90/184.44 [6821]~P96(x68211)+E(f333(f333(f104(x68211),f333(f333(f113(x68211),x68212),x68213)),f333(f333(f113(x68211),x68214),x68213)),f333(f333(f113(x68211),f333(f333(f104(x68211),x68212),x68214)),x68213)) % 183.90/184.44 [6822]~P82(x68221)+E(f333(f333(f245(x68221),f333(f333(f22(x68221),x68222),x68223)),f333(f333(f22(x68221),x68224),x68223)),f333(f333(f22(x68221),f333(f333(f245(x68221),x68222),x68224)),x68223)) % 183.90/184.44 [6823]~P82(x68231)+E(f333(f333(f246(x68231),f333(f333(f22(x68231),x68232),x68233)),f333(f333(f22(x68231),x68234),x68233)),f333(f333(f22(x68231),f333(f333(f246(x68231),x68232),x68234)),x68233)) % 183.90/184.44 [6824]~P96(x68241)+E(f333(f333(f113(x68241),f333(f333(f104(x68241),x68242),x68243)),f333(f333(f104(x68241),x68244),x68243)),f333(f333(f104(x68241),f333(f333(f113(x68241),x68242),x68244)),x68243)) % 183.90/184.44 [6825]~P80(x68251)+E(f333(f333(f245(x68251),f333(f333(f79(x68251),x68252),x68253)),f333(f333(f79(x68251),x68254),x68253)),f333(f333(f79(x68251),f333(f333(f245(x68251),x68252),x68254)),x68253)) % 183.90/184.44 [6826]~P80(x68261)+E(f333(f333(f246(x68261),f333(f333(f79(x68261),x68262),x68263)),f333(f333(f79(x68261),x68264),x68263)),f333(f333(f79(x68261),f333(f333(f246(x68261),x68262),x68264)),x68263)) % 183.90/184.44 [6828]~P110(x68281)+E(f333(f333(f79(x68281),f333(f333(f80(x68281),x68282),x68283)),f333(f333(f80(x68281),x68284),x68283)),f333(f333(f80(x68281),f333(f333(f79(x68281),x68282),x68284)),x68283)) % 183.90/184.44 [6829]~P109(x68291)+E(f333(f333(f80(x68291),f333(f333(f258(x68291),x68292),x68293)),f333(f333(f258(x68291),x68294),x68293)),f333(f333(f258(x68291),f333(f333(f80(x68291),x68292),x68294)),x68293)) % 183.90/184.44 [6830]~P73(x68301)+E(f333(f333(f80(x68301),f333(f333(f258(x68301),x68302),x68303)),f333(f333(f258(x68301),x68304),x68303)),f333(f333(f258(x68301),f333(f333(f80(x68301),x68302),x68304)),x68303)) % 183.90/184.44 [6831]~P58(x68311)+E(f333(f333(f291(x68311),f333(f333(f258(x68311),x68312),x68313)),f333(f333(f258(x68311),x68314),x68313)),f333(f333(f258(x68311),f333(f333(f291(x68311),x68312),x68314)),x68313)) % 183.90/184.44 [6832]~P117(x68321)+E(f333(f333(f22(x68321),f333(f333(f291(x68321),x68322),x68323)),f333(f333(f291(x68321),x68324),x68323)),f333(f333(f291(x68321),f333(f333(f22(x68321),x68322),x68324)),x68323)) % 183.90/184.44 [6833]~P117(x68331)+E(f333(f333(f79(x68331),f333(f333(f291(x68331),x68332),x68333)),f333(f333(f291(x68331),x68334),x68333)),f333(f333(f291(x68331),f333(f333(f79(x68331),x68332),x68334)),x68333)) % 183.90/184.44 [6834]~P106(x68341)+E(f333(f333(f246(x68341),f333(f333(f245(x68341),x68342),x68343)),f333(f333(f245(x68341),x68344),x68343)),f333(f333(f245(x68341),f333(f333(f246(x68341),x68342),x68344)),x68343)) % 183.90/184.44 [6835]~P106(x68351)+E(f333(f333(f245(x68351),f333(f333(f246(x68351),x68352),x68353)),f333(f333(f246(x68351),x68354),x68353)),f333(f333(f246(x68351),f333(f333(f245(x68351),x68352),x68354)),x68353)) % 183.90/184.44 [6836]~P109(x68361)+E(f333(f333(f79(x68361),f333(f333(f80(x68361),x68362),x68363)),f333(f333(f80(x68361),x68364),x68363)),f333(f333(f80(x68361),f333(f333(f79(x68361),x68362),x68364)),x68363)) % 183.90/184.44 [6868]E(f333(f333(f160(x68681,x68682),x68683),x68684),x68682)+~P1(f333(f333(f247(a875),f333(f197(f876(x68681)),x68682)),x68683)) % 183.90/184.44 [6893]~P1(f333(x68933,x68934))+P1(f333(f333(f333(f113(f882(x68931,a870)),x68932),x68933),x68934)) % 183.90/184.44 [6895]~P1(f333(x68952,x68954))+P1(f333(f333(f333(f113(f882(x68951,a870)),x68952),x68953),x68954)) % 183.90/184.44 [6916]E(f333(f333(f166(x69161),f333(f333(f135(x69161),x69162),x69163)),x69164),f333(f333(f166(x69161),x69162),x69164))+~P1(f333(f333(f248(a875),x69164),f333(f197(f876(x69161)),x69162))) % 183.90/184.44 [6926]E(f333(f333(f22(f882(x69261,a870)),f333(f333(f311(x69261),x69262),x69263)),x69264),f333(f333(f22(f882(x69261,a870)),x69263),x69264))+~P1(f333(f333(f335(x69261),x69262),x69264)) % 183.90/184.44 [6967]~E(f140(a875,f333(f303(a875,x69671),x69672)),f333(f333(f152(a875),x69674),x69673))+E(f140(a875,f333(f303(a875,f333(f333(f79(a875),x69671),f77(a875))),x69672)),x69673) % 183.90/184.44 [7040]E(x70401,f2(a875))+E(f333(f333(f152(x70402),x70403),f333(f333(f177(x70402),f333(f333(f22(a875),x70401),f77(a875))),x70404)),f333(f333(f177(x70402),x70401),f333(f333(f152(x70402),x70403),x70404))) % 183.90/184.44 [7140]E(f333(f333(f166(x71401),x71402),f333(f333(f22(a875),x71403),f333(f197(f876(x71401)),x71404))),f333(f333(f166(x71401),f333(f333(f135(x71401),x71404),x71402)),x71403))+P1(f333(f333(f248(a875),x71403),f333(f197(f876(x71401)),x71404))) % 183.90/184.44 [7170]E(f333(f333(f104(f882(x71701,a870)),x71702),f333(f333(f311(x71701),x71703),x71704)),f333(f333(f311(x71701),x71703),f333(f333(f104(f882(x71701,a870)),x71702),x71704)))+~P1(f333(f333(f335(x71701),x71703),x71702)) % 183.90/184.44 [7205]E(f333(f333(f166(x72051),f333(f333(f160(x72051,x72052),x72053),x72054)),x72053),x72054)+~P1(f333(f333(f248(a875),x72053),f333(f197(f876(x72051)),x72052))) % 183.90/184.44 [7226]E(x72261,f196(f882(x72262,a870)))+E(f333(f312(f881(x72263,x72262),x72263,f267(x72263,x72262)),f333(f333(f270(x72263,x72262),x72264),f333(f16(f882(x72262,a870),x72263),x72261))),x72264) % 183.90/184.44 [7227]E(x72271,f196(f882(x72272,a870)))+E(f333(f312(f881(x72272,x72273),x72273,f271(x72272,x72273)),f333(f333(f270(x72272,x72273),x72271),f333(f16(f882(x72273,a870),x72272),x72274))),x72274) % 183.90/184.44 [7294]E(f333(f333(f22(f882(x72941,a870)),f333(f333(f311(x72941),x72942),x72943)),x72944),f333(f333(f311(x72941),x72942),f333(f333(f22(f882(x72941,a870)),x72943),x72944)))+P1(f333(f333(f335(x72941),x72942),x72944)) % 183.90/184.44 [7326]P1(f333(x73261,x73262))+P1(f333(f333(f333(f333(a204,f31(x73261,x73263)),x73262),x73264),x73262)) % 183.90/184.44 [7333]~E(x73334,f196(f882(x73332,a870)))+E(f333(f312(f881(x73331,x73332),x73331,f267(x73331,x73332)),f333(f333(f270(x73331,x73332),x73333),f333(f16(f882(x73332,a870),x73331),x73334))),f196(f882(x73331,a870))) % 183.90/184.44 [7334]~E(x73343,f196(f882(x73341,a870)))+E(f333(f312(f881(x73341,x73342),x73342,f271(x73341,x73342)),f333(f333(f270(x73341,x73342),x73343),f333(f16(f882(x73342,a870),x73341),x73344))),f196(f882(x73342,a870))) % 183.90/184.44 [7390]~P1(f333(f333(f335(x73901),x73902),x73904))+P1(f333(f333(f335(x73901),x73902),f333(f333(f113(f882(x73901,a870)),x73903),x73904))) % 183.90/184.44 [7393]~P1(f333(f333(f335(x73931),x73932),x73933))+P1(f333(f333(f335(x73931),x73932),f333(f333(f113(f882(x73931,a870)),x73933),x73934))) % 183.90/184.44 [7412]E(f333(f333(f104(f882(x74121,a870)),f333(f333(f311(x74121),x74122),x74123)),x74124),f333(f333(f311(x74121),x74122),f333(f333(f104(f882(x74121,a870)),x74123),x74124)))+~P1(f333(f333(f335(x74121),x74122),x74124)) % 183.90/184.44 [7692]P1(f333(x76921,x76922))+~P1(f333(f333(f333(f104(f882(x76923,a870)),x76924),x76921),x76922)) % 183.90/184.44 [7693]P1(f333(x76931,x76932))+~P1(f333(f333(f333(f104(f882(x76933,a870)),x76931),x76934),x76932)) % 183.90/184.44 [7696]E(f333(f333(f6(x76961,a875),x76962),f333(f333(f22(f882(x76961,a870)),x76963),f333(f333(f311(x76961),x76964),f196(f882(x76961,a870))))),f333(f333(f6(x76961,a875),x76962),x76963))+P1(f333(f333(f335(x76961),x76964),x76963)) % 183.90/184.44 [7702]~P66(x77021)+E(f333(f167(x77021),f333(f333(f155(a875,x77021),x77022),f140(a875,f333(f303(a875,x77023),x77024)))),f333(f333(f6(a875,x77021),x77022),f333(f174(a875),f140(a875,f333(f303(a875,x77023),x77024))))) % 183.90/184.44 [7703]~P66(x77031)+E(f333(f333(f6(a875,x77031),x77032),f333(f174(a875),f140(a875,f333(f303(a875,x77033),x77034)))),f333(f167(x77031),f333(f333(f155(a875,x77031),x77032),f140(a875,f333(f303(a875,x77033),x77034))))) % 183.90/184.44 [7818]~E(x78183,x78184)+P1(f333(f62(x78181,x78182,f333(f333(f311(x78181),x78183),f196(f882(x78181,a870)))),x78184)) % 183.90/184.44 [7915]P1(f333(f333(f335(x79151),x79152),f333(f174(x79151),x79153)))+~P1(f333(f333(f335(x79151),x79152),f333(f174(x79151),f333(f333(f177(x79151),x79154),x79153)))) % 183.90/184.44 [7916]P1(f333(f333(f335(x79161),x79162),f333(f174(x79161),x79163)))+~P1(f333(f333(f335(x79161),x79162),f333(f174(x79161),f333(f333(f139(x79161),x79164),x79163)))) % 183.90/184.44 [7990]P1(f333(f333(f335(x79901),x79902),x79903))+~P1(f333(f333(f335(x79901),x79902),f333(f333(f22(f882(x79901,a870)),x79903),x79904))) % 183.90/184.44 [7992]P1(f333(f333(f335(x79921),x79922),x79923))+~P1(f333(f333(f335(x79921),x79922),f333(f333(f104(f882(x79921,a870)),x79924),x79923))) % 183.90/184.44 [7995]P1(f333(f333(f335(x79951),x79952),x79953))+~P1(f333(f333(f335(x79951),x79952),f333(f333(f104(f882(x79951,a870)),x79953),x79954))) % 183.90/184.44 [8013]E(f333(f333(f135(x80131),f333(f333(f177(x80131),x80132),x80133)),f333(f333(f152(x80131),x80134),f333(f333(f139(x80131),f333(a115,x80132)),x80133))),f333(f333(f160(x80131,x80133),x80132),x80134))+~P1(f333(f333(f248(a875),x80132),f333(f197(f876(x80131)),x80133))) % 183.90/184.44 [8038]P1(f333(f333(f335(x80381),x80382),x80383))+~P1(f333(f333(f247(f882(x80381,a870)),f333(f333(f311(x80381),x80382),x80384)),x80383)) % 183.90/184.44 [8071]~P1(f333(f333(f335(x80711),x80712),x80713))+~P1(f333(f333(f335(x80711),x80712),f333(f333(f22(f882(x80711,a870)),x80714),x80713))) % 183.90/184.44 [8104]~P1(f333(f333(f248(a875),x81044),f333(f197(f876(x81041)),x81043)))+P1(f333(f333(f335(x81041),x81042),f333(f174(x81041),f333(f333(f160(x81041,x81043),x81044),x81042)))) % 183.90/184.44 [8160]E(f333(f333(f166(x81601),f333(f333(f139(x81601),x81602),x81603)),x81604),f333(f333(f166(x81601),x81603),f333(f333(f79(a875),x81602),x81604)))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x81602),x81604)),f333(f197(f876(x81601)),x81603))) % 183.90/184.44 [8170]~P141(x81702)+E(f333(f333(f6(x81701,x81702),f333(f333(f8(a875,x81702,x81701),f103(x81702)),x81703)),x81704),f333(f103(x81702),f333(f333(f6(x81701,a875),x81703),x81704))) % 183.90/184.44 [8171]~P138(x81712)+E(f333(f333(f6(x81711,x81712),f333(f333(f8(a1,x81712,x81711),f105(x81712)),x81713)),x81714),f333(f105(x81712),f333(f333(f6(x81711,a1),x81713),x81714))) % 183.90/184.44 [8224]~P61(x82242)+E(f333(f333(f9(x82241,x82242),f333(f333(f8(x82242,x82242,x82241),f74(x82242)),x82243)),x82244),f333(f74(x82242),f333(f333(f9(x82241,x82242),x82243),x82244))) % 183.90/184.44 [8225]~P65(x82252)+E(f333(f333(f6(x82251,x82252),f333(f333(f8(x82252,x82252,x82251),f78(x82252)),x82253)),x82254),f333(f78(x82252),f333(f333(f6(x82251,x82252),x82253),x82254))) % 183.90/184.44 [8227]E(f333(f333(f6(x82271,a875),x82272),f333(f333(f22(f882(x82271,a870)),x82273),f333(f333(f311(x82271),x82274),f196(f882(x82271,a870))))),f333(f333(f22(a875),f333(f333(f6(x82271,a875),x82272),x82273)),f333(x82272,x82274)))+~P1(f333(f333(f335(x82271),x82274),x82273)) % 183.90/184.44 [8247]P1(f333(f333(f247(f882(x82471,a870)),x82472),x82473))+~P1(f333(f333(f247(f882(x82471,a870)),f333(f333(f311(x82471),x82474),x82472)),x82473)) % 183.90/184.44 [8456]E(f333(a115,f477(x84561,x84562,x84563,x84564)),x84562)+~P1(f333(f333(f333(f333(a204,f333(a25,x84564)),x84563),x84562),x84561)) % 183.90/184.44 [8458]E(f333(f333(f180(x84581,x84582),x84583),x84584),f209(x84582))+P1(f333(f333(f335(x84581),x84584),f333(f312(f881(x84581,x84582),x84581,f267(x84581,x84582)),f333(f174(f881(x84581,x84582)),x84583)))) % 183.90/184.44 [8459]P37(x84591,x84592)+~P37(x84591,f333(f333(f311(f881(x84591,x84591)),f333(f333(f268(x84591,x84591),x84593),x84594)),x84592)) % 183.90/184.44 [8460]P52(x84601,x84602)+~P52(x84601,f333(f333(f311(f881(x84601,x84601)),f333(f333(f268(x84601,x84601),x84603),x84604)),x84602)) % 183.90/184.44 [8468]~P106(x84681)+E(f333(f333(f149(x84681,x84681,f5(x84681)),x84682),f333(f333(f149(x84681,x84681,f5(x84681)),x84683),x84684)),f333(f333(f149(x84681,x84681,f5(x84681)),x84683),f333(f333(f149(x84681,x84681,f5(x84681)),x84682),x84684))) % 183.90/184.44 [8478]E(x84781,x84782)+~P1(f333(f62(x84783,x84784,f333(f333(f311(x84783),x84781),f196(f882(x84783,a870)))),x84782)) % 183.90/184.44 [8488]E(f333(f333(f135(x84881),f333(f333(f177(x84881),x84882),x84883)),f333(f333(f177(x84881),x84884),f333(f333(f139(x84881),x84882),x84883))),f333(f333(f177(x84881),f333(f333(f79(a875),x84882),x84884)),x84883))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x84882),x84884)),f333(f197(f876(x84881)),x84883))) % 183.90/184.44 [8528]P1(f333(f61(x85281),x85282))+~E(x85282,f333(f312(a875,x85281,x85283),f333(f253(a875),f333(f333(f7(a875,a875,a870),f248(a875)),x85284)))) % 183.90/184.44 [8548]~P88(x85481)+E(f333(f143(x85481,x85481,f79(x85481),f333(f333(f79(x85481),x85482),x85483)),x85484),f333(f333(f79(x85481),x85482),f333(f143(x85481,x85481,f79(x85481),x85483),x85484))) % 183.90/184.44 [8581]P1(f333(f333(f247(f882(x85811,a870)),f333(f266(x85811,x85812),x85813)),f333(f266(x85811,x85812),x85814)))+~P1(f333(f333(f247(f882(f881(x85811,x85812),a870)),x85813),x85814)) % 183.90/184.44 [8594]~P1(f333(f333(f247(a875),x85942),x85944))+P1(f333(f333(f247(f882(x85941,a870)),f333(f174(x85941),f333(f333(f177(x85941),x85942),x85943))),f333(f174(x85941),f333(f333(f177(x85941),x85944),x85943)))) % 183.90/184.44 [8595]~P1(f333(f333(f247(a875),x85954),x85952))+P1(f333(f333(f247(f882(x85951,a870)),f333(f174(x85951),f333(f333(f139(x85951),x85952),x85953))),f333(f174(x85951),f333(f333(f139(x85951),x85954),x85953)))) % 183.90/184.44 [8648]~P1(f333(f61(x86481),f333(f333(f22(f882(x86481,a870)),x86482),x86484)))+P1(f333(f61(x86481),f333(f333(f22(f882(x86481,a870)),x86482),f333(f333(f311(x86481),x86483),x86484)))) % 183.90/184.44 [8684]P1(f333(f333(f335(f881(x86841,x86841)),x86842),f309(x86841,x86843)))+~P1(f333(f333(f335(f881(x86841,x86841)),x86842),f333(f333(f191(f881(x86841,x86841),a870),x86844),x86843))) % 183.90/184.44 [8761]~P1(f333(f61(x87611),f333(f333(f22(f882(x87611,a870)),x87612),f333(f333(f311(x87611),x87614),x87613))))+P1(f333(f61(x87611),f333(f333(f22(f882(x87611,a870)),x87612),x87613))) % 183.90/184.44 [8910]~E(f333(f333(f180(x89101,x89102),x89103),x89104),f209(x89102))+~P1(f333(f333(f335(x89101),x89104),f333(f312(f881(x89101,x89102),x89101,f267(x89101,x89102)),f333(f174(f881(x89101,x89102)),x89103)))) % 183.90/184.44 [8978]~P62(x89781)+P1(f333(f333(f247(x89781),f333(f333(f113(x89781),x89782),f333(f333(f104(x89781),x89783),x89784))),f333(f333(f104(x89781),f333(f333(f113(x89781),x89782),x89783)),f333(f333(f113(x89781),x89782),x89784)))) % 183.90/184.44 [8979]~P106(x89791)+P1(f333(f333(f247(x89791),f333(f333(f246(x89791),x89792),f333(f333(f245(x89791),x89793),x89794))),f333(f333(f245(x89791),f333(f333(f246(x89791),x89792),x89793)),f333(f333(f246(x89791),x89792),x89794)))) % 183.90/184.44 [9124]E(x91241,x91242)+~P1(f333(f333(f335(f881(x91243,x91243)),f333(f333(f268(x91243,x91243),x91241),x91242)),f333(f174(f881(x91243,x91243)),f333(f333(f184(x91243,x91243),x91244),x91244)))) % 183.90/184.44 [9157]~P1(f333(f333(f335(f881(x91571,x91571)),f333(f333(f268(x91571,x91571),x91573),x91572)),f309(x91571,x91574)))+~P37(x91571,f333(f333(f311(f881(x91571,x91571)),f333(f333(f268(x91571,x91571),x91572),x91573)),x91574)) % 183.90/184.44 [9158]~P1(f333(f333(f335(f881(x91581,x91581)),f333(f333(f268(x91581,x91581),x91583),x91582)),f309(x91581,x91584)))+~P52(x91581,f333(f333(f311(f881(x91581,x91581)),f333(f333(f268(x91581,x91581),x91582),x91583)),x91584)) % 183.90/184.44 [9163]E(x91631,x91632)+E(f333(f137(x91633,f333(f333(f8(a870,a870,x91633),a328),f333(a330,x91631))),f333(f333(f152(x91633),x91632),x91634)),f333(f333(f152(x91633),x91632),f333(f137(x91633,f333(f333(f8(a870,a870,x91633),a328),f333(a330,x91631))),x91634))) % 183.90/184.44 [9207]~P62(x92071)+P1(f333(f333(f247(x92071),f333(f333(f113(x92071),f333(f333(f104(x92071),x92072),x92073)),f333(f333(f104(x92071),x92072),x92074))),f333(f333(f104(x92071),x92072),f333(f333(f113(x92071),x92073),x92074)))) % 183.90/184.44 [9208]~P106(x92081)+P1(f333(f333(f247(x92081),f333(f333(f246(x92081),f333(f333(f245(x92081),x92082),x92083)),f333(f333(f245(x92081),x92082),x92084))),f333(f333(f245(x92081),x92082),f333(f333(f246(x92081),x92083),x92084)))) % 183.90/184.44 [9282]~E(f333(f312(x92822,x92821,x92823),f256(f882(x92822,a870))),f256(f882(x92821,a870)))+P1(f333(f333(f247(f882(x92821,a870)),f333(f78(f882(x92821,a870)),f333(f312(x92822,x92821,x92823),x92824))),f333(f312(x92822,x92821,x92823),f333(f78(f882(x92822,a870)),x92824)))) % 183.90/184.44 [9360]P1(f333(f333(f333(f333(a204,f333(f244(a871),f333(a27,x93601))),x93602),f477(x93603,x93604,x93602,x93601)),x93603))+~P1(f333(f333(f333(f333(a204,f333(a25,x93601)),x93602),x93604),x93603)) % 183.90/184.44 [9602]P1(f333(f333(f335(f881(x96021,x96021)),f333(f333(f268(x96021,x96021),x96022),x96023)),f333(f288(x96021,x96021),f333(f333(f290(x96021,x96021,x96021),x96024),f309(x96021,x96024)))))+~P1(f333(f333(f335(f881(x96021,x96021)),f333(f333(f268(x96021,x96021),x96022),x96023)),f333(f333(f290(x96021,x96021,x96021),f333(f288(x96021,x96021),x96024)),f309(x96021,f333(f288(x96021,x96021),x96024))))) % 183.90/184.44 [9603]~P1(f333(f333(f335(f881(x96031,x96031)),f333(f333(f268(x96031,x96031),x96032),x96033)),f333(f288(x96031,x96031),f333(f333(f290(x96031,x96031,x96031),x96034),f309(x96031,x96034)))))+P1(f333(f333(f335(f881(x96031,x96031)),f333(f333(f268(x96031,x96031),x96032),x96033)),f333(f333(f290(x96031,x96031,x96031),f333(f288(x96031,x96031),x96034)),f309(x96031,f333(f288(x96031,x96031),x96034))))) % 183.90/184.44 [9624]~P1(f333(f333(f335(x96242),x96244),f333(f264(x96241,x96242),x96243)))+P1(f333(f333(f335(f881(x96241,x96242)),f333(f333(f268(x96241,x96242),f570(x96243,x96241,x96244,x96242)),x96244)),x96243)) % 183.90/184.44 [9625]~P1(f333(f333(f335(x96252),x96254),f333(f264(x96251,x96252),x96253)))+P1(f333(f333(f335(f881(x96251,x96252)),f333(f333(f268(x96251,x96252),f573(x96253,x96251,x96254,x96252)),x96254)),x96253)) % 183.90/184.44 [9650]~P1(f333(f333(f335(x96501),x96504),f333(f333(f113(f882(x96501,a870)),x96502),x96503)))+P1(f333(f333(f333(f113(f882(x96501,a870)),f333(f333(f7(x96501,f882(x96501,a870),a870),f335(x96501)),x96502)),f333(f333(f7(x96501,f882(x96501,a870),a870),f335(x96501)),x96503)),x96504)) % 183.90/184.44 [9651]~P1(f333(f333(f335(x96511),x96514),f333(f333(f104(f882(x96511,a870)),x96512),x96513)))+P1(f333(f333(f333(f104(f882(x96511,a870)),f333(f333(f7(x96511,f882(x96511,a870),a870),f335(x96511)),x96512)),f333(f333(f7(x96511,f882(x96511,a870),a870),f335(x96511)),x96513)),x96514)) % 183.90/184.44 [9727]~P1(f333(f333(f335(f881(x97271,x97271)),f333(f333(f268(x97271,x97271),x97274),x97273)),f333(f333(f290(x97271,x97271,x97271),x97272),f309(x97271,x97272))))+P1(f333(f333(f335(f881(x97271,x97271)),f333(f333(f268(x97271,x97271),f650(x97272,x97273,x97274,x97271)),x97273)),x97272)) % 183.90/184.44 [9772]P1(f333(f333(f335(x97721),x97722),f333(f333(f113(f882(x97721,a870)),x97723),x97724)))+~P1(f333(f333(f333(f113(f882(x97721,a870)),f333(f333(f7(x97721,f882(x97721,a870),a870),f335(x97721)),x97723)),f333(f333(f7(x97721,f882(x97721,a870),a870),f335(x97721)),x97724)),x97722)) % 183.90/184.44 [9773]P1(f333(f333(f335(x97731),x97732),f333(f333(f104(f882(x97731,a870)),x97733),x97734)))+~P1(f333(f333(f333(f104(f882(x97731,a870)),f333(f333(f7(x97731,f882(x97731,a870),a870),f335(x97731)),x97733)),f333(f333(f7(x97731,f882(x97731,a870),a870),f335(x97731)),x97734)),x97732)) % 183.90/184.44 [10052]P32(x100521,f333(f333(f7(x100521,f882(f881(x100521,x100521),a870),f882(x100521,a870)),f333(f333(f8(f882(x100521,f882(f882(f881(x100521,x100521),a870),a870)),f882(f882(f881(x100521,x100521),a870),f882(x100521,a870)),x100521),f7(x100521,f882(f881(x100521,x100521),a870),a870)),f333(f333(f8(f882(x100521,f881(x100521,x100521)),f882(x100521,f882(f882(f881(x100521,x100521),a870),a870)),x100521),f333(f8(f881(x100521,x100521),f882(f882(f881(x100521,x100521),a870),a870),x100521),f335(f881(x100521,x100521)))),f268(x100521,x100521)))),x100522),x100523,x100524)+~P1(f333(f333(f335(f881(f876(x100521),f876(x100521))),f333(f333(f268(f876(x100521),f876(x100521)),x100523),x100524)),f159(x100521,x100522))) % 183.90/184.44 [10056]P53(x100561,f333(f333(f7(x100561,f882(f881(x100561,x100561),a870),f882(x100561,a870)),f333(f333(f8(f882(x100561,f882(f882(f881(x100561,x100561),a870),a870)),f882(f882(f881(x100561,x100561),a870),f882(x100561,a870)),x100561),f7(x100561,f882(f881(x100561,x100561),a870),a870)),f333(f333(f8(f882(x100561,f881(x100561,x100561)),f882(x100561,f882(f882(f881(x100561,x100561),a870),a870)),x100561),f333(f8(f881(x100561,x100561),f882(f882(f881(x100561,x100561),a870),a870),x100561),f335(f881(x100561,x100561)))),f268(x100561,x100561)))),x100562),x100563,x100564)+~P1(f333(f333(f335(f881(f882(x100561,a870),f882(x100561,a870))),f333(f333(f268(f882(x100561,a870),f882(x100561,a870)),x100563),x100564)),f325(x100561,x100562))) % 183.90/184.44 [10085]E(x100851,x100852)+~E(f333(f333(f7(x100853,f882(f881(x100853,x100854),a870),f882(x100854,a870)),f333(f333(f8(f882(x100854,f882(f882(f881(x100853,x100854),a870),a870)),f882(f882(f881(x100853,x100854),a870),f882(x100854,a870)),x100853),f7(x100854,f882(f881(x100853,x100854),a870),a870)),f333(f333(f8(f882(x100854,f881(x100853,x100854)),f882(x100854,f882(f882(f881(x100853,x100854),a870),a870)),x100853),f333(f8(f881(x100853,x100854),f882(f882(f881(x100853,x100854),a870),a870),x100854),f335(f881(x100853,x100854)))),f268(x100853,x100854)))),x100851),f333(f333(f7(x100853,f882(f881(x100853,x100854),a870),f882(x100854,a870)),f333(f333(f8(f882(x100854,f882(f882(f881(x100853,x100854),a870),a870)),f882(f882(f881(x100853,x100854),a870),f882(x100854,a870)),x100853),f7(x100854,f882(f881(x100853,x100854),a870),a870)),f333(f333(f8(f882(x100854,f881(x100853,x100854)),f882(x100854,f882(f882(f881(x100853,x100854),a870),a870)),x100853),f333(f8(f881(x100853,x100854),f882(f882(f881(x100853,x100854),a870),a870),x100854),f335(f881(x100853,x100854)))),f268(x100853,x100854)))),x100852)) % 183.90/184.44 [10089]~P32(x100891,f333(f333(f7(x100891,f882(f881(x100891,x100891),a870),f882(x100891,a870)),f333(f333(f8(f882(x100891,f882(f882(f881(x100891,x100891),a870),a870)),f882(f882(f881(x100891,x100891),a870),f882(x100891,a870)),x100891),f7(x100891,f882(f881(x100891,x100891),a870),a870)),f333(f333(f8(f882(x100891,f881(x100891,x100891)),f882(x100891,f882(f882(f881(x100891,x100891),a870),a870)),x100891),f333(f8(f881(x100891,x100891),f882(f882(f881(x100891,x100891),a870),a870),x100891),f335(f881(x100891,x100891)))),f268(x100891,x100891)))),x100894),x100892,x100893)+P1(f333(f333(f335(f881(f876(x100891),f876(x100891))),f333(f333(f268(f876(x100891),f876(x100891)),x100892),x100893)),f159(x100891,x100894))) % 183.90/184.44 [10090]~P53(x100901,f333(f333(f7(x100901,f882(f881(x100901,x100901),a870),f882(x100901,a870)),f333(f333(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)),f333(f333(f8(f882(x100901,f881(x100901,x100901)),f882(x100901,f882(f882(f881(x100901,x100901),a870),a870)),x100901),f333(f8(f881(x100901,x100901),f882(f882(f881(x100901,x100901),a870),a870),x100901),f335(f881(x100901,x100901)))),f268(x100901,x100901)))),x100904),x100902,x100903)+P1(f333(f333(f335(f881(f882(x100901,a870),f882(x100901,a870))),f333(f333(f268(f882(x100901,a870),f882(x100901,a870)),x100902),x100903)),f325(x100901,x100904))) % 183.90/184.44 [7464]~P90(x74641)+E(f333(f333(f79(x74641),f333(f106(x74641),x74642)),f333(f333(f22(x74641),f333(f106(x74641),x74643)),x74644)),f333(f333(f22(x74641),f333(f106(x74641),f333(f333(f79(a1),x74642),x74643))),x74644)) % 183.90/184.44 [7465]~P90(x74651)+E(f333(f333(f79(x74651),f333(f106(x74651),x74652)),f333(f333(f79(x74651),f333(f106(x74651),x74653)),x74654)),f333(f333(f79(x74651),f333(f106(x74651),f333(f333(f79(a1),x74652),x74653))),x74654)) % 183.90/184.44 [7466]~P90(x74661)+E(f333(f333(f80(x74661),f333(f106(x74661),x74662)),f333(f333(f80(x74661),f333(f106(x74661),x74663)),x74664)),f333(f333(f80(x74661),f333(f106(x74661),f333(f333(f80(a1),x74662),x74663))),x74664)) % 183.90/184.44 [7511]~P141(x75111)+E(f333(f167(x75111),f333(f333(f155(x75112,x75111),f333(f16(x75111,x75112),x75113)),x75114)),f333(f333(f80(x75111),f333(f103(x75111),f333(f197(f876(x75112)),x75114))),x75113)) % 183.90/184.44 [7749]E(f333(f279(x77491,f333(f333(f152(f881(a102,x77491)),x77492),x77493)),x77494),f333(f271(a102,x77491),x77492))+~P1(f333(f333(f248(a102),x77494),f333(f267(a102,x77491),x77492))) % 183.90/184.44 [7796]~P90(x77961)+E(f333(f333(f79(x77961),f333(f106(x77961),x77962)),f333(f333(f22(x77961),x77963),f333(f106(x77961),x77964))),f333(f333(f79(x77961),f333(f106(x77961),f333(f333(f79(a1),x77962),f333(f78(a1),x77964)))),x77963)) % 183.90/184.44 [7928]E(f333(f279(x79281,x79282),f333(f333(f22(a102),x79283),f333(f267(a102,x79281),x79284))),f333(f279(x79281,f333(f333(f152(f881(a102,x79281)),x79284),x79282)),x79283))+P1(f333(f333(f248(a102),x79283),f333(f267(a102,x79281),x79284))) % 183.90/184.44 [8373]~P1(f333(f333(f335(x83731),x83732),f333(f174(x83731),f117(x83731,x83734))))+P1(f333(f333(f335(x83731),x83732),f333(f174(x83731),f117(x83731,f333(f333(f135(x83731),x83733),x83734))))) % 183.90/184.44 [8374]~P1(f333(f333(f335(x83741),x83742),f333(f174(x83741),f117(x83741,x83743))))+P1(f333(f333(f335(x83741),x83742),f333(f174(x83741),f117(x83741,f333(f333(f135(x83741),x83743),x83744))))) % 183.90/184.44 [8394]E(f333(f333(f113(f882(x83941,a870)),f333(f333(f104(f882(x83941,a870)),x83942),x83943)),x83944),f333(f333(f104(f882(x83941,a870)),x83942),f333(f333(f113(f882(x83941,a870)),x83943),x83944)))+~P1(f333(f333(f247(f882(x83941,a870)),x83944),x83942)) % 183.90/184.44 [8697]~E(f333(f333(f113(f882(x86971,a870)),f333(f333(f104(f882(x86971,a870)),x86973),x86974)),x86972),f333(f333(f104(f882(x86971,a870)),x86973),f333(f333(f113(f882(x86971,a870)),x86974),x86972)))+P1(f333(f333(f247(f882(x86971,a870)),x86972),x86973)) % 183.90/184.44 [8984]~P1(f333(f333(f247(f882(x89841,a870)),x89842),f333(f333(f113(f882(x89841,a870)),x89843),x89844)))+P1(f333(f333(f247(f882(x89841,a870)),f333(f333(f22(f882(x89841,a870)),x89842),x89843)),x89844)) % 183.90/184.44 [9043]~P1(f333(f333(f333(f333(a204,f333(a25,x90431)),x90432),f333(a115,x90433)),x90434))+P1(f333(f333(f333(f333(a204,f333(f244(a871),f333(a27,x90431))),x90432),x90433),x90434)) % 183.90/184.44 [9103]P1(f333(f333(f247(f882(x91031,a870)),x91032),f333(f333(f113(f882(x91031,a870)),x91033),x91034)))+~P1(f333(f333(f247(f882(x91031,a870)),f333(f333(f22(f882(x91031,a870)),x91032),x91033)),x91034)) % 183.90/184.44 [9156]P1(f333(f333(f333(f333(a204,f333(a25,x91561)),x91562),f333(a115,x91563)),x91564))+~P1(f333(f333(f333(f333(a204,f333(f244(a871),f333(a27,x91561))),x91562),x91563),x91564)) % 183.90/184.44 [9188]~P83(x91881)+E(f333(f74(x91881),f333(f333(f6(x91882,x91881),f333(f333(f8(x91881,x91881,x91882),f74(x91881)),x91883)),x91884)),f333(f333(f6(x91882,x91881),f333(f333(f8(x91881,x91881,x91882),f74(x91881)),x91883)),x91884)) % 183.90/184.44 [9358]~P83(x93581)+P1(f333(f333(f247(x93581),f2(x93581)),f333(f333(f6(x93582,x93581),f333(f333(f8(x93581,x93581,x93582),f74(x93581)),x93583)),x93584))) % 183.90/184.44 [9363]~P65(x93631)+E(f333(f167(x93631),f333(f333(f155(x93632,x93631),f333(f72(x93631,x93631,x93632,f78(x93631)),x93633)),x93634)),f333(f78(x93631),f333(f167(x93631),f333(f333(f155(x93632,x93631),x93633),x93634)))) % 183.90/184.44 [9497]~P83(x94971)+P1(f333(f333(f247(x94971),f333(f74(x94971),f333(f333(f6(x94972,x94971),x94973),x94974))),f333(f333(f6(x94972,x94971),f333(f333(f8(x94971,x94971,x94972),f74(x94971)),x94973)),x94974))) % 183.90/184.44 [9527]~E(f333(f333(f79(a875),x95271),x95274),f333(f333(f79(a875),x95273),x95272))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x95271),x95272)),f333(f333(f268(a875,a875),x95273),x95274))),a111)) % 183.90/184.44 [9528]~P1(f333(f333(f248(a875),x95281),x95283))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x95281),x95282)),f333(f333(f268(a875,a875),x95283),x95284))),a34)) % 183.90/184.44 [9529]~P1(f333(f333(f248(a875),x95291),x95293))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x95291),x95292)),f333(f333(f268(a875,a875),x95293),x95294))),a69)) % 183.90/184.44 [9675]E(f333(f333(f79(a875),x96751),x96752),f333(f333(f79(a875),x96753),x96754))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x96751),x96754)),f333(f333(f268(a875,a875),x96753),x96752))),a111)) % 183.90/184.44 [9701]E(f333(f333(f166(x97011),f333(f333(f139(x97011),f333(f197(f876(x97011)),f179(x97011,x97012,x97013))),x97013)),x97014),f333(f333(f166(x97011),x97013),f333(f333(f79(a875),x97014),f333(f197(f876(x97011)),f179(x97011,x97012,x97013)))))+~P1(f333(f333(f248(a875),x97014),f333(f197(f876(x97011)),f333(f333(f139(x97011),f333(f197(f876(x97011)),f179(x97011,x97012,x97013))),x97013)))) % 183.90/184.44 [9718]~P1(f333(f333(f335(x97182),x97184),f333(f333(f41(x97181,f882(x97182,a870)),f256(f882(x97181,a870))),x97183)))+P1(f333(f333(f333(f41(x97181,f882(x97182,a870)),f256(f882(x97181,a870))),f333(f333(f8(f882(x97182,a870),f882(x97182,a870),x97181),f333(f7(x97182,f882(x97182,a870),a870),f335(x97182))),x97183)),x97184)) % 183.90/184.44 [9719]~P1(f333(f333(f335(x97192),x97194),f333(f333(f42(x97191,f882(x97192,a870)),f256(f882(x97191,a870))),x97193)))+P1(f333(f333(f333(f42(x97191,f882(x97192,a870)),f256(f882(x97191,a870))),f333(f333(f8(f882(x97192,a870),f882(x97192,a870),x97191),f333(f7(x97192,f882(x97192,a870),a870),f335(x97192))),x97193)),x97194)) % 183.90/184.44 [9800]~P1(f333(f48(x98001,x98002),f333(f333(f268(a1,a1),x98004),x98003)))+P1(f333(f48(f333(f78(a1),x98001),x98002),f333(f333(f268(a1,a1),f333(f333(f333(f99(a1),f333(f333(a330,x98003),f2(a1))),f333(f78(a1),x98004)),f333(f333(f22(a1),f333(f78(a1),x98004)),f77(a1)))),f333(f333(f333(f99(a1),f333(f333(a330,x98003),f2(a1))),f2(a1)),f333(f333(f22(a1),x98002),x98003))))) % 183.90/184.44 [9809]P1(f333(f333(f335(x98091),x98092),f333(f333(f41(x98093,f882(x98091,a870)),f256(f882(x98093,a870))),x98094)))+~P1(f333(f333(f333(f41(x98093,f882(x98091,a870)),f256(f882(x98093,a870))),f333(f333(f8(f882(x98091,a870),f882(x98091,a870),x98093),f333(f7(x98091,f882(x98091,a870),a870),f335(x98091))),x98094)),x98092)) % 183.90/184.44 [9810]P1(f333(f333(f335(x98101),x98102),f333(f333(f42(x98103,f882(x98101,a870)),f256(f882(x98103,a870))),x98104)))+~P1(f333(f333(f333(f42(x98103,f882(x98101,a870)),f256(f882(x98103,a870))),f333(f333(f8(f882(x98101,a870),f882(x98101,a870),x98103),f333(f7(x98101,f882(x98101,a870),a870),f335(x98101))),x98104)),x98102)) % 183.90/184.44 [9822]E(f333(f333(f41(a875,f882(x98221,a870)),f256(f882(a875,a870))),x98222),f333(f333(f41(a875,f882(x98221,a870)),f256(f882(a875,a870))),x98223))+~E(f333(f333(f41(a875,f882(x98221,a870)),f333(f303(a875,f2(a875)),f394(x98222,x98224,x98223,x98221))),x98223),f333(f333(f41(a875,f882(x98221,a870)),f333(f303(a875,f2(a875)),f333(f333(f79(a875),f394(x98222,x98224,x98223,x98221)),x98224))),x98222)) % 183.90/184.44 [10143]~P1(f333(f333(f247(f882(f881(x101431,x101432),a870)),x101433),x101434))+P1(f333(f333(f247(f882(x101431,f882(x101432,a870))),f333(f333(f7(x101431,f882(f881(x101431,x101432),a870),f882(x101432,a870)),f333(f333(f8(f882(x101432,f882(f882(f881(x101431,x101432),a870),a870)),f882(f882(f881(x101431,x101432),a870),f882(x101432,a870)),x101431),f7(x101432,f882(f881(x101431,x101432),a870),a870)),f333(f333(f8(f882(x101432,f881(x101431,x101432)),f882(x101432,f882(f882(f881(x101431,x101432),a870),a870)),x101431),f333(f8(f881(x101431,x101432),f882(f882(f881(x101431,x101432),a870),a870),x101432),f335(f881(x101431,x101432)))),f268(x101431,x101432)))),x101433)),f333(f333(f7(x101431,f882(f881(x101431,x101432),a870),f882(x101432,a870)),f333(f333(f8(f882(x101432,f882(f882(f881(x101431,x101432),a870),a870)),f882(f882(f881(x101431,x101432),a870),f882(x101432,a870)),x101431),f7(x101432,f882(f881(x101431,x101432),a870),a870)),f333(f333(f8(f882(x101432,f881(x101431,x101432)),f882(x101432,f882(f882(f881(x101431,x101432),a870),a870)),x101431),f333(f8(f881(x101431,x101432),f882(f882(f881(x101431,x101432),a870),a870),x101432),f335(f881(x101431,x101432)))),f268(x101431,x101432)))),x101434))) % 183.90/184.44 [10160]P1(f333(f333(f247(f882(f881(x101601,x101602),a870)),x101603),x101604))+~P1(f333(f333(f247(f882(x101601,f882(x101602,a870))),f333(f333(f7(x101601,f882(f881(x101601,x101602),a870),f882(x101602,a870)),f333(f333(f8(f882(x101602,f882(f882(f881(x101601,x101602),a870),a870)),f882(f882(f881(x101601,x101602),a870),f882(x101602,a870)),x101601),f7(x101602,f882(f881(x101601,x101602),a870),a870)),f333(f333(f8(f882(x101602,f881(x101601,x101602)),f882(x101602,f882(f882(f881(x101601,x101602),a870),a870)),x101601),f333(f8(f881(x101601,x101602),f882(f882(f881(x101601,x101602),a870),a870),x101602),f335(f881(x101601,x101602)))),f268(x101601,x101602)))),x101603)),f333(f333(f7(x101601,f882(f881(x101601,x101602),a870),f882(x101602,a870)),f333(f333(f8(f882(x101602,f882(f882(f881(x101601,x101602),a870),a870)),f882(f882(f881(x101601,x101602),a870),f882(x101602,a870)),x101601),f7(x101602,f882(f881(x101601,x101602),a870),a870)),f333(f333(f8(f882(x101602,f881(x101601,x101602)),f882(x101602,f882(f882(f881(x101601,x101602),a870),a870)),x101601),f333(f8(f881(x101601,x101602),f882(f882(f881(x101601,x101602),a870),a870),x101602),f335(f881(x101601,x101602)))),f268(x101601,x101602)))),x101604))) % 183.90/184.44 [9237]~P1(f333(f333(f335(f881(x92371,x92371)),x92372),f309(x92371,x92374)))+P1(f333(f333(f335(f881(x92371,x92371)),x92372),f309(x92371,f333(f333(f113(f882(f881(x92371,x92371),a870)),x92373),x92374)))) % 183.90/184.44 [9238]~P1(f333(f333(f335(f881(x92381,x92381)),x92382),f309(x92381,x92383)))+P1(f333(f333(f335(f881(x92381,x92381)),x92382),f309(x92381,f333(f333(f113(f882(f881(x92381,x92381),a870)),x92383),x92384)))) % 183.90/184.44 [9594]~E(f333(f174(x95941),x95944),f186(x95941,x95942,x95943))+E(f333(f180(x95941,x95942),f333(f333(f155(x95941,f881(x95941,x95942)),f333(f333(f18(x95941,x95942,f881(x95941,x95942)),f268(x95941,x95942)),f333(f333(f8(f879(x95942),x95942,x95941),f244(x95942)),x95943))),x95944)),x95943) % 183.90/184.44 [9916]~P1(f333(f333(f248(a875),f333(f333(f79(a875),x99161),x99164)),f333(f333(f79(a875),x99163),x99162)))+P1(f333(f333(f248(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99161),x99162)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99163),x99164)),f196(f882(f881(a875,a875),a870))))))) % 183.90/184.44 [9917]~P1(f333(f333(f247(a875),f333(f333(f79(a875),x99171),x99174)),f333(f333(f79(a875),x99173),x99172)))+P1(f333(f333(f247(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99171),x99172)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99173),x99174)),f196(f882(f881(a875,a875),a870))))))) % 183.90/184.44 [9994]P1(f333(f333(f248(a875),f333(f333(f79(a875),x99941),x99942)),f333(f333(f79(a875),x99943),x99944)))+~P1(f333(f333(f248(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99941),x99944)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99943),x99942)),f196(f882(f881(a875,a875),a870))))))) % 183.90/184.44 [9995]P1(f333(f333(f247(a875),f333(f333(f79(a875),x99951),x99952)),f333(f333(f79(a875),x99953),x99954)))+~P1(f333(f333(f247(a1),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99951),x99954)),f196(f882(f881(a875,a875),a870)))))),f333(a88,f333(f287(f881(a875,a875),f881(a875,a875),a111),f333(f333(f311(f881(a875,a875)),f333(f333(f268(a875,a875),x99953),x99952)),f196(f882(f881(a875,a875),a870))))))) % 183.90/184.44 [10037]P1(f333(f333(f247(f882(x100371,a870)),f333(f333(f41(a875,f882(x100371,a870)),f256(f882(a875,a870))),x100372)),f333(f333(f41(a875,f882(x100371,a870)),f256(f882(a875,a870))),x100373)))+~P1(f333(f333(f247(f882(x100371,a870)),f333(f333(f41(a875,f882(x100371,a870)),f333(f303(a875,f2(a875)),f395(x100373,x100374,x100372,x100371))),x100372)),f333(f333(f41(a875,f882(x100371,a870)),f333(f303(a875,f2(a875)),f333(f333(f79(a875),f395(x100373,x100374,x100372,x100371)),x100374))),x100373))) % 183.90/184.44 [10134]~P1(f333(f333(f335(x101342),x101344),f333(f264(x101341,x101342),x101343)))+P1(f333(f263(x101341,x101342,f333(f333(f7(x101341,f882(f881(x101341,x101342),a870),f882(x101342,a870)),f333(f333(f8(f882(x101342,f882(f882(f881(x101341,x101342),a870),a870)),f882(f882(f881(x101341,x101342),a870),f882(x101342,a870)),x101341),f7(x101342,f882(f881(x101341,x101342),a870),a870)),f333(f333(f8(f882(x101342,f881(x101341,x101342)),f882(x101342,f882(f882(f881(x101341,x101342),a870),a870)),x101341),f333(f8(f881(x101341,x101342),f882(f882(f881(x101341,x101342),a870),a870),x101342),f335(f881(x101341,x101342)))),f268(x101341,x101342)))),x101343)),x101344)) % 183.90/184.44 [10135]~P1(f333(f333(f335(x101351),x101354),f333(f266(x101351,x101352),x101353)))+P1(f333(f262(x101351,x101352,f333(f333(f7(x101351,f882(f881(x101351,x101352),a870),f882(x101352,a870)),f333(f333(f8(f882(x101352,f882(f882(f881(x101351,x101352),a870),a870)),f882(f882(f881(x101351,x101352),a870),f882(x101352,a870)),x101351),f7(x101352,f882(f881(x101351,x101352),a870),a870)),f333(f333(f8(f882(x101352,f881(x101351,x101352)),f882(x101352,f882(f882(f881(x101351,x101352),a870),a870)),x101351),f333(f8(f881(x101351,x101352),f882(f882(f881(x101351,x101352),a870),a870),x101352),f335(f881(x101351,x101352)))),f268(x101351,x101352)))),x101353)),x101354)) % 183.90/184.44 [10146]P1(f333(f333(f335(x101461),x101462),f333(f264(x101463,x101461),x101464)))+~P1(f333(f263(x101463,x101461,f333(f333(f7(x101463,f882(f881(x101463,x101461),a870),f882(x101461,a870)),f333(f333(f8(f882(x101461,f882(f882(f881(x101463,x101461),a870),a870)),f882(f882(f881(x101463,x101461),a870),f882(x101461,a870)),x101463),f7(x101461,f882(f881(x101463,x101461),a870),a870)),f333(f333(f8(f882(x101461,f881(x101463,x101461)),f882(x101461,f882(f882(f881(x101463,x101461),a870),a870)),x101463),f333(f8(f881(x101463,x101461),f882(f882(f881(x101463,x101461),a870),a870),x101461),f335(f881(x101463,x101461)))),f268(x101463,x101461)))),x101464)),x101462)) % 183.90/184.44 [10147]P1(f333(f333(f335(x101471),x101472),f333(f266(x101471,x101473),x101474)))+~P1(f333(f262(x101471,x101473,f333(f333(f7(x101471,f882(f881(x101471,x101473),a870),f882(x101473,a870)),f333(f333(f8(f882(x101473,f882(f882(f881(x101471,x101473),a870),a870)),f882(f882(f881(x101471,x101473),a870),f882(x101473,a870)),x101471),f7(x101473,f882(f881(x101471,x101473),a870),a870)),f333(f333(f8(f882(x101473,f881(x101471,x101473)),f882(x101473,f882(f882(f881(x101471,x101473),a870),a870)),x101471),f333(f8(f881(x101471,x101473),f882(f882(f881(x101471,x101473),a870),a870),x101473),f335(f881(x101471,x101473)))),f268(x101471,x101473)))),x101474)),x101472)) % 183.90/184.44 [9832]P1(f333(f161(x98321,x98322),x98323))+~P1(f333(f161(x98321,f333(f333(f18(x98321,a870,a870),f333(f333(f8(a870,f882(a870,a870),x98321),a331),x98324)),x98322)),x98323)) % 183.90/184.44 [9833]P1(f333(f161(x98331,x98332),x98333))+~P1(f333(f161(x98331,f333(f333(f18(x98331,a870,a870),f333(f333(f8(a870,f882(a870,a870),x98331),a331),x98332)),x98334)),x98333)) % 183.90/184.44 [9918]~P109(x99181)+E(f333(f333(f80(x99181),f333(f333(f79(x99181),f77(x99181)),f77(x99181))),f333(f333(f6(a875,x99181),f333(f333(f8(x99181,x99181,a875),f333(f79(x99181),x99182)),f333(f333(f7(a875,x99181,x99181),f333(f333(f8(x99181,f882(x99181,x99181),a875),f80(x99181)),f103(x99181))),x99183))),f333(f254(a875),x99184))),f333(f333(f80(x99181),f333(f103(x99181),x99184)),f333(f333(f79(x99181),x99182),f333(f333(f79(x99181),x99182),f333(f333(f80(x99181),f333(f103(x99181),f333(f333(f22(a875),x99184),f77(a875)))),x99183))))) % 183.90/184.44 [10059]P1(f333(x100591,f569(x100592,x100593,x100594,x100591)))+P37(x100592,f333(f253(f881(x100592,x100592)),f333(f272(x100592,x100592,a870),f333(f333(f8(f882(x100592,a870),f882(x100592,a870),x100592),f333(f18(x100592,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100592),a331),x100591))),f333(f333(f7(x100592,f882(x100592,x100592),f882(x100592,a870)),f333(f333(f8(f882(x100592,a870),f882(f882(x100592,x100592),f882(x100592,a870)),x100592),f8(x100592,a870,x100592)),a330)),x100593))))) % 183.90/184.44 [10073]~P1(f333(f333(f248(a875),f333(x100734,f333(x100733,f569(x100731,x100733,x100734,x100732)))),f333(x100734,f569(x100731,x100733,x100734,x100732))))+P37(x100731,f333(f253(f881(x100731,x100731)),f333(f272(x100731,x100731,a870),f333(f333(f8(f882(x100731,a870),f882(x100731,a870),x100731),f333(f18(x100731,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100731),a331),x100732))),f333(f333(f7(x100731,f882(x100731,x100731),f882(x100731,a870)),f333(f333(f8(f882(x100731,a870),f882(f882(x100731,x100731),f882(x100731,a870)),x100731),f8(x100731,a870,x100731)),a330)),x100733))))) % 183.90/184.44 [10173]~P1(f333(f333(f335(f881(x101731,x101731)),f333(f333(f268(x101731,x101731),x101733),x101734)),f333(f333(f113(f882(f881(x101731,x101731),a870)),x101732),f309(x101731,f196(f882(f881(x101731,x101731),a870))))))+P1(f333(f333(f333(f333(f113(f882(x101731,f882(x101731,a870))),f333(f333(f7(x101731,f882(f881(x101731,x101731),a870),f882(x101731,a870)),f333(f333(f8(f882(x101731,f882(f882(f881(x101731,x101731),a870),a870)),f882(f882(f881(x101731,x101731),a870),f882(x101731,a870)),x101731),f7(x101731,f882(f881(x101731,x101731),a870),a870)),f333(f333(f8(f882(x101731,f881(x101731,x101731)),f882(x101731,f882(f882(f881(x101731,x101731),a870),a870)),x101731),f333(f8(f881(x101731,x101731),f882(f882(f881(x101731,x101731),a870),a870),x101731),f335(f881(x101731,x101731)))),f268(x101731,x101731)))),x101732)),a330),x101733),x101734)) % 183.90/184.44 [10183]P1(f333(f333(f335(f881(x101831,x101831)),f333(f333(f268(x101831,x101831),x101832),x101833)),f333(f333(f113(f882(f881(x101831,x101831),a870)),x101834),f309(x101831,f196(f882(f881(x101831,x101831),a870))))))+~P1(f333(f333(f333(f333(f113(f882(x101831,f882(x101831,a870))),f333(f333(f7(x101831,f882(f881(x101831,x101831),a870),f882(x101831,a870)),f333(f333(f8(f882(x101831,f882(f882(f881(x101831,x101831),a870),a870)),f882(f882(f881(x101831,x101831),a870),f882(x101831,a870)),x101831),f7(x101831,f882(f881(x101831,x101831),a870),a870)),f333(f333(f8(f882(x101831,f881(x101831,x101831)),f882(x101831,f882(f882(f881(x101831,x101831),a870),a870)),x101831),f333(f8(f881(x101831,x101831),f882(f882(f881(x101831,x101831),a870),a870),x101831),f335(f881(x101831,x101831)))),f268(x101831,x101831)))),x101834)),a330),x101832),x101833)) % 183.90/184.44 [10045]~P107(x100453)+E(f89(x100451,f333(f333(f18(x100451,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100451),a331),x100452)),f333(f333(f8(f882(x100451,a870),a870,x100451),f87(x100451)),f333(f333(f8(f882(x100451,a870),f882(x100451,a870),x100451),f333(f18(x100451,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100451),a336),x100452))),f333(f333(f8(x100453,f882(x100451,a870),x100451),f333(f7(x100451,x100453,a870),f333(f333(f8(x100453,f882(x100453,a870),x100451),f247(x100453)),x100454))),x100454))))),f333(f92(x100451,x100453,x100454),x100452)) % 183.90/184.44 [10088]~P107(x100883)+E(f89(x100881,f333(f333(f18(x100881,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100881),a331),x100882)),f333(f333(f8(f882(x100881,a870),a870,x100881),f87(x100881)),f333(f333(f8(f882(x100881,a870),f882(x100881,a870),x100881),f333(f18(x100881,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100881),a336),x100882))),f333(f333(f7(x100881,f882(x100881,x100883),f882(x100881,a870)),f333(f333(f8(f882(x100883,a870),f882(f882(x100881,x100883),f882(x100881,a870)),x100881),f8(x100883,a870,x100881)),f333(f333(f8(x100883,f882(x100883,a870),x100881),f247(x100883)),x100884))),x100884))))),f95(x100881,x100883,x100884,x100882)) % 183.90/184.44 [10132]E(f333(f333(f152(f876(x101321)),f333(f333(f152(x101321),x101322),f333(f143(f876(x101321),f876(x101321),f135(x101321),f116(x101321)),f333(f333(f155(f876(x101321),f876(x101321)),f157(f876(x101321),x101321,f116(x101321),f333(f333(f8(f876(x101321),f882(f876(x101321),f876(x101321)),x101321),f16(f876(x101321),f876(x101321))),f333(f333(f7(x101321,f876(x101321),f876(x101321)),f152(x101321)),f116(x101321))))),x101323)))),f182(x101321,f333(f333(f152(f876(x101321)),x101324),f333(f143(f876(f876(x101321)),f876(f876(x101321)),f135(f876(x101321)),f116(f876(x101321))),f333(f333(f155(f876(x101321),f876(f876(x101321))),f157(f876(f876(x101321)),x101321,f116(f876(x101321)),f333(f16(f882(f876(x101321),f876(f876(x101321))),x101321),f333(f333(f7(f876(x101321),f876(f876(x101321)),f876(f876(x101321))),f152(f876(x101321))),f116(f876(x101321)))))),x101323))))),f182(x101321,f333(f333(f152(f876(x101321)),f333(f333(f152(x101321),x101322),x101324)),x101323)))+~P1(f333(f321(f876(f876(x101321)),f183(x101321)),f333(f333(f152(f876(x101321)),f333(f333(f152(x101321),x101322),x101324)),x101323))) % 183.90/184.44 [10172]~P1(f333(f61(x101722),f333(f253(x101722),x101724)))+P1(f333(f61(x101721),f333(f253(x101721),f333(f333(f8(f882(x101722,a870),a870,x101721),f86(x101722)),f333(f333(f7(x101721,f882(x101722,a870),f882(x101722,a870)),f333(f333(f8(f882(x101722,f882(a870,a870)),f882(f882(x101722,a870),f882(x101722,a870)),x101721),f18(x101722,a870,a870)),f333(f333(f8(f882(x101722,a870),f882(x101722,f882(a870,a870)),x101721),f333(f8(a870,f882(a870,a870),x101722),a331)),f333(f333(f7(x101721,f882(x101722,x101721),f882(x101722,a870)),f333(f333(f8(f882(x101721,a870),f882(f882(x101722,x101721),f882(x101722,a870)),x101721),f8(x101721,a870,x101722)),a330)),x101723)))),x101724))))) % 183.90/184.44 [5260]E(x52601,x52602)+~E(f128(x52603,x52604,x52601),f128(x52603,x52605,x52602)) % 183.90/184.44 [5261]E(x52611,x52612)+~E(f128(x52613,x52611,x52614),f128(x52613,x52612,x52615)) % 183.90/184.44 [5262]E(x52621,x52622)+~E(f171(x52623,x52621,x52624),f171(x52623,x52622,x52625)) % 183.90/184.44 [5640]E(f333(f333(f311(x56401),x56402),f186(x56401,x56403,x56404)),f186(x56401,x56403,x56404))+~E(f333(x56404,x56402),f333(f240(x56403),x56405)) % 183.90/184.44 [6046]P1(f333(f263(x60461,x60462,x60463),x60464))+~P1(f333(f333(x60463,x60465),x60464)) % 183.90/184.44 [6048]P1(f333(f262(x60481,x60482,x60483),x60484))+~P1(f333(f333(x60483,x60484),x60485)) % 183.90/184.44 [6051]~E(f333(x60514,x60512),f333(f240(x60513),x60515))+P1(f333(f333(f335(x60511),x60512),f186(x60511,x60513,x60514))) % 183.90/184.44 [6052]~E(f333(x60524,x60525),f333(f240(x60521),x60522))+P1(f333(f333(f335(x60521),x60522),f188(x60523,x60521,x60524))) % 183.90/184.44 [6511]~E(x65115,f2(a102))+E(f333(f208(x65111,x65112,x65113,x65114),x65115),f118(x65112)) % 183.90/184.44 [6512]~E(x65125,f2(a102))+E(f333(f206(x65121,x65122,x65123,x65124),x65125),f129(x65122)) % 183.90/184.44 [6648]~E(x66483,f2(a102))+E(f333(f282(x66481,x66482,x66483,x66484),x66485),f333(f268(x66481,x66482),x66485)) % 183.90/184.44 [6720]~E(f333(x67204,x67205),f209(x67202))+E(f333(f242(f879(x67201),x67202,f209(x67201),x67203),f333(x67204,x67205)),f209(x67201)) % 183.90/184.44 [7345]E(f333(x73451,x73452),f209(x73453))+~E(f333(f187(x73454,x73453,x73455,x73451),x73452),f209(x73453)) % 183.90/184.44 [7346]E(f333(x73461,x73462),f209(x73463))+~E(f333(f187(x73464,x73463,x73461,x73465),x73462),f209(x73463)) % 183.90/184.44 [7382]E(f333(f187(x73821,x73822,x73823,x73824),x73825),f333(x73823,x73825))+P1(f333(f333(f335(x73821),x73825),f186(x73821,x73822,x73824))) % 183.90/184.44 [7383]E(f333(f187(x73831,x73832,x73833,x73834),x73835),f333(x73834,x73835))+P1(f333(f333(f335(x73831),x73835),f186(x73831,x73832,x73833))) % 183.90/184.44 [7707]~P20(x77074,x77071,x77072,x77075)+E(f333(f72(x77071,x77071,x77071,f333(x77072,x77073)),f333(x77072,x77073)),f333(x77072,x77073)) % 183.90/184.44 [7753]E(f333(f187(x77531,x77532,x77533,x77534),x77535),f333(x77534,x77535))+~P1(f333(f333(f335(x77531),x77535),f186(x77531,x77532,x77534))) % 183.90/184.44 [8105]~P16(x81055,x81051,x81052)+E(f333(f72(x81051,x81051,x81051,f333(x81052,x81053)),f333(x81052,x81054)),f333(f72(x81051,x81051,x81051,f333(x81052,x81054)),f333(x81052,x81053))) % 183.90/184.44 [8437]P1(f333(f333(f335(f881(x84371,x84371)),f333(f333(f268(x84371,x84371),x84372),x84373)),f327(x84371,x84374,x84375)))+~P1(f333(f333(f248(a875),f333(x84374,x84372)),f333(x84374,x84373))) % 183.90/184.44 [8534]~P1(f333(f333(f335(x85344),x85343),f300(x85344,x85341,x85342,x85345)))+P1(f333(f333(x85341,x85342),x85343)) % 183.90/184.44 [8535]~P1(f333(f333(f335(x85354),x85353),f297(x85354,x85351,x85352,x85355)))+P1(f333(f333(x85351,x85352),x85353)) % 183.90/184.44 [8536]~P1(f333(f333(f335(x85364),x85362),f300(x85364,x85361,x85365,x85363)))+P1(f333(f333(x85361,x85362),x85363)) % 183.90/184.44 [8537]~P1(f333(f333(f335(x85374),x85372),f297(x85374,x85371,x85375,x85373)))+P1(f333(f333(x85371,x85372),x85373)) % 183.90/184.44 [8674]~P51(x86742,x86741,x86745,x86743,x86744)+E(f333(f312(x86741,x86742,x86743),x86744),f256(f882(x86742,a870))) % 183.90/184.44 [9114]~P34(x91141,x91142,x91143,x91144,x91145)+P34(x91141,x91142,x91143,f333(f170(x91141),x91144),f333(f170(x91142),x91145)) % 183.90/184.44 [9116]~P34(x91161,x91162,x91163,f333(f170(x91161),x91164),x91165)+P34(x91161,x91162,x91163,x91164,f333(f170(x91162),x91165)) % 183.90/184.44 [9117]~P34(x91171,x91172,x91173,x91174,f333(f170(x91172),x91175))+P34(x91171,x91172,x91173,f333(f170(x91171),x91174),x91175) % 183.90/184.44 [9123]P34(x91231,x91232,x91233,x91234,x91235)+~P34(x91231,x91232,x91233,f333(f170(x91231),x91234),f333(f170(x91232),x91235)) % 183.90/184.44 [9518]P1(f333(f333(f335(f881(f876(x95181),f876(x95181))),f333(f333(f268(f876(x95181),f876(x95181)),f333(f333(f152(x95181),x95182),x95183)),f333(f333(f152(x95181),x95182),x95184))),f158(x95181,x95185)))+~P1(f333(f333(f335(f881(f876(x95181),f876(x95181))),f333(f333(f268(f876(x95181),f876(x95181)),x95183),x95184)),f158(x95181,x95185))) % 183.90/184.44 [9519]P1(f333(f333(f335(f881(f876(x95191),f876(x95191))),f333(f333(f268(f876(x95191),f876(x95191)),f333(f333(f135(x95191),x95192),x95193)),f333(f333(f135(x95191),x95192),x95194))),f148(x95191,x95195)))+~P1(f333(f333(f335(f881(f876(x95191),f876(x95191))),f333(f333(f268(f876(x95191),f876(x95191)),x95193),x95194)),f148(x95191,x95195))) % 183.90/184.44 [9708]E(f333(f333(f152(x97081),f670(x97082,x97083,x97084,x97085,x97081)),f672(x97082,x97083,x97084,x97085,x97081)),x97085)+~P1(f333(f333(f335(f881(f876(x97081),f876(x97081))),f333(f333(f268(f876(x97081),f876(x97081)),x97085),f333(f333(f152(x97081),x97084),x97083))),f159(x97081,x97082))) % 183.90/184.44 [9730]E(f333(f333(f152(x97301),f674(x97302,x97303,x97304,x97305,x97301)),f675(x97302,x97303,x97304,x97305,x97301)),x97303)+~P1(f333(f333(f335(f881(f876(x97301),f876(x97301))),f333(f333(f268(f876(x97301),f876(x97301)),f333(f333(f152(x97301),x97305),x97304)),x97303)),f159(x97301,x97302))) % 183.90/184.44 [9892]~P1(f333(f333(f335(f881(f876(x98921),f876(x98921))),f333(f333(f268(f876(x98921),f876(x98921)),f333(f333(f152(x98921),x98925),x98922)),x98924)),f159(x98921,x98923)))+P1(f333(f333(f335(f881(f876(x98921),f876(x98921))),f333(f333(f268(f876(x98921),f876(x98921)),x98922),f675(x98923,x98924,x98922,x98925,x98921))),f159(x98921,x98923))) % 183.90/184.44 [9962]~P1(f333(f333(f335(f881(f876(x99621),f876(x99621))),f333(f333(f268(f876(x99621),f876(x99621)),x99625),f333(f333(f152(x99621),x99624),x99623))),f159(x99621,x99622)))+P1(f333(f333(f335(f881(f876(x99621),f876(x99621))),f333(f333(f268(f876(x99621),f876(x99621)),f672(x99622,x99623,x99624,x99625,x99621)),x99623)),f159(x99621,x99622))) % 183.90/184.44 [10127]P1(f333(f333(f335(f881(x101271,x101271)),f333(f333(f268(x101271,x101271),f333(x101272,f333(f333(f79(a875),x101273),x101274))),f333(x101272,x101273))),f309(x101271,x101275)))+~P1(f333(f333(f335(f881(x101271,x101271)),f333(f333(f268(x101271,x101271),f333(x101272,f333(a115,f626(x101274,x101273,x101275,x101272,x101271)))),f333(x101272,f626(x101274,x101273,x101275,x101272,x101271)))),f309(x101271,x101275))) % 183.90/184.44 [5226]E(x52261,x52262)+~E(f333(f333(f152(x52263),x52264),x52261),f333(f333(f152(x52263),x52265),x52262)) % 183.90/184.44 [5227]E(x52271,x52272)+~E(f333(f333(f152(x52273),x52271),x52274),f333(f333(f152(x52273),x52272),x52275)) % 183.90/184.44 [5278]P1(f333(x52781,x52782))+~E(f333(f137(x52783,x52781),x52784),f333(f333(f152(x52783),x52782),x52785)) % 183.90/184.44 [5279]P1(f333(x52791,x52792))+~E(f333(f333(f152(x52793),x52792),x52794),f333(f137(x52793,x52791),x52795)) % 183.90/184.44 [5436]~E(f333(f333(f139(x54361),x54363),x54362),f333(f333(f152(x54361),x54364),x54365))+E(f333(f333(f166(x54361),x54362),x54363),x54364) % 183.90/184.44 [5570]~P15(x55704,x55705,x55701)+E(f333(f333(x55701,x55702),f333(f333(x55701,x55702),x55703)),f333(f333(x55701,x55702),x55703)) % 183.90/184.44 [6104]~E(x61044,f2(a102))+E(f333(f333(f120(x61041,x61042,x61043),x61044),x61045),f333(f333(f268(f876(x61042),x61041),f116(x61042)),x61045)) % 183.90/184.44 [6171]~P106(x61712)+~E(f333(f333(f149(x61711,x61712,x61713),x61714),x61715),f116(x61711)) % 183.90/184.44 [6548]E(x65481,x65482)+~E(f333(f333(f135(x65483),x65484),f333(f333(f152(x65483),x65481),f116(x65483))),f333(f333(f135(x65483),x65485),f333(f333(f152(x65483),x65482),f116(x65483)))) % 183.90/184.44 [6549]E(x65491,x65492)+~E(f333(f333(f135(x65493),x65491),f333(f333(f152(x65493),x65494),f116(x65493))),f333(f333(f135(x65493),x65492),f333(f333(f152(x65493),x65495),f116(x65493)))) % 183.90/184.44 [6804]E(f333(f190(x68041,x68042,x68043,x68044),x68045),f209(x68042))+P1(f333(f333(f335(x68041),x68045),x68044)) % 183.90/184.44 [6866]E(f333(f333(f311(x68661),f333(x68662,x68663)),f333(f312(x68664,x68661,x68662),x68665)),f333(f312(x68664,x68661,x68662),x68665))+~P1(f333(f333(f335(x68664),x68663),x68665)) % 183.90/184.44 [6873]~P1(f333(x68734,f333(x68733,x68735)))+P1(f333(f333(f313(x68731,x68732,x68733),x68734),x68735)) % 183.90/184.44 [6876]~P1(f333(f333(x68763,x68765),x68764))+P1(f333(f333(f257(x68761,x68762,x68763),x68764),x68765)) % 183.90/184.44 [6971]~E(f333(f312(x69711,x69712,x69713),x69714),x69715)+E(f333(f312(f882(x69711,a870),f882(x69712,a870),f312(x69711,x69712,x69713)),f333(f310(x69711),x69714)),f333(f310(x69712),x69715)) % 183.90/184.44 [7003]E(f333(f190(x70031,x70032,x70033,x70034),x70035),f333(x70033,x70035))+~P1(f333(f333(f335(x70031),x70035),x70034)) % 183.90/184.44 [7302]P25(x73021,x73022,x73023,x73024)+~P25(x73021,x73022,x73023,f333(f333(f311(x73021),x73025),x73024)) % 183.90/184.44 [7372]P1(f333(x73721,x73722))+~P1(f333(f333(f94(x73723,x73724,x73721),x73725),x73722)) % 183.90/184.44 [7416]~P1(f333(f333(f335(x74164),x74163),x74165))+P1(f333(f333(f335(x74161),f333(x74162,x74163)),f333(f312(x74164,x74161,x74162),x74165))) % 183.90/184.44 [7440]~P106(x74402)+E(f151(x74401,x74402,x74403,f333(f137(x74401,x74404),x74405)),f333(f137(x74401,x74404),f151(x74401,x74402,x74403,x74405))) % 183.90/184.44 [7473]P1(f333(x74731,f333(x74732,x74733)))+~P1(f333(f333(f313(x74734,x74735,x74732),x74731),x74733)) % 183.90/184.44 [7476]P1(f333(f333(x74761,x74762),x74763))+~P1(f333(f333(f257(x74764,x74765,x74761),x74763),x74762)) % 183.90/184.44 [7477]P1(f333(f333(x74771,x74772),x74773))+~P1(f333(f333(f94(x74774,x74771,x74775),x74772),x74773)) % 183.90/184.44 [7541]~P1(f333(f333(f335(x75413),f333(x75414,x75412)),x75415))+P1(f333(f333(f335(x75411),x75412),f333(f313(x75411,x75413,x75414),x75415))) % 183.90/184.44 [7942]~P1(f333(f333(f335(x79425),x79423),f333(f313(x79425,x79421,x79422),x79424)))+P1(f333(f333(f335(x79421),f333(x79422,x79423)),x79424)) % 183.90/184.44 [8172]~E(x81723,f333(f333(f333(f71(x81721,f879(x81722)),f333(f16(f879(x81722),x81721),f209(x81722))),x81724),f333(f240(x81722),x81725)))+E(f186(x81721,x81722,x81723),f333(f333(f311(x81721),x81724),f196(f882(x81721,a870)))) % 183.90/184.44 [8252]~P16(x82522,x82521,x82523)+E(f333(f143(x82521,x82522,f333(f7(x82522,x82521,x82521),x82523),x82524),f153(x82522,x82525)),f333(f333(f64(x82522,x82521,x82523),x82524),f333(f174(x82522),x82525))) % 183.90/184.44 [8271]E(f333(x82711,f476(x82712,x82711,x82713,x82714)),x82714)+~P1(f333(f333(f335(x82715),x82714),f333(f312(x82713,x82715,x82711),x82712))) % 183.90/184.44 [8579]~E(x85792,f333(f333(f152(x85791),x85794),x85795))+P1(f333(f333(f335(f881(f876(x85791),f876(x85791))),f333(f333(f268(f876(x85791),f876(x85791)),f116(x85791)),x85792)),f148(x85791,x85793))) % 183.90/184.44 [8632]~P34(x86321,x86323,x86325,x86322,x86324)+E(f333(f197(f876(x86321)),x86322),f333(f197(f876(x86323)),x86324)) % 183.90/184.44 [8642]P1(f333(f333(f247(f882(x86421,a870)),f333(f333(f42(x86422,f882(x86421,a870)),x86423),x86424)),f333(x86424,x86425)))+~P1(f333(f333(f335(x86422),x86425),x86423)) % 183.90/184.44 [8690]~P51(x86901,x86902,x86903,x86905,x86904)+E(f333(f312(x86901,x86902,x86903),f256(f882(x86901,a870))),x86904) % 183.90/184.44 [8896]E(f333(f333(f333(f71(x88961,f879(x88962)),f190(x88961,x88962,x88963,x88964)),x88965),f209(x88962)),f190(x88961,x88962,x88963,x88964))+P1(f333(f333(f335(x88961),x88965),x88964)) % 183.90/184.44 [8901]E(f333(f137(x89011,x89012),f781(x89013,x89014,x89015,x89012,x89011)),x89013)+~E(f333(f137(x89011,x89012),x89015),f333(f333(f152(x89011),x89014),x89013)) % 183.90/184.44 [8902]E(f333(f137(x89021,x89022),f782(x89023,x89022,x89024,x89025,x89021)),x89024)+~E(f333(f333(f152(x89021),x89025),x89024),f333(f137(x89021,x89022),x89023)) % 183.90/184.44 [8903]E(f333(x89031,f710(x89032,x89033,x89031,x89034,x89035)),x89032)+~E(f333(f333(f210(x89035,x89034),x89031),x89033),f333(f240(x89034),x89032)) % 183.90/184.44 [8907]E(f333(f240(x89071),f710(x89072,x89073,x89074,x89075,x89071)),x89073)+~E(f333(f333(f210(x89071,x89075),x89074),x89073),f333(f240(x89075),x89072)) % 183.90/184.44 [9006]E(f333(f197(f876(x90061)),x90062),x90063)+~P1(f333(f333(f335(f881(f876(x90061),f876(x90061))),f333(f333(f268(f876(x90061),f876(x90061)),x90064),x90062)),f333(f144(x90061,x90065),x90063))) % 183.90/184.44 [9007]E(f333(f197(f876(x90071)),x90072),x90073)+~P1(f333(f333(f335(f881(f876(x90071),f876(x90071))),f333(f333(f268(f876(x90071),f876(x90071)),x90072),x90074)),f333(f144(x90071,x90075),x90073))) % 183.90/184.44 [9074]P1(f333(f333(f335(x90741),f476(x90742,x90743,x90741,x90744)),x90742))+~P1(f333(f333(f335(x90745),x90744),f333(f312(x90741,x90745,x90743),x90742))) % 183.90/184.44 [9235]E(f333(f312(x92351,x92352,x92353),f350(x92354,x92353,x92351,x92355,x92352)),x92355)+~P1(f333(f333(f247(f882(x92352,a870)),x92355),f333(f312(x92351,x92352,x92353),x92354))) % 183.90/184.44 [9488]E(f333(x94881,f770(x94882,x94881,x94883,x94884,x94885)),f333(f240(x94885),x94884))+~P1(f333(f333(f335(x94885),x94884),f188(x94883,x94885,f190(x94883,x94885,x94881,x94882)))) % 183.90/184.44 [9534]P1(f333(f333(f335(f881(f876(x95341),f876(x95341))),f333(f333(f268(f876(x95341),f876(x95341)),f333(f333(f152(x95341),x95342),x95343)),f333(f333(f152(x95341),x95342),x95344))),f309(f876(x95341),f158(x95341,x95345))))+~P1(f333(f333(f335(f881(f876(x95341),f876(x95341))),f333(f333(f268(f876(x95341),f876(x95341)),x95343),x95344)),f309(f876(x95341),f158(x95341,x95345)))) % 183.90/184.44 [9565]~E(f333(x95653,f712(x95655,x95654,x95653,x95652,x95651)),f333(x95655,f712(x95655,x95654,x95653,x95652,x95651)))+E(f333(f333(f155(x95651,x95652),x95653),x95654),f333(f333(f155(x95651,x95652),x95655),x95654)) % 183.90/184.44 [9641]~E(f333(f137(x96411,x96415),x96414),f333(f333(f152(x96411),x96413),x96412))+E(f333(f333(f135(x96411),f787(x96412,x96413,x96414,x96415,x96411)),f333(f333(f152(x96411),x96413),f781(x96412,x96413,x96414,x96415,x96411))),x96414) % 183.90/184.44 [9642]~E(f333(f333(f152(x96421),x96425),x96424),f333(f137(x96421,x96423),x96422))+E(f333(f333(f135(x96421),f784(x96422,x96423,x96424,x96425,x96421)),f333(f333(f152(x96421),x96425),f782(x96422,x96423,x96424,x96425,x96421))),x96422) % 183.90/184.44 [9646]E(f333(f333(f155(x96461,x96462),x96463),x96464),f333(f333(f155(x96461,x96462),x96465),x96464))+P1(f333(f333(f335(x96461),f712(x96463,x96464,x96465,x96462,x96461)),f333(f174(x96461),x96464))) % 183.90/184.44 [9676]~P1(f333(f333(f335(x96765),x96764),f333(f287(x96761,x96765,x96763),x96762)))+P1(f333(f333(f335(x96761),f532(x96762,x96763,x96761,x96764,x96765)),x96762)) % 183.90/184.44 [9677]~P1(f333(f333(f335(x96775),x96774),f333(f287(x96771,x96775,x96773),x96772)))+P1(f333(f333(f335(x96771),f554(x96772,x96773,x96771,x96774,x96775)),x96772)) % 183.90/184.44 [9702]~P1(f333(f333(f247(f882(x97025,a870)),x97024),f333(f312(x97021,x97025,x97023),x97022)))+P1(f333(f333(f247(f882(x97021,a870)),f350(x97022,x97023,x97021,x97024,x97025)),x97022)) % 183.90/184.44 [9753]~P1(f333(f333(f335(x97535),x97534),f188(x97531,x97535,f190(x97531,x97535,x97533,x97532))))+P1(f333(f333(f335(x97531),f770(x97532,x97533,x97531,x97534,x97535)),x97532)) % 183.90/184.44 [10149]E(x101491,f2(a102))+E(f333(f242(f881(f876(x101492),x101493),f881(x101492,x101493),f333(f333(f268(f876(x101492),x101493),f116(x101492)),x101494),f333(f272(x101492,x101493,f881(f876(x101492),x101493)),f333(f333(f7(x101492,f882(x101493,f881(f876(x101492),x101493)),f882(x101493,f881(f876(x101492),x101493))),f333(f333(f8(f882(f881(f876(x101492),x101493),f881(f876(x101492),x101493)),f882(f882(x101493,f881(f876(x101492),x101493)),f882(x101493,f881(f876(x101492),x101493))),x101492),f8(f881(f876(x101492),x101493),f881(f876(x101492),x101493),x101493)),f333(f333(f8(f882(f876(x101492),f882(x101493,f881(f876(x101492),x101493))),f882(f881(f876(x101492),x101493),f881(f876(x101492),x101493)),x101492),f272(f876(x101492),x101493,f881(f876(x101492),x101493))),f333(f333(f8(f882(f876(x101492),f876(x101492)),f882(f876(x101492),f882(x101493,f881(f876(x101492),x101493))),x101492),f333(f8(f876(x101492),f882(x101493,f881(f876(x101492),x101493)),f876(x101492)),f268(f876(x101492),x101493))),f152(x101492))))),f333(f120(x101493,x101492,x101495),f333(f333(f22(a102),x101491),f77(a102)))))),f333(x101495,x101494)),f333(f333(f120(x101493,x101492,x101495),x101491),x101494)) % 183.90/184.44 [5449]~E(f333(x54493,x54494),x54495)+E(f333(f333(f333(f71(x54491,x54492),x54493),x54494),x54495),x54493) % 183.90/184.44 [5891]E(f333(x58911,x58912),x58913)+~E(f333(f333(f333(f71(x58914,x58915),x58911),x58912),x58913),x58911) % 183.90/184.44 [5985]E(x59851,x59852)+~E(f333(f271(x59853,x59854),f333(f333(f268(x59853,x59854),x59855),x59851)),x59852) % 183.90/184.44 [5986]E(x59861,x59862)+~E(f333(f267(x59863,x59864),f333(f333(f268(x59863,x59864),x59861),x59865)),x59862) % 183.90/184.44 [6246]~E(x62463,f333(f333(f135(x62461),x62464),f333(f333(f152(x62461),x62462),x62465)))+P1(f333(f333(f335(x62461),x62462),f333(f174(x62461),x62463))) % 183.90/184.44 [6635]E(f333(f312(x66351,x66352,f333(f16(x66352,x66351),x66353)),x66354),f333(f333(f311(x66352),x66353),f196(f882(x66352,a870))))+~P1(f333(f333(f335(x66351),x66355),x66354)) % 183.90/184.44 [6705]E(f333(f333(f113(f882(x67051,a870)),f333(f174(x67051),x67052)),f333(f174(x67051),x67053)),f333(f174(x67051),x67054))+~E(f168(x67051,x67055,x67054),f333(f333(f268(f876(x67051),f876(x67051)),x67052),x67053)) % 183.90/184.44 [6808]~P106(x68082)+E(f333(f197(f876(x68081)),f333(f333(f149(x68081,x68082,x68083),x68084),x68085)),f333(a115,f333(f197(f876(x68081)),x68085))) % 183.90/184.44 [6820]~P106(x68202)+E(f333(f174(x68201),f333(f333(f149(x68201,x68202,x68203),x68204),x68205)),f333(f333(f311(x68201),x68204),f333(f174(x68201),x68205))) % 183.90/184.44 [7094]~P109(x70941)+E(f333(f333(f79(x70941),f333(f333(f79(x70941),x70942),x70943)),f333(f333(f79(x70941),x70944),x70945)),f333(f333(f79(x70941),f333(f333(f79(x70941),x70942),x70944)),f333(f333(f79(x70941),x70943),x70945))) % 183.90/184.44 [7095]~P109(x70951)+E(f333(f333(f80(x70951),f333(f333(f80(x70951),x70952),x70953)),f333(f333(f80(x70951),x70954),x70955)),f333(f333(f80(x70951),f333(f333(f80(x70951),x70952),x70954)),f333(f333(f80(x70951),x70953),x70955))) % 183.90/184.44 [7096]~P58(x70961)+E(f333(f333(f291(x70961),f333(f333(f80(x70961),x70962),x70963)),f333(f333(f80(x70961),x70964),x70965)),f333(f333(f80(x70961),f333(f333(f291(x70961),x70962),x70964)),f333(f333(f291(x70961),x70963),x70965))) % 183.90/184.44 [7110]~P106(x71101)+E(f307(x71101,f333(f333(f246(x71101),x71102),x71103),f333(f333(f245(x71101),x71104),x71105)),f333(f333(f104(f882(x71101,a870)),f307(x71101,x71102,x71104)),f307(x71101,x71103,x71105))) % 183.90/184.44 [7111]~P106(x71111)+E(f306(x71111,f333(f333(f246(x71111),x71112),x71113),f333(f333(f245(x71111),x71114),x71115)),f333(f333(f104(f882(x71111,a870)),f306(x71111,x71112,x71114)),f306(x71111,x71113,x71115))) % 183.90/184.44 [7112]~P106(x71121)+E(f304(x71121,f333(f333(f246(x71121),x71122),x71123),f333(f333(f245(x71121),x71124),x71125)),f333(f333(f104(f882(x71121,a870)),f304(x71121,x71122,x71124)),f304(x71121,x71123,x71125))) % 183.90/184.44 [7113]~P106(x71131)+E(f333(f333(f104(f882(x71131,a870)),f333(f303(x71131,x71132),x71133)),f333(f303(x71131,x71134),x71135)),f333(f303(x71131,f333(f333(f246(x71131),x71132),x71134)),f333(f333(f245(x71131),x71133),x71135))) % 183.90/184.44 [7228]~P1(f333(x72281,f527(x72283,x72282,x72281)))+P1(f333(x72281,f333(f333(f268(x72282,x72283),x72284),x72285))) % 183.90/184.44 [7315]~E(f333(x73153,x73154),f209(x73152))+E(f188(x73151,x73152,f333(f333(f333(f71(x73151,f879(x73152)),x73153),x73154),f333(f240(x73152),x73155))),f333(f333(f311(x73152),x73155),f188(x73151,x73152,x73153))) % 183.90/184.44 [7336]~E(x73362,f333(x73364,x73365))+P1(f333(f333(f335(x73361),x73362),f333(f312(x73363,x73361,x73364),f256(f882(x73363,a870))))) % 183.90/184.44 [7394]~E(f333(x73943,x73944),f209(x73942))+E(f333(f333(f22(f882(x73941,a870)),f186(x73941,x73942,x73943)),f333(f333(f311(x73941),x73944),x73945)),f333(f333(f22(f882(x73941,a870)),f186(x73941,x73942,x73943)),x73945)) % 183.90/184.44 [7413]~P15(x74133,x74132,x74134)+P15(x74131,x74132,f333(f333(f8(x74133,f882(x74132,x74132),x74131),x74134),x74135)) % 183.90/184.44 [7414]~P16(x74143,x74142,x74144)+P16(x74141,x74142,f333(f333(f8(x74143,f882(x74142,x74142),x74141),x74144),x74145)) % 183.90/184.44 [7557]~P25(x75571,x75572,x75573,x75574)+P25(x75571,x75572,x75573,f333(f333(f22(f882(x75571,a870)),x75574),x75575)) % 183.90/184.44 [7716]~P1(f333(f333(x77163,x77164),x77165))+P1(f333(f333(f272(x77161,x77162,a870),x77163),f333(f333(f268(x77161,x77162),x77164),x77165))) % 183.90/184.44 [7831]~P1(f333(x78312,x78314))+~E(f333(f333(f139(x78311),f333(f197(f876(x78311)),f179(x78311,x78312,x78313))),x78313),f333(f333(f152(x78311),x78314),x78315)) % 183.90/184.44 [7851]P25(x78511,x78512,x78513,x78514)+~P25(x78511,x78512,x78513,f333(f333(f113(f882(x78511,a870)),x78515),x78514)) % 183.90/184.44 [7852]P25(x78521,x78522,x78523,x78524)+~P25(x78521,x78522,x78523,f333(f333(f113(f882(x78521,a870)),x78524),x78525)) % 183.90/184.44 [7899]~P106(x78992)+E(f333(f333(f149(x78991,x78992,x78993),x78994),f151(x78991,x78992,x78993,x78995)),f151(x78991,x78992,x78993,f333(f333(f152(x78991),x78994),x78995))) % 183.90/184.44 [8064]~P27(x80641,f333(a115,x80642),f333(f333(f333(f91(x80641),x80643),f333(a25,x80644)),x80645))+P27(x80641,x80642,f333(f333(f333(f91(x80641),x80643),f333(f244(a871),f333(a27,x80644))),x80645)) % 183.90/184.44 [8199]P27(x81991,f333(a115,x81992),f333(f333(f333(f91(x81991),x81993),f333(a25,x81994)),x81995))+~P27(x81991,x81992,f333(f333(f333(f91(x81991),x81993),f333(f244(a871),f333(a27,x81994))),x81995)) % 183.90/184.44 [8228]~P15(x82282,x82281,x82283)+E(f333(f143(x82281,x82282,f333(f7(x82282,x82281,x82281),x82283),x82284),x82285),f333(f333(f64(x82282,x82281,x82283),x82284),f333(f174(x82282),x82285))) % 183.90/184.44 [8257]~E(f333(f333(f139(x82571),f333(f197(f876(x82571)),f179(x82571,x82572,x82573))),x82573),f333(f333(f152(x82571),x82574),x82575))+E(f333(f333(f135(x82571),f179(x82571,x82572,x82573)),f333(f333(f152(x82571),x82574),x82575)),x82573) % 183.90/184.44 [8281]P1(f333(f333(x82811,x82812),x82813))+~P1(f333(f333(f272(x82814,x82815,a870),x82811),f333(f333(f268(x82814,x82815),x82812),x82813))) % 183.90/184.44 [8344]~E(f333(f333(f180(x83441,x83442),x83445),x83443),f333(f240(x83442),x83444))+P1(f333(f333(f335(f881(x83441,x83442)),f333(f333(f268(x83441,x83442),x83443),x83444)),f333(f174(f881(x83441,x83442)),x83445))) % 183.90/184.44 [8745]P1(f333(f333(f247(f882(x87451,a870)),f333(f312(x87452,x87451,x87453),x87454)),f333(f312(x87452,x87451,x87453),x87455)))+~P1(f333(f333(f247(f882(x87452,a870)),x87454),x87455)) % 183.90/184.44 [8746]P1(f333(f333(f247(f882(x87461,a870)),f333(f313(x87461,x87462,x87463),x87464)),f333(f313(x87461,x87462,x87463),x87465)))+~P1(f333(f333(f247(f882(x87462,a870)),x87464),x87465)) % 183.90/184.44 [8822]E(x88221,f2(a102))+E(f333(f333(f274(x88222,x88223,x88222,f881(x88223,x88222)),f333(x88224,x88225)),f282(x88223,x88222,f333(f333(f22(a102),x88221),f77(a102)),x88224)),f333(f282(x88223,x88222,x88221,x88224),x88225)) % 183.90/184.44 [9144]P27(x91441,x91442,f333(f333(f333(f91(x91441),x91443),x91444),x91445))+P1(f333(f333(x91443,f479(x91445,x91444,x91443,x91442)),f482(x91445,x91444,x91443,x91442))) % 183.90/184.44 [9344]E(f333(f240(x93441),f715(x93442,x93443,x93444,x93441,x93445)),f333(f333(f180(x93445,x93441),x93442),x93444))+~P1(f333(f333(f335(f881(x93445,x93441)),f333(f333(f268(x93445,x93441),x93444),x93443)),f333(f174(f881(x93445,x93441)),x93442))) % 183.90/184.44 [9389]P27(x93891,x93892,f333(f333(f333(f91(x93891),x93893),x93894),x93895))+~P1(f333(f333(x93895,f479(x93895,x93894,x93893,x93892)),f483(x93895,x93894,x93893,x93892))) % 183.90/184.44 [9448]P27(x94481,x94482,f333(f333(f333(f91(x94481),x94483),x94484),x94485))+P1(f333(f333(f333(f333(a204,x94484),f482(x94485,x94484,x94483,x94482)),x94482),f483(x94485,x94484,x94483,x94482))) % 183.90/184.44 [9451]~P24(x94511,x94512,f333(f333(f311(f874(x94511)),f333(f333(f333(f91(x94511),x94513),f333(f244(a871),f333(a27,x94514))),x94515)),f196(f882(f874(x94511),a870))))+P24(x94511,x94512,f333(f333(f311(f874(x94511)),f333(f333(f333(f91(x94511),x94513),f333(a25,x94514)),x94515)),f196(f882(f874(x94511),a870)))) % 183.90/184.44 [9479]~P1(f333(f61(x94793),f333(f312(x94792,x94793,x94795),f256(f882(x94792,a870)))))+P1(f333(f61(x94791),f333(f312(x94792,x94791,f333(f333(f8(x94793,x94791,x94792),x94794),x94795)),f256(f882(x94792,a870))))) % 183.90/184.44 [9501]P1(f333(f333(f247(f882(f882(x95011,a870),a870)),f333(f312(f882(x95012,a870),f882(x95011,a870),f312(x95012,x95011,x95013)),f333(f310(x95012),x95014))),f333(f310(x95011),x95015)))+~P1(f333(f333(f247(f882(x95011,a870)),f333(f312(x95012,x95011,x95013),x95014)),x95015)) % 183.90/184.44 [9514]~P1(f333(f61(f879(x95141)),f333(f312(x95142,f879(x95141),x95143),f256(f882(x95142,a870)))))+P1(f333(f61(f879(x95141)),f333(f312(x95142,f879(x95141),f333(f333(f333(f71(x95142,f879(x95141)),x95143),x95144),f333(f240(x95141),x95145))),f256(f882(x95142,a870))))) % 183.90/184.44 [9574]E(x95741,x95742)+~P1(f333(f66(x95743,x95744,x95745,x95741,f196(f882(x95743,a870))),x95742)) % 183.90/184.44 [9589]E(f333(f333(f268(x95891,x95892),f584(x95893,x95894,x95895,x95892,x95891)),f585(x95893,x95894,x95895,x95892,x95891)),x95895)+~P1(f333(f333(f335(f881(x95891,x95892)),x95895),f333(f333(f270(x95891,x95892),x95894),x95893))) % 183.90/184.44 [9681]P1(f333(f333(f335(x96811),f584(x96812,x96813,x96814,x96815,x96811)),x96813))+~P1(f333(f333(f335(f881(x96811,x96815)),x96814),f333(f333(f270(x96811,x96815),x96813),x96812))) % 183.90/184.44 [9789]P24(x97895,x97894,f333(f333(f311(f874(x97895)),f333(f333(f333(f91(x97895),x97891),x97893),x97892)),f196(f882(f874(x97895),a870))))+P1(f333(f333(x97891,f561(x97892,x97893,x97894,x97895,x97891)),f673(x97892,x97893,x97894,x97895,x97891))) % 183.90/184.44 [9840]P1(f333(f333(f335(x98401),f585(x98402,x98403,x98404,x98401,x98405)),f333(x98402,f584(x98402,x98403,x98404,x98401,x98405))))+~P1(f333(f333(f335(f881(x98405,x98401)),x98404),f333(f333(f270(x98405,x98401),x98403),x98402))) % 183.90/184.44 [9868]P1(f333(f333(f335(f881(x98681,x98681)),f333(f333(f268(x98681,x98681),x98682),f647(x98683,x98684,x98685,x98682,x98681))),x98683))+~P1(f333(f333(f335(f881(x98681,x98681)),f333(f333(f268(x98681,x98681),x98682),x98685)),f333(f333(f191(f881(x98681,x98681),a870),f333(a115,x98684)),x98683))) % 183.90/184.44 [9869]P1(f333(f333(f335(f881(x98691,x98691)),f333(f333(f268(x98691,x98691),x98692),f648(x98693,x98694,x98695,x98692,x98691))),x98693))+~P1(f333(f333(f335(f881(x98691,x98691)),f333(f333(f268(x98691,x98691),x98692),x98695)),f333(f333(f191(f881(x98691,x98691),a870),f333(a115,x98694)),x98693))) % 183.90/184.44 [9887]~P1(f333(f333(f335(f881(f876(x98871),f876(x98871))),f333(f333(f268(f876(x98871),f876(x98871)),f333(f333(f152(x98871),x98872),x98875)),x98874)),f159(x98871,x98873)))+P1(f333(f333(f335(f881(x98871,x98871)),f333(f333(f268(x98871,x98871),x98872),f674(x98873,x98874,x98875,x98872,x98871))),x98873)) % 183.90/184.44 [9889]~P24(x98891,x98892,f333(f333(f311(f874(x98891)),f333(f333(f333(f91(x98891),f94(x98891,x98893,x98894)),x98895),x98893)),f196(f882(f874(x98891),a870))))+P24(x98891,x98892,f333(f333(f311(f874(x98891)),f333(f333(f333(f91(x98891),x98893),f31(x98894,x98895)),f94(x98891,x98893,f333(f72(a870,a870,a872,a328),x98894)))),f196(f882(f874(x98891),a870)))) % 183.90/184.44 [9890]~P28(x98901,x98902,f333(f333(f311(f874(x98901)),f333(f333(f333(f91(x98901),f94(x98901,x98903,x98904)),x98905),x98903)),f196(f882(f874(x98901),a870))))+P28(x98901,x98902,f333(f333(f311(f874(x98901)),f333(f333(f333(f91(x98901),x98903),f31(x98904,x98905)),f94(x98901,x98903,f333(f72(a870,a870,a872,a328),x98904)))),f196(f882(f874(x98901),a870)))) % 183.90/184.44 [10150]P24(x101501,x101502,f333(f333(f311(f874(x101501)),f333(f333(f333(f91(x101501),x101503),x101504),x101505)),f196(f882(f874(x101501),a870))))+~P24(x101501,x101502,f333(f333(f311(f874(x101501)),f333(f333(f333(f91(x101501),f333(f16(f882(a872,a870),x101501),f333(f333(f7(a872,a872,a870),a330),f673(x101505,x101504,x101502,x101501,x101503)))),x101504),f333(f16(f882(a872,a870),x101501),f333(x101505,f561(x101505,x101504,x101502,x101501,x101503))))),f196(f882(f874(x101501),a870)))) % 183.90/184.44 [6320]P1(f333(x63202,x63204))+E(f179(x63201,x63202,f333(f333(f135(x63201),x63203),f333(f333(f152(x63201),x63204),x63205))),f179(x63201,x63202,x63203)) % 183.90/184.44 [6368]~P62(x63682)+E(f333(f333(f333(f113(f882(x63681,x63682)),x63683),x63684),x63685),f333(f333(f113(x63682),f333(x63683,x63685)),f333(x63684,x63685))) % 183.90/184.44 [6370]~P64(x63702)+E(f333(f333(f333(f22(f882(x63701,x63702)),x63703),x63704),x63705),f333(f333(f22(x63702),f333(x63703,x63705)),f333(x63704,x63705))) % 183.90/184.44 [6372]~P62(x63722)+E(f333(f333(f333(f104(f882(x63721,x63722)),x63723),x63724),x63725),f333(f333(f104(x63722),f333(x63723,x63725)),f333(x63724,x63725))) % 183.90/184.44 [6390]E(x63901,x63902)+E(f333(f333(f166(x63903),f333(f333(f160(x63903,x63904),x63901),x63905)),x63902),f333(f333(f166(x63903),x63904),x63902)) % 183.90/184.44 [6653]~E(x66534,f196(f882(x66533,a870)))+E(f333(f333(f113(f882(x66531,a870)),x66532),f333(f333(f41(x66533,f882(x66531,a870)),x66534),x66535)),x66532) % 183.90/184.44 [6654]~E(x66544,f196(f882(x66543,a870)))+E(f333(f333(f22(f882(x66541,a870)),x66542),f333(f333(f41(x66543,f882(x66541,a870)),x66544),x66545)),x66542) % 183.90/184.44 [6655]~E(x66554,f196(f882(x66553,a870)))+E(f333(f333(f104(f882(x66551,a870)),x66552),f333(f333(f42(x66553,f882(x66551,a870)),x66554),x66555)),x66552) % 183.90/184.44 [6669]~E(x66694,f196(f882(x66693,a870)))+E(f333(f333(f311(x66691),x66692),f333(f333(f41(x66693,f882(x66691,a870)),x66694),x66695)),f333(f333(f311(x66691),x66692),f196(f882(x66691,a870)))) % 183.90/184.44 [7462]E(f333(f333(f166(x74621),f333(f333(f155(x74622,x74621),x74623),x74624)),x74625),f333(x74623,f333(f333(f166(x74622),x74624),x74625)))+~P1(f333(f333(f248(a875),x74625),f333(f197(f876(x74622)),x74624))) % 183.90/184.44 [7529]E(f333(f333(f113(f882(x75291,a870)),f333(x75292,x75293)),f333(f333(f41(x75294,f882(x75291,a870)),x75295),x75292)),f333(f333(f41(x75294,f882(x75291,a870)),x75295),x75292))+~P1(f333(f333(f335(x75294),x75293),x75295)) % 183.90/184.44 [7530]E(f333(f333(f104(f882(x75301,a870)),f333(x75302,x75303)),f333(f333(f42(x75304,f882(x75301,a870)),x75305),x75302)),f333(f333(f42(x75304,f882(x75301,a870)),x75305),x75302))+~P1(f333(f333(f335(x75304),x75303),x75305)) % 183.90/184.44 [8144]~E(x81443,f196(f882(x81441,a870)))+E(f333(f333(f41(x81441,f882(x81442,a870)),x81443),f333(f333(f8(f882(x81442,a870),f882(x81442,a870),x81441),f333(f311(x81442),x81444)),x81445)),f196(f882(x81442,a870))) % 183.90/184.44 [8150]~P1(f333(f333(f335(x81504),x81503),x81505))+P1(f333(f333(f247(f882(x81501,a870)),f333(x81502,x81503)),f333(f333(f41(x81504,f882(x81501,a870)),x81505),x81502))) % 183.90/184.44 [8280]~E(f333(x82804,x82802),x82805)+P1(f333(f333(f335(x82801),x82802),f333(f313(x82801,x82803,x82804),f333(f333(f311(x82803),x82805),f196(f882(x82803,a870)))))) % 183.90/184.44 [8326]~P49(x83261,x83262,f333(f288(x83262,x83261),x83263))+E(f333(f333(f104(f882(x83261,a870)),f333(f287(x83262,x83261,x83263),x83264)),f333(f287(x83262,x83261,x83263),x83265)),f333(f287(x83262,x83261,x83263),f333(f333(f104(f882(x83262,a870)),x83264),x83265))) % 183.90/184.44 [8403]E(x84031,f2(a102))+E(f333(f121(x84032,x84033,f333(x84034,f333(f333(f22(a102),x84031),f77(a102)))),f333(f333(f7(x84032,a102,f877(x84033)),x84035),x84031)),f333(f208(x84032,x84033,x84034,x84035),x84031)) % 183.90/184.44 [8447]E(x84471,f196(f882(x84472,a870)))+E(f333(f333(f41(x84472,f882(x84473,a870)),x84471),f333(f333(f8(f882(x84473,a870),f882(x84473,a870),x84472),f333(f311(x84473),x84474)),x84475)),f333(f333(f311(x84473),x84474),f333(f333(f41(x84472,f882(x84473,a870)),x84471),x84475))) % 183.90/184.44 [8501]~P25(x85012,x85011,x85013,f256(f882(x85012,a870)))+E(f333(f333(f22(f882(x85011,a870)),f333(f312(x85012,x85011,x85013),x85014)),f333(f312(x85012,x85011,x85013),x85015)),f333(f312(x85012,x85011,x85013),f333(f333(f22(f882(x85012,a870)),x85014),x85015))) % 183.90/184.44 [8502]~P25(x85022,x85021,x85023,f256(f882(x85022,a870)))+E(f333(f333(f104(f882(x85021,a870)),f333(f312(x85022,x85021,x85023),x85024)),f333(f312(x85022,x85021,x85023),x85025)),f333(f312(x85022,x85021,x85023),f333(f333(f104(f882(x85022,a870)),x85024),x85025))) % 183.90/184.44 [8566]~P1(f333(f333(f67(x85661,x85662,x85665),x85663),x85664))+P1(f333(f333(f335(f881(x85661,x85662)),f333(f333(f268(x85661,x85662),x85663),x85664)),x85665)) % 183.90/184.44 [8597]P1(f333(f333(f335(x85971),x85972),f333(f264(x85973,x85971),x85974)))+~P1(f333(f333(f335(f881(x85973,x85971)),f333(f333(f268(x85973,x85971),x85975),x85972)),x85974)) % 183.90/184.44 [8599]P1(f333(f333(f335(x85991),x85992),f333(f266(x85991,x85993),x85994)))+~P1(f333(f333(f335(f881(x85991,x85993)),f333(f333(f268(x85991,x85993),x85992),x85995)),x85994)) % 183.90/184.44 [8732]P1(f333(f333(f67(x87321,x87322,x87323),x87324),x87325))+~P1(f333(f333(f335(f881(x87321,x87322)),f333(f333(f268(x87321,x87322),x87324),x87325)),x87323)) % 183.90/184.44 [8767]E(f333(x87671,x87672),x87673)+~P1(f333(f333(f335(x87674),x87672),f333(f313(x87674,x87675,x87671),f333(f333(f311(x87675),x87673),f196(f882(x87675,a870)))))) % 183.90/184.44 [9003]P1(f333(f333(f335(f881(x90031,x90032)),f333(f333(f268(x90031,x90032),x90033),x90034)),f333(f288(x90032,x90031),x90035)))+~P1(f333(f333(f335(f881(x90032,x90031)),f333(f333(f268(x90032,x90031),x90034),x90033)),x90035)) % 183.90/184.44 [9021]~P1(f333(f333(x90211,x90215),x90214))+P1(f333(f333(x90211,f333(f271(x90212,x90213),f333(f333(f268(x90212,x90213),x90214),x90215))),f333(f267(x90212,x90213),f333(f333(f268(x90212,x90213),x90214),x90215)))) % 183.90/184.44 [9051]~P1(f333(f333(f335(f881(x90512,x90511)),f333(f333(f268(x90512,x90511),x90514),x90513)),f333(f288(x90511,x90512),x90515)))+P1(f333(f333(f335(f881(x90511,x90512)),f333(f333(f268(x90511,x90512),x90513),x90514)),x90515)) % 183.90/184.44 [9081]~P1(f333(f333(f335(f881(x90813,x90811)),f333(f333(f268(x90813,x90811),x90815),x90812)),x90814))+P1(f333(f333(f335(x90811),x90812),f333(f287(x90813,x90811,x90814),f333(f333(f311(x90813),x90815),f196(f882(x90813,a870)))))) % 183.90/184.44 [9126]P1(f333(f333(f335(f881(x91261,x91262)),f333(f333(f268(x91261,x91262),x91263),x91264)),x91265))+~P1(f333(f333(f335(x91262),x91264),f333(f287(x91261,x91262,x91265),f333(f333(f311(x91261),x91263),f196(f882(x91261,a870)))))) % 183.90/184.44 [9147]E(f333(f333(f333(f71(x91471,f879(x91472)),f190(x91471,x91472,x91473,x91474)),x91475),f209(x91472)),f190(x91471,x91472,x91473,f333(f333(f22(f882(x91471,a870)),x91474),f333(f333(f311(x91471),x91475),f196(f882(x91471,a870))))))+~P1(f333(f333(f335(x91471),x91475),x91474)) % 183.90/184.44 [9215]~P66(x92151)+E(f333(f333(f6(a875,x92151),x92152),f304(a875,f333(f333(f79(a875),x92153),x92154),f333(f333(f79(a875),x92155),x92154))),f333(f333(f6(a875,x92151),f333(f333(f8(a875,x92151,a875),x92152),f333(f333(f7(a875,a875,a875),f79(a875)),x92154))),f304(a875,x92153,x92155))) % 183.90/184.44 [9239]~P66(x92391)+E(f333(f333(f6(a875,x92391),x92392),f333(f303(a875,f333(f333(f79(a875),x92393),x92394)),f333(f333(f79(a875),x92395),x92394))),f333(f333(f6(a875,x92391),f333(f333(f8(a875,x92391,a875),x92392),f333(f333(f7(a875,a875,a875),f79(a875)),x92394))),f333(f303(a875,x92393),x92395))) % 183.90/184.44 [9292]~P25(x92921,x92922,x92923,f256(f882(x92921,a870)))+E(f333(f333(f155(x92921,x92922),x92923),f333(f137(x92921,f333(f333(f8(a870,a870,x92921),a328),f333(a330,x92924))),x92925)),f333(f137(x92922,f333(f333(f8(a870,a870,x92922),a328),f333(a330,f333(x92923,x92924)))),f333(f333(f155(x92921,x92922),x92923),x92925))) % 183.90/184.44 [9310]~P25(x93101,x93102,x93103,f333(f333(f311(x93101),x93104),f333(f174(x93101),x93105)))+E(f333(f333(f155(x93101,x93102),x93103),f333(f137(x93101,f333(f333(f8(a870,a870,x93101),a328),f333(a330,x93104))),x93105)),f333(f137(x93102,f333(f333(f8(a870,a870,x93102),a328),f333(a330,f333(x93103,x93104)))),f333(f333(f155(x93101,x93102),x93103),x93105))) % 183.90/184.44 [9466]P1(f333(f333(f335(f881(f876(x94661),f876(x94661))),f333(f333(f268(f876(x94661),f876(x94661)),f333(f333(f152(x94661),x94662),x94663)),f333(f333(f152(x94661),x94664),x94663))),f158(x94661,x94665)))+~P1(f333(f333(f335(f881(x94661,x94661)),f333(f333(f268(x94661,x94661),x94662),x94664)),x94665)) % 183.90/184.44 [9502]P1(f333(f333(f333(f333(a204,x95021),x95022),x95023),f480(x95024,x95023,x95022,x95025,x95021)))+~P1(f333(f333(f333(f333(a204,f32(x95021,x95025)),x95022),x95023),x95024)) % 183.90/184.44 [9572]P24(x95721,x95722,f333(f333(f311(f874(x95721)),f333(f333(f333(f91(x95721),x95723),f333(a25,x95724)),x95725)),f196(f882(f874(x95721),a870))))+~P24(x95721,f333(f333(f311(f874(x95721)),f333(f333(f333(f91(x95721),x95723),f333(a25,x95724)),x95725)),x95722),f333(f333(f311(f874(x95721)),f333(f333(f333(f91(x95721),x95723),f333(f244(a871),f333(a27,x95724))),x95725)),f196(f882(f874(x95721),a870)))) % 183.90/184.44 [9584]E(f333(f333(f311(x95841),f750(x95842,x95843,x95844,x95845,x95841)),f758(x95842,x95843,x95844,x95845,x95841)),f333(f333(f311(x95841),x95844),x95843))+~P1(f333(f62(x95841,x95845,f333(f333(f311(x95841),x95844),x95843)),x95842)) % 183.90/184.44 [9585]E(f333(f333(f311(x95851),f771(x95852,x95853,x95854,x95855,x95851)),f783(x95852,x95853,x95854,x95855,x95851)),f333(f333(f311(x95851),x95854),x95853))+~P1(f333(f62(x95851,x95855,f333(f333(f311(x95851),x95854),x95853)),x95852)) % 183.90/184.44 [9667]P1(f333(f333(f335(x96671),f843(x96672,x96673,x96674,x96675,x96671)),x96674))+P1(f333(f333(f333(f42(x96671,f882(x96675,a870)),x96674),x96673),x96672)) % 183.90/184.44 [9672]P1(f333(f333(f335(x96721),f838(x96722,x96723,x96721,x96724,x96725)),x96723))+P1(f333(f333(f335(x96725),x96724),f333(f333(f42(x96721,f882(x96725,a870)),x96723),x96722))) % 183.90/184.44 [9680]P1(f333(f333(f335(x96801),f351(x96802,x96803,x96801,x96804,x96805)),x96803))+P1(f333(f333(f247(f882(x96805,a870)),x96804),f333(f333(f42(x96801,f882(x96805,a870)),x96803),x96802))) % 183.90/184.44 [9682]P1(f333(f333(x96821,f839(x96822,x96821,x96823,x96824,x96825)),x96822))+~P1(f333(f333(f333(f41(x96825,f882(x96824,a870)),x96823),x96821),x96822)) % 183.90/184.44 [9685]P1(f333(f333(f335(x96851),f839(x96852,x96853,x96854,x96855,x96851)),x96854))+~P1(f333(f333(f333(f41(x96851,f882(x96855,a870)),x96854),x96853),x96852)) % 183.90/184.44 [9695]P1(f333(f333(f335(x96951),f816(x96952,x96953,x96951,x96954,x96955)),x96953))+~P1(f333(f333(f335(x96955),x96954),f333(f333(f41(x96951,f882(x96955,a870)),x96953),x96952))) % 183.90/184.44 [9700]P1(f333(f333(f335(x97001),x97002),f333(x97003,f816(x97003,x97004,x97005,x97002,x97001))))+~P1(f333(f333(f335(x97001),x97002),f333(f333(f41(x97005,f882(x97001,a870)),x97004),x97003))) % 183.90/184.44 [9794]~P1(f333(f333(x97944,f843(x97945,x97944,x97943,x97942,x97941)),x97945))+P1(f333(f333(f333(f42(x97941,f882(x97942,a870)),x97943),x97944),x97945)) % 183.90/184.44 [9797]~P1(f333(f333(f335(x97971),x97972),f333(x97975,f838(x97975,x97974,x97973,x97972,x97971))))+P1(f333(f333(f335(x97971),x97972),f333(f333(f42(x97973,f882(x97971,a870)),x97974),x97975))) % 183.90/184.44 [9801]~P1(f333(f333(f247(f882(x98011,a870)),x98012),f333(x98015,f351(x98015,x98014,x98013,x98012,x98011))))+P1(f333(f333(f247(f882(x98011,a870)),x98012),f333(f333(f42(x98013,f882(x98011,a870)),x98014),x98015))) % 183.90/184.44 [9846]P1(f333(f333(f333(f333(a204,x98461),f480(x98462,x98463,x98464,x98461,x98465)),x98463),x98462))+~P1(f333(f333(f333(f333(a204,f32(x98465,x98461)),x98464),x98463),x98462)) % 183.90/184.44 [9872]~P1(f333(f333(f335(x98721),f750(x98725,x98724,x98723,x98722,x98721)),f758(x98725,x98724,x98723,x98722,x98721)))+~P1(f333(f62(x98721,x98722,f333(f333(f311(x98721),x98723),x98724)),x98725)) % 183.90/184.44 [9873]~P1(f333(f333(f335(x98731),f771(x98735,x98734,x98733,x98732,x98731)),f783(x98735,x98734,x98733,x98732,x98731)))+~P1(f333(f62(x98731,x98732,f333(f333(f311(x98731),x98733),x98734)),x98735)) % 183.90/184.44 [9874]~P1(f333(f333(f335(f881(x98741,x98741)),f333(f333(f268(x98741,x98741),x98742),x98745)),f333(f333(f191(f881(x98741,x98741),a870),f333(a115,x98744)),x98743)))+P1(f333(f333(f335(f881(x98741,x98741)),f333(f333(f268(x98741,x98741),x98742),f649(x98743,x98744,x98745,x98742,x98741))),f333(f333(f191(f881(x98741,x98741),a870),x98744),x98743))) % 183.90/184.44 [9881]P1(f333(f66(x98811,x98811,x98812,f750(x98813,x98814,x98815,x98812,x98811),f758(x98813,x98814,x98815,x98812,x98811)),x98813))+~P1(f333(f62(x98811,x98812,f333(f333(f311(x98811),x98815),x98814)),x98813)) % 183.90/184.44 [9882]P1(f333(f66(x98821,x98821,x98822,f771(x98823,x98824,x98825,x98822,x98821),f783(x98823,x98824,x98825,x98822,x98821)),x98823))+~P1(f333(f62(x98821,x98822,f333(f333(f311(x98821),x98825),x98824)),x98823)) % 183.90/184.44 [9894]~P106(x98941)+P14(x98941,f333(f333(f155(x98942,x98941),x98943),f333(f137(x98942,f333(f333(f7(x98942,x98941,a870),f333(f333(f8(x98941,f882(x98941,a870),x98942),a330),x98943)),f333(x98944,x98945))),x98945))) % 183.90/184.44 [9934]~P1(f333(f333(f335(x99342),x99345),f333(f287(x99341,x99342,x99344),x99343)))+P1(f333(f333(f335(f881(x99341,x99342)),f333(f333(f268(x99341,x99342),f532(x99343,x99344,x99341,x99345,x99342)),x99345)),x99344)) % 183.90/184.44 [9935]~P1(f333(f333(f335(x99352),x99355),f333(f287(x99351,x99352,x99354),x99353)))+P1(f333(f333(f335(f881(x99351,x99352)),f333(f333(f268(x99351,x99352),f554(x99353,x99354,x99351,x99355,x99352)),x99355)),x99354)) % 183.90/184.44 [9955]~P1(f333(f333(f335(f881(x99551,x99551)),f333(f333(f268(x99551,x99551),x99555),x99554)),f333(f333(f191(f881(x99551,x99551),a870),f333(a115,x99553)),x99552)))+P1(f333(f333(f335(f881(x99551,x99551)),f333(f333(f268(x99551,x99551),f649(x99552,x99553,x99554,x99555,x99551)),x99554)),x99552)) % 183.90/184.44 [9958]~P1(f333(f333(f335(f881(x99581,x99581)),f333(f333(f268(x99581,x99581),x99585),x99584)),f333(f333(f191(f881(x99581,x99581),a870),f333(a115,x99583)),x99582)))+P1(f333(f333(f335(f881(x99581,x99581)),f333(f333(f268(x99581,x99581),f647(x99582,x99583,x99584,x99585,x99581)),x99584)),f333(f333(f191(f881(x99581,x99581),a870),x99583),x99582))) % 183.90/184.44 [9959]~P1(f333(f333(f335(f881(x99591,x99591)),f333(f333(f268(x99591,x99591),x99595),x99594)),f333(f333(f191(f881(x99591,x99591),a870),f333(a115,x99593)),x99592)))+P1(f333(f333(f335(f881(x99591,x99591)),f333(f333(f268(x99591,x99591),f648(x99592,x99593,x99594,x99595,x99591)),x99594)),f333(f333(f191(f881(x99591,x99591),a870),x99593),x99592))) % 183.90/184.44 [9960]~P1(f333(f333(f335(f881(f876(x99601),f876(x99601))),f333(f333(f268(f876(x99601),f876(x99601)),x99605),f333(f333(f152(x99601),x99604),x99603))),f159(x99601,x99602)))+P1(f333(f333(f335(f881(x99601,x99601)),f333(f333(f268(x99601,x99601),f670(x99602,x99603,x99604,x99605,x99601)),x99604)),x99602)) % 183.90/184.44 [7056]E(x70561,f209(x70562))+E(f186(x70563,x70562,f333(f333(f333(f71(x70563,f879(x70562)),x70564),x70565),x70561)),f333(f333(f311(x70563),x70565),f186(x70563,x70562,x70564))) % 183.90/184.44 [7550]~E(x75503,f196(f882(x75502,a870)))+E(f333(f333(f113(f882(x75501,a870)),f333(f333(f41(x75502,f882(x75501,a870)),x75503),x75504)),x75505),x75505) % 183.90/184.44 [7551]~E(x75513,f196(f882(x75512,a870)))+E(f333(f333(f104(f882(x75511,a870)),f333(f333(f42(x75512,f882(x75511,a870)),x75513),x75514)),x75515),x75515) % 183.90/184.44 [7914]~E(x79145,f209(x79142))+E(f186(x79141,x79142,f333(f333(f333(f71(x79141,f879(x79142)),x79143),x79144),x79145)),f333(f333(f22(f882(x79141,a870)),f186(x79141,x79142,x79143)),f333(f333(f311(x79141),x79144),f196(f882(x79141,a870))))) % 183.90/184.44 [7984]~E(x79843,f196(f882(x79842,a870)))+E(f333(f333(f22(f882(x79841,a870)),f333(f333(f42(x79842,f882(x79841,a870)),x79843),x79844)),x79845),f333(f333(f22(f882(x79841,a870)),f256(f882(x79841,a870))),x79845)) % 183.90/184.44 [8115]E(f333(f333(f160(x81151,f333(f333(f135(x81151),x81152),x81153)),x81154),x81155),f333(f333(f135(x81151),f333(f333(f160(x81151,x81152),x81154),x81155)),x81153))+~P1(f333(f333(f248(a875),x81154),f333(f197(f876(x81151)),x81152))) % 183.90/184.44 [8232]P1(f333(f333(f335(x82321),x82325),f333(f174(x82321),x82323)))+E(f333(f333(f180(x82321,x82322),f333(f333(f184(x82321,x82322),x82323),f333(f333(f155(x82321,x82322),x82324),x82323))),x82325),f209(x82322)) % 183.90/184.44 [8353]~P1(f333(f333(f335(x83531),x83535),f333(f174(x83531),x83533)))+E(f333(f333(f180(x83531,x83532),f333(f333(f184(x83531,x83532),x83533),f333(f333(f155(x83531,x83532),x83534),x83533))),x83535),f333(f240(x83532),f333(x83534,x83535))) % 183.90/184.44 [8393]E(f333(f333(f166(x83931),f333(f333(f155(a875,x83931),x83932),f140(a875,f333(f303(a875,x83933),x83934)))),x83935),f333(x83932,f333(f333(f79(a875),x83933),x83935)))+~P1(f333(f333(f248(a875),x83935),f333(f333(f22(a875),x83934),x83933))) % 183.90/184.44 [8408]E(x84081,f2(a102))+E(f123(x84082,x84083,f333(x84084,f333(f333(f22(a102),x84081),f77(a102))),f333(f333(f7(x84082,a102,f877(f879(x84083))),x84085),x84081)),f333(f206(x84082,x84083,x84084,x84085),x84081)) % 183.90/184.44 [8434]~E(x84343,f196(f882(x84341,a870)))+E(f333(f333(f41(x84341,f882(x84342,a870)),x84343),f333(f333(f8(f882(x84342,a870),f882(x84342,a870),x84341),f333(f113(f882(x84342,a870)),x84344)),x84345)),f196(f882(x84342,a870))) % 183.90/184.44 [8435]~E(x84353,f196(f882(x84351,a870)))+E(f333(f333(f42(x84351,f882(x84352,a870)),x84353),f333(f333(f8(f882(x84352,a870),f882(x84352,a870),x84351),f333(f22(f882(x84352,a870)),x84354)),x84355)),f256(f882(x84352,a870))) % 183.90/184.44 [8436]~E(x84363,f196(f882(x84361,a870)))+E(f333(f333(f42(x84361,f882(x84362,a870)),x84363),f333(f333(f8(f882(x84362,a870),f882(x84362,a870),x84361),f333(f104(f882(x84362,a870)),x84364)),x84365)),f256(f882(x84362,a870))) % 183.90/184.44 [8441]~P134(x84412)+E(f333(f333(f6(x84411,x84412),f333(f333(f8(x84412,x84412,x84411),f333(f80(x84412),x84413)),x84414)),x84415),f333(f333(f80(x84412),x84413),f333(f333(f6(x84411,x84412),x84414),x84415))) % 183.90/184.44 [8717]E(x87171,f196(f882(x87172,a870)))+E(f333(f333(f41(x87172,f882(x87173,a870)),x87171),f333(f333(f8(f882(x87173,a870),f882(x87173,a870),x87172),f333(f113(f882(x87173,a870)),x87174)),x87175)),f333(f333(f113(f882(x87173,a870)),x87174),f333(f333(f41(x87172,f882(x87173,a870)),x87171),x87175))) % 183.90/184.44 [8718]E(x87181,f196(f882(x87182,a870)))+E(f333(f333(f42(x87182,f882(x87183,a870)),x87181),f333(f333(f8(f882(x87183,a870),f882(x87183,a870),x87182),f333(f22(f882(x87183,a870)),x87184)),x87185)),f333(f333(f22(f882(x87183,a870)),x87184),f333(f333(f41(x87182,f882(x87183,a870)),x87181),x87185))) % 183.90/184.44 [8719]E(x87191,f196(f882(x87192,a870)))+E(f333(f333(f42(x87192,f882(x87193,a870)),x87191),f333(f333(f8(f882(x87193,a870),f882(x87193,a870),x87192),f333(f104(f882(x87193,a870)),x87194)),x87195)),f333(f333(f104(f882(x87193,a870)),x87194),f333(f333(f42(x87192,f882(x87193,a870)),x87191),x87195))) % 183.90/184.44 [8916]~P1(f333(f333(f248(a875),f333(x89164,x89162)),f333(x89164,x89163)))+P1(f333(f333(f335(f881(x89161,x89161)),f333(f333(f268(x89161,x89161),x89162),x89163)),f154(x89161,f333(f333(f152(f882(x89161,a875)),x89164),x89165)))) % 183.90/184.44 [9182]~P25(x91822,x91821,x91823,f333(f333(f113(f882(x91822,a870)),x91824),x91825))+E(f333(f333(f104(f882(x91821,a870)),f333(f312(x91822,x91821,x91823),f333(f333(f22(f882(x91822,a870)),x91824),x91825))),f333(f312(x91822,x91821,x91823),f333(f333(f22(f882(x91822,a870)),x91825),x91824))),f196(f882(x91821,a870))) % 183.90/184.44 [9462]~P1(f333(f333(f247(f882(x94623,a870)),f333(f287(x94621,x94623,x94624),x94622)),x94625))+P1(f333(f333(f247(f882(x94621,a870)),x94622),f333(f78(f882(x94621,a870)),f333(f287(x94623,x94621,f333(f288(x94621,x94623),x94624)),f333(f78(f882(x94623,a870)),x94625))))) % 183.90/184.44 [9487]~P25(x94871,x94872,x94873,f333(f333(f311(x94871),x94874),x94875))+~P1(f333(f333(f335(x94872),f333(x94873,x94874)),f333(f312(x94871,x94872,x94873),f333(f333(f22(f882(x94871,a870)),x94875),f333(f333(f311(x94871),x94874),f196(f882(x94871,a870))))))) % 183.90/184.44 [9538]P1(f333(f333(f247(f882(x95381,a870)),f333(f287(x95382,x95381,x95383),x95384)),x95385))+~P1(f333(f333(f247(f882(x95382,a870)),x95384),f333(f78(f882(x95382,a870)),f333(f287(x95381,x95382,f333(f288(x95382,x95381),x95383)),f333(f78(f882(x95381,a870)),x95385))))) % 183.90/184.44 [9612]~P83(x96121)+P1(f333(f333(f247(x96121),f333(f74(x96121),f333(f333(f22(x96121),f333(f333(f79(x96121),x96122),x96123)),f333(f333(f79(x96121),x96124),x96125)))),f333(f333(f79(x96121),f333(f74(x96121),f333(f333(f22(x96121),x96122),x96124))),f333(f74(x96121),f333(f333(f22(x96121),x96123),x96125))))) % 183.90/184.44 [9715]P1(f333(f333(f335(x97151),f352(x97152,x97153,x97154,x97151,x97155)),x97154))+P1(f333(f333(f247(f882(x97155,a870)),f333(f333(f41(x97151,f882(x97155,a870)),x97154),x97153)),x97152)) % 183.90/184.44 [9912]~P1(f333(f333(f247(f882(x99121,a870)),f333(x99124,f352(x99125,x99124,x99123,x99122,x99121))),x99125))+P1(f333(f333(f247(f882(x99121,a870)),f333(f333(f41(x99122,f882(x99121,a870)),x99123),x99124)),x99125)) % 183.90/184.44 [8547]E(f333(f333(f135(x85471),x85472),f333(f333(f160(x85471,x85473),f333(f333(f22(a875),x85474),f333(f197(f876(x85471)),x85472))),x85475)),f333(f333(f160(x85471,f333(f333(f135(x85471),x85472),x85473)),x85474),x85475))+P1(f333(f333(f248(a875),x85474),f333(f197(f876(x85471)),x85472))) % 183.90/184.44 [8573]~P135(x85731)+E(f333(f333(f79(x85731),f333(f333(f80(x85731),x85732),x85733)),f333(f333(f79(x85731),f333(f333(f80(x85731),x85734),x85733)),x85735)),f333(f333(f79(x85731),f333(f333(f80(x85731),f333(f333(f79(x85731),x85732),x85734)),x85733)),x85735)) % 183.90/184.44 [9136]~P134(x91361)+E(f333(f167(x91361),f333(f333(f155(x91362,x91361),f333(f333(f8(x91361,x91361,x91362),f333(f80(x91361),x91363)),x91364)),x91365)),f333(f333(f80(x91361),x91363),f333(f167(x91361),f333(f333(f155(x91362,x91361),x91364),x91365)))) % 183.90/184.44 [9309]E(f333(f197(f876(x93091)),f333(f333(f177(x93091),f333(f333(f245(a875),f333(f197(f876(x93091)),x93092)),f333(f197(f876(x93093)),x93094))),x93092)),f333(f197(f876(x93093)),f333(f333(f177(x93093),f333(f333(f245(a875),f333(f197(f876(x93091)),x93092)),f333(f197(f876(x93093)),x93094))),x93094)))+P1(f333(x93095,f333(f333(f184(x93091,x93093),x93092),x93094))) % 183.90/184.44 [9549]~P134(x95492)+E(f333(f333(f6(x95491,x95492),f333(f333(f7(x95491,x95492,x95492),f333(f333(f8(x95492,f882(x95492,x95492),x95491),f80(x95492)),x95493)),x95494)),x95495),f333(f333(f80(x95492),f333(f333(f6(x95491,x95492),x95493),x95495)),x95494)) % 183.90/184.44 [9550]~P59(x95502)+E(f333(f333(f6(x95501,x95502),f333(f333(f7(x95501,x95502,x95502),f333(f333(f8(x95502,f882(x95502,x95502),x95501),f291(x95502)),x95503)),x95504)),x95505),f333(f333(f291(x95502),f333(f333(f6(x95501,x95502),x95503),x95505)),x95504)) % 183.90/184.44 [9557]~P65(x95572)+E(f333(f333(f6(x95571,x95572),f333(f333(f18(x95571,x95572,x95572),f333(f333(f8(x95572,f882(x95572,x95572),x95571),f22(x95572)),x95573)),x95574)),x95575),f333(f333(f22(x95572),f333(f333(f6(x95571,x95572),x95573),x95575)),f333(f333(f6(x95571,x95572),x95574),x95575))) % 183.90/184.44 [9558]~P66(x95582)+E(f333(f333(f6(x95581,x95582),f333(f333(f18(x95581,x95582,x95582),f333(f333(f8(x95582,f882(x95582,x95582),x95581),f79(x95582)),x95583)),x95584)),x95585),f333(f333(f79(x95582),f333(f333(f6(x95581,x95582),x95583),x95585)),f333(f333(f6(x95581,x95582),x95584),x95585))) % 183.90/184.44 [9559]~P73(x95592)+E(f333(f333(f9(x95591,x95592),f333(f333(f18(x95591,x95592,x95592),f333(f333(f8(x95592,f882(x95592,x95592),x95591),f80(x95592)),x95593)),x95594)),x95595),f333(f333(f80(x95592),f333(f333(f9(x95591,x95592),x95593),x95595)),f333(f333(f9(x95591,x95592),x95594),x95595))) % 183.90/184.44 [9597]~E(x95973,f196(f882(x95971,a870)))+E(f333(f333(f41(x95971,f882(x95972,a870)),x95973),f333(f333(f7(x95971,f882(x95972,a870),f882(x95972,a870)),f333(f333(f8(f882(x95972,a870),f882(f882(x95972,a870),f882(x95972,a870)),x95971),f113(f882(x95972,a870))),x95974)),x95975)),f196(f882(x95972,a870))) % 183.90/184.44 [9598]~E(x95983,f196(f882(x95981,a870)))+E(f333(f333(f42(x95981,f882(x95982,a870)),x95983),f333(f333(f7(x95981,f882(x95982,a870),f882(x95982,a870)),f333(f333(f8(f882(x95982,a870),f882(f882(x95982,a870),f882(x95982,a870)),x95981),f22(f882(x95982,a870))),x95984)),x95985)),f256(f882(x95982,a870))) % 183.90/184.44 [9599]~E(x95993,f196(f882(x95991,a870)))+E(f333(f333(f42(x95991,f882(x95992,a870)),x95993),f333(f333(f7(x95991,f882(x95992,a870),f882(x95992,a870)),f333(f333(f8(f882(x95992,a870),f882(f882(x95992,a870),f882(x95992,a870)),x95991),f104(f882(x95992,a870))),x95994)),x95995)),f256(f882(x95992,a870))) % 183.90/184.44 [9620]E(x96201,f196(f882(x96202,a870)))+E(f333(f333(f41(x96202,f882(x96203,a870)),x96201),f333(f333(f7(x96202,f882(x96203,a870),f882(x96203,a870)),f333(f333(f8(f882(x96203,a870),f882(f882(x96203,a870),f882(x96203,a870)),x96202),f113(f882(x96203,a870))),x96204)),x96205)),f333(f333(f113(f882(x96203,a870)),f333(f333(f41(x96202,f882(x96203,a870)),x96201),x96204)),x96205)) % 183.90/184.44 [9621]E(x96211,f196(f882(x96212,a870)))+E(f333(f333(f42(x96212,f882(x96213,a870)),x96211),f333(f333(f7(x96212,f882(x96213,a870),f882(x96213,a870)),f333(f333(f8(f882(x96213,a870),f882(f882(x96213,a870),f882(x96213,a870)),x96212),f22(f882(x96213,a870))),x96214)),x96215)),f333(f333(f22(f882(x96213,a870)),f333(f333(f42(x96212,f882(x96213,a870)),x96211),x96214)),x96215)) % 183.90/184.44 [9622]E(x96221,f196(f882(x96222,a870)))+E(f333(f333(f42(x96222,f882(x96223,a870)),x96221),f333(f333(f7(x96222,f882(x96223,a870),f882(x96223,a870)),f333(f333(f8(f882(x96223,a870),f882(f882(x96223,a870),f882(x96223,a870)),x96222),f104(f882(x96223,a870))),x96224)),x96225)),f333(f333(f104(f882(x96223,a870)),f333(f333(f42(x96222,f882(x96223,a870)),x96221),x96224)),x96225)) % 183.90/184.44 [9189]~P1(f333(f333(f247(a875),x91891),x91894))+E(f333(f333(f22(a875),f333(f333(f79(a875),f333(f333(f80(a875),x91891),x91892)),x91893)),f333(f333(f79(a875),f333(f333(f80(a875),x91894),x91892)),x91895)),f333(f333(f22(a875),x91893),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x91894),x91891)),x91892)),x91895))) % 183.90/184.44 [9775]~P134(x97751)+E(f333(f167(x97751),f333(f333(f155(x97752,x97751),f333(f333(f7(x97752,x97751,x97751),f333(f333(f8(x97751,f882(x97751,x97751),x97752),f80(x97751)),x97753)),x97754)),x97755)),f333(f333(f80(x97751),f333(f167(x97751),f333(f333(f155(x97752,x97751),x97753),x97755))),x97754)) % 183.90/184.44 [9781]~P65(x97811)+E(f333(f167(x97811),f333(f333(f155(x97812,x97811),f333(f333(f18(x97812,x97811,x97811),f333(f333(f8(x97811,f882(x97811,x97811),x97812),f22(x97811)),x97813)),x97814)),x97815)),f333(f333(f22(x97811),f333(f167(x97811),f333(f333(f155(x97812,x97811),x97813),x97815))),f333(f167(x97811),f333(f333(f155(x97812,x97811),x97814),x97815)))) % 183.90/184.44 [9782]~P66(x97821)+E(f333(f167(x97821),f333(f333(f155(x97822,x97821),f333(f333(f18(x97822,x97821,x97821),f333(f333(f8(x97821,f882(x97821,x97821),x97822),f79(x97821)),x97823)),x97824)),x97825)),f333(f333(f79(x97821),f333(f167(x97821),f333(f333(f155(x97822,x97821),x97823),x97825))),f333(f167(x97821),f333(f333(f155(x97822,x97821),x97824),x97825)))) % 183.90/184.44 [9925]P1(f333(x99251,f333(f333(f184(x99252,x99253),x99254),x99255)))+~P1(f333(x99251,f333(f333(f184(x99252,x99253),f333(f333(f177(x99252),f333(f333(f245(a875),f333(f197(f876(x99252)),x99254)),f333(f197(f876(x99253)),x99255))),x99254)),f333(f333(f177(x99253),f333(f333(f245(a875),f333(f197(f876(x99252)),x99254)),f333(f197(f876(x99253)),x99255))),x99255)))) % 183.90/184.44 [10159]~P1(f333(f333(f335(f881(x101592,x101591)),f333(f333(f268(x101592,x101591),x101594),x101595)),f333(f288(x101591,x101592),x101593)))+P1(f333(f333(f257(x101591,x101592,f333(f333(f7(x101591,f882(f881(x101591,x101592),a870),f882(x101592,a870)),f333(f333(f8(f882(x101592,f882(f882(f881(x101591,x101592),a870),a870)),f882(f882(f881(x101591,x101592),a870),f882(x101592,a870)),x101591),f7(x101592,f882(f881(x101591,x101592),a870),a870)),f333(f333(f8(f882(x101592,f881(x101591,x101592)),f882(x101592,f882(f882(f881(x101591,x101592),a870),a870)),x101591),f333(f8(f881(x101591,x101592),f882(f882(f881(x101591,x101592),a870),a870),x101592),f335(f881(x101591,x101592)))),f268(x101591,x101592)))),x101593)),x101594),x101595)) % 183.90/184.44 [10168]P1(f333(f333(f335(f881(x101681,x101682)),f333(f333(f268(x101681,x101682),x101683),x101684)),f333(f288(x101682,x101681),x101685)))+~P1(f333(f333(f257(x101682,x101681,f333(f333(f7(x101682,f882(f881(x101682,x101681),a870),f882(x101681,a870)),f333(f333(f8(f882(x101681,f882(f882(f881(x101682,x101681),a870),a870)),f882(f882(f881(x101682,x101681),a870),f882(x101681,a870)),x101682),f7(x101681,f882(f881(x101682,x101681),a870),a870)),f333(f333(f8(f882(x101681,f881(x101682,x101681)),f882(x101681,f882(f882(f881(x101682,x101681),a870),a870)),x101682),f333(f8(f881(x101682,x101681),f882(f882(f881(x101682,x101681),a870),a870),x101681),f335(f881(x101682,x101681)))),f268(x101682,x101681)))),x101685)),x101683),x101684)) % 183.90/184.44 [9430]~P1(f333(f333(f247(a875),x94304),x94301))+E(f333(f333(f22(a875),f333(f333(f79(a875),f333(f333(f80(a875),x94301),x94302)),x94303)),f333(f333(f79(a875),f333(f333(f80(a875),x94304),x94302)),x94305)),f333(f333(f22(a875),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x94301),x94304)),x94302)),x94303)),x94305)) % 183.90/184.44 [10177]P24(x101771,x101772,f333(f312(a873,f874(x101771),f333(f333(f18(a873,f882(x101771,f882(a872,a870)),f874(x101771)),f333(f333(f18(a873,a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),f333(f333(f8(f882(x101771,f882(a872,a870)),f882(a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),a873),f91(x101771)),x101773)),a25)),x101774)),x101775))+~P24(x101771,f333(f333(f113(f882(f874(x101771),a870)),x101772),f333(f312(a873,f874(x101771),f333(f333(f18(a873,f882(x101771,f882(a872,a870)),f874(x101771)),f333(f333(f18(a873,a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),f333(f333(f8(f882(x101771,f882(a872,a870)),f882(a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),a873),f91(x101771)),x101773)),a25)),x101774)),x101775)),f333(f312(a873,f874(x101771),f333(f333(f18(a873,f882(x101771,f882(a872,a870)),f874(x101771)),f333(f333(f18(a873,a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),f333(f333(f8(f882(x101771,f882(a872,a870)),f882(a871,f882(f882(x101771,f882(a872,a870)),f874(x101771))),a873),f91(x101771)),x101773)),f333(f333(f8(f879(a871),a871,a873),f244(a871)),a27))),x101774)),x101775)) % 183.90/184.44 [10178]P28(x101781,x101782,f333(f312(a873,f874(x101781),f333(f333(f18(a873,f882(x101781,f882(a872,a870)),f874(x101781)),f333(f333(f18(a873,a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),f333(f333(f8(f882(x101781,f882(a872,a870)),f882(a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),a873),f91(x101781)),x101783)),a25)),x101784)),x101785))+~P28(x101781,f333(f333(f113(f882(f874(x101781),a870)),x101782),f333(f312(a873,f874(x101781),f333(f333(f18(a873,f882(x101781,f882(a872,a870)),f874(x101781)),f333(f333(f18(a873,a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),f333(f333(f8(f882(x101781,f882(a872,a870)),f882(a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),a873),f91(x101781)),x101783)),a25)),x101784)),x101785)),f333(f312(a873,f874(x101781),f333(f333(f18(a873,f882(x101781,f882(a872,a870)),f874(x101781)),f333(f333(f18(a873,a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),f333(f333(f8(f882(x101781,f882(a872,a870)),f882(a871,f882(f882(x101781,f882(a872,a870)),f874(x101781))),a873),f91(x101781)),x101783)),f333(f333(f8(f879(a871),a871,a873),f244(a871)),a27))),x101784)),x101785)) % 183.90/184.44 [5254]E(x52541,x52542)+~E(f29(x52543,x52544,x52541),f29(x52545,x52546,x52542)) % 183.90/184.44 [5255]E(x52551,x52552)+~E(f29(x52553,x52551,x52554),f29(x52555,x52552,x52556)) % 183.90/184.44 [5256]E(x52561,x52562)+~E(f29(x52561,x52563,x52564),f29(x52562,x52565,x52566)) % 183.90/184.44 [5257]E(x52571,x52572)+~E(f28(x52573,x52574,x52571),f28(x52575,x52576,x52572)) % 183.90/184.44 [5258]E(x52581,x52582)+~E(f28(x52583,x52581,x52584),f28(x52585,x52582,x52586)) % 183.90/184.44 [5259]E(x52591,x52592)+~E(f28(x52591,x52593,x52594),f28(x52592,x52595,x52596)) % 183.90/184.44 [6696]E(f333(f187(x66961,x66962,x66963,x66964),x66965),f333(f240(x66962),x66966))+~E(f333(x66964,x66965),f333(f240(x66962),x66966)) % 183.90/184.44 [6840]E(f333(f242(f879(x68401),x68402,f209(x68401),x68403),f333(x68404,x68405)),f333(x68403,x68406))+~E(f333(x68404,x68405),f333(f240(x68402),x68406)) % 183.90/184.44 [8376]~P19(x83765,x83761,x83762,x83766)+E(f333(f72(x83761,x83761,x83761,f333(x83762,x83763)),f333(x83762,x83764)),f333(f72(x83761,x83761,x83761,f333(x83762,x83764)),f333(x83762,x83763))) % 183.90/184.44 [8614]~P51(x86144,x86145,x86142,x86141,x86146)+E(f333(x86141,f333(x86142,x86143)),x86143) % 183.90/184.44 [8765]P25(x87651,x87652,x87653,x87654)+~P25(x87651,x87655,f333(f72(x87652,x87655,x87651,x87656),x87653),x87654) % 183.90/184.44 [8849]~P25(x88494,x88492,f333(f72(x88491,x88492,x88494,x88493),x88495),x88496)+P25(x88491,x88492,x88493,f333(f312(x88494,x88491,x88495),x88496)) % 183.90/184.44 [9560]P1(f333(f61(x95601),x95602))+~P1(f333(f66(x95601,x95603,x95604,x95605,x95602),x95606)) % 183.90/184.44 [9568]~P1(f333(f333(f335(x95684),x95683),f301(x95684,x95685,x95681,x95682,x95686)))+P1(f333(f333(x95681,x95682),x95683)) % 183.90/184.44 [9569]~P1(f333(f333(f335(x95694),x95693),f298(x95694,x95691,x95695,x95692,x95696)))+P1(f333(f333(x95691,x95692),x95693)) % 183.90/184.44 [9570]~P1(f333(f333(f335(x95704),x95702),f301(x95704,x95701,x95705,x95706,x95703)))+P1(f333(f333(x95701,x95702),x95703)) % 183.90/184.44 [9571]~P1(f333(f333(f335(x95714),x95712),f298(x95714,x95715,x95711,x95716,x95713)))+P1(f333(f333(x95711,x95712),x95713)) % 183.90/184.44 [5759]E(x57591,x57592)+~E(f333(f333(f268(x57593,x57594),x57595),x57591),f333(f333(f268(x57593,x57594),x57596),x57592)) % 183.90/184.44 [5761]E(x57611,x57612)+~E(f333(f333(f268(x57613,x57614),x57611),x57615),f333(f333(f268(x57613,x57614),x57612),x57616)) % 183.90/184.44 [5885]~P16(x58855,x58856,x58851)+E(f333(f333(x58851,x58852),f333(f333(x58851,x58853),x58854)),f333(f333(x58851,x58853),f333(f333(x58851,x58852),x58854))) % 183.90/184.44 [7296]~P32(x72964,x72961,f333(f333(f152(x72964),x72962),x72965),f333(f333(f152(x72964),x72963),x72966))+P1(f333(f333(x72961,x72962),x72963)) % 183.90/184.44 [7664]P32(x76641,x76642,x76643,x76644)+~P32(x76641,x76642,f333(f333(f152(x76641),x76645),x76643),f333(f333(f152(x76641),x76646),x76644)) % 183.90/184.44 [8708]~P51(x87085,x87081,x87082,x87086,x87084)+P1(f333(f333(f335(x87081),f333(x87082,x87083)),x87084)) % 183.90/184.44 [8877]E(f333(f75(x88771,x88772,x88773,x88774,x88775),x88776),f333(x88773,x88776))+P1(f333(f333(f335(x88771),x88776),x88775)) % 183.90/184.44 [8899]~E(x88993,f333(f333(f152(x88991),x88995),x88996))+P1(f333(f333(f335(f881(f876(x88991),f876(x88991))),f333(f333(f268(f876(x88991),f876(x88991)),x88992),f333(f333(f135(x88991),x88992),x88993))),f148(x88991,x88994))) % 183.90/184.44 [8906]E(f333(f75(x89061,x89062,x89063,x89064,x89065),x89066),f333(x89064,x89066))+~P1(f333(f333(f335(x89061),x89066),x89065)) % 183.90/184.44 [8911]E(f333(f189(x89111,x89112,x89113,x89114,x89115),x89116),f333(x89113,x89116))+P1(f333(f333(f335(x89111),x89116),f333(f174(x89111),x89114))) % 183.90/184.44 [9140]~P34(x91401,x91402,x91403,x91405,x91406)+P34(x91401,x91402,x91403,f333(f333(f177(x91401),x91404),x91405),f333(f333(f177(x91402),x91404),x91406)) % 183.90/184.44 [9141]~P34(x91411,x91412,x91413,x91415,x91416)+P34(x91411,x91412,x91413,f333(f333(f139(x91411),x91414),x91415),f333(f333(f139(x91412),x91414),x91416)) % 183.90/184.44 [9632]~P23(x96324,x96322,x96325,x96323,x96326,x96321)+E(f333(x96321,f196(f882(x96322,a870))),x96323) % 183.90/184.44 [9875]~E(f333(x98754,f333(f267(x98751,x98753),x98755)),f333(x98756,f333(f267(x98751,x98753),x98755)))+E(f333(f273(x98751,x98752,x98753,x98753,x98754,f33(x98753)),x98755),f333(f273(x98751,x98752,x98753,x98753,x98756,f33(x98753)),x98755)) % 183.90/184.44 [9876]~E(f333(x98764,f333(f271(x98761,x98762),x98765)),f333(x98766,f333(f271(x98761,x98762),x98765)))+E(f333(f273(x98761,x98761,x98762,x98763,f33(x98761),x98764),x98765),f333(f273(x98761,x98761,x98762,x98763,f33(x98761),x98766),x98765)) % 183.90/184.44 [9921]~E(f333(f273(x99212,x99216,x99213,x99213,x99211,f33(x99213)),x99214),f333(f273(x99212,x99216,x99213,x99213,x99215,f33(x99213)),x99214))+E(f333(x99211,f333(f267(x99212,x99213),x99214)),f333(x99215,f333(f267(x99212,x99213),x99214))) % 183.90/184.44 [9922]~E(f333(f273(x99222,x99222,x99223,x99226,f33(x99222),x99221),x99224),f333(f273(x99222,x99222,x99223,x99226,f33(x99222),x99225),x99224))+E(f333(x99221,f333(f271(x99222,x99223),x99224)),f333(x99225,f333(f271(x99222,x99223),x99224))) % 183.90/184.44 [8804]P1(f333(f333(f335(x88041),x88042),x88043))+~P1(f333(f333(f335(f881(x88041,x88044)),f333(f333(f268(x88041,x88044),x88042),x88045)),f333(f333(f270(x88041,x88044),x88043),x88046))) % 183.90/184.44 [8819]P1(f333(f333(f335(x88191),x88192),f333(x88193,x88194)))+~P1(f333(f333(f335(f881(x88195,x88191)),f333(f333(f268(x88195,x88191),x88194),x88192)),f333(f333(f270(x88195,x88191),x88196),x88193))) % 183.90/184.44 [8908]~E(f333(f197(f876(x89081)),x89084),f333(f197(f876(x89082)),x89085))+E(f189(x89081,x89082,x89083,x89084,f333(f333(f135(x89082),x89085),x89086)),f189(x89081,x89082,x89083,x89084,x89085)) % 183.90/184.44 [8909]~E(f333(f197(f876(x89091)),x89094),f333(f197(f876(x89092)),x89096))+E(f189(x89091,x89092,x89093,f333(f333(f135(x89091),x89094),x89095),x89096),f189(x89091,x89092,x89093,x89094,x89096)) % 183.90/184.44 [9161]P1(f333(f333(f335(x91611),x91614),f186(x91611,x91612,x91616)))+E(f187(x91611,x91612,f333(f333(f333(f71(x91611,f879(x91612)),x91613),x91614),f333(f240(x91612),x91615)),x91616),f333(f333(f333(f71(x91611,f879(x91612)),f187(x91611,x91612,x91613,x91616)),x91614),f333(f240(x91612),x91615))) % 183.90/184.44 [9260]P1(f333(f333(f335(f881(x92601,x92601)),f333(f333(f268(x92601,x92601),f333(x92602,x92603)),f333(x92602,x92604))),x92605))+~P1(f333(f333(f335(f881(x92606,x92606)),f333(f333(f268(x92606,x92606),x92603),x92604)),f333(f333(f289(x92601,x92606),x92605),x92602))) % 183.90/184.44 [9280]~P1(f333(f333(f335(f881(x92804,x92804)),f333(f333(f268(x92804,x92804),f333(x92806,x92802)),f333(x92806,x92803))),x92805))+P1(f333(f333(f335(f881(x92801,x92801)),f333(f333(f268(x92801,x92801),x92802),x92803)),f333(f333(f289(x92804,x92801),x92805),x92806))) % 183.90/184.44 [9924]E(f333(f333(f268(x99241,x99242),f663(x99243,x99244,x99245,x99246,x99242,x99241)),f664(x99243,x99244,x99245,x99246,x99242,x99241)),x99246)+~P1(f333(f333(f335(f881(x99241,x99242)),x99246),f333(f333(f290(x99241,x99245,x99242),x99244),x99243))) % 183.90/184.44 [10125]~P1(f333(f333(f335(f881(x101251,x101256)),x101255),f333(f333(f290(x101251,x101252,x101256),x101254),x101253)))+P1(f333(f333(f335(f881(x101251,x101252)),f333(f333(f268(x101251,x101252),f663(x101253,x101254,x101252,x101255,x101256,x101251)),f665(x101253,x101254,x101252,x101255,x101256,x101251))),x101254)) % 183.90/184.44 [10126]~P1(f333(f333(f335(f881(x101266,x101262)),x101265),f333(f333(f290(x101266,x101261,x101262),x101264),x101263)))+P1(f333(f333(f335(f881(x101261,x101262)),f333(f333(f268(x101261,x101262),f665(x101263,x101264,x101261,x101265,x101262,x101266)),f664(x101263,x101264,x101261,x101265,x101262,x101266))),x101263)) % 183.90/184.44 [6159]~E(x61596,x61594)+E(f333(f333(f333(f333(f71(x61591,x61592),x61593),x61594),x61595),x61596),x61595) % 183.90/184.44 [6209]E(x62091,x62092)+E(f333(f333(f333(f333(f71(x62093,x62094),x62095),x62092),x62096),x62091),f333(x62095,x62091)) % 183.90/184.44 [7737]~P4(x77372)+E(f333(f333(f41(x77371,x77372),x77373),f333(f333(f7(x77371,x77374,x77372),x77375),x77376)),f333(f333(f333(f41(x77371,f882(x77374,x77372)),x77373),x77375),x77376)) % 183.90/184.44 [7738]~P4(x77382)+E(f333(f333(f42(x77381,x77382),x77383),f333(f333(f7(x77381,x77384,x77382),x77385),x77386)),f333(f333(f333(f42(x77381,f882(x77384,x77382)),x77383),x77385),x77386)) % 183.90/184.44 [8529]E(f333(f333(f41(x85291,f882(x85292,a870)),x85293),f333(f333(f8(f882(x85292,a870),f882(x85292,a870),x85291),f333(f311(x85292),x85294)),x85295)),f333(f333(f311(x85292),x85294),f333(f333(f41(x85291,f882(x85292,a870)),x85293),x85295)))+~P1(f333(f333(f335(x85291),x85296),x85293)) % 183.90/184.44 [8963]~P4(x89632)+E(f333(f333(f41(x89631,x89632),x89633),f333(f333(f8(f882(x89634,x89632),x89632,x89631),f333(f41(x89634,x89632),x89635)),f333(f7(x89634,x89631,x89632),x89636))),f333(f333(f41(x89634,x89632),x89635),f333(f333(f8(f882(x89631,x89632),x89632,x89634),f333(f41(x89631,x89632),x89633)),x89636))) % 183.90/184.44 [8964]~P4(x89642)+E(f333(f333(f42(x89641,x89642),x89643),f333(f333(f8(f882(x89644,x89642),x89642,x89641),f333(f42(x89644,x89642),x89645)),f333(f7(x89644,x89641,x89642),x89646))),f333(f333(f42(x89644,x89642),x89645),f333(f333(f8(f882(x89641,x89642),x89642,x89644),f333(f42(x89641,x89642),x89643)),x89646))) % 183.90/184.44 [9170]P1(f333(f333(f335(x91701),x91702),f333(f174(x91701),x91703)))+~P1(f333(f333(f335(f881(x91704,x91701)),f333(f333(f268(x91704,x91701),x91705),x91702)),f333(f174(f881(x91704,x91701)),f333(f333(f184(x91704,x91701),x91706),x91703)))) % 183.90/184.44 [9171]P1(f333(f333(f335(x91711),x91712),f333(f174(x91711),x91713)))+~P1(f333(f333(f335(f881(x91711,x91714)),f333(f333(f268(x91711,x91714),x91712),x91715)),f333(f174(f881(x91711,x91714)),f333(f333(f184(x91711,x91714),x91713),x91716)))) % 183.90/184.44 [9274]P1(f333(f333(f247(f882(x92741,a870)),f333(f287(x92742,x92741,x92743),x92744)),x92745))+~P1(f333(f333(f247(f882(f881(x92742,x92741),a870)),x92743),f333(f333(f270(x92742,x92741),x92746),f333(f16(f882(x92741,a870),x92742),x92745)))) % 183.90/184.44 [9465]P1(f333(f333(f335(f881(f876(x94651),f876(x94651))),f333(f333(f268(f876(x94651),f876(x94651)),f333(f333(f152(x94651),x94652),x94653)),f333(f333(f152(x94651),x94654),x94655))),f148(x94651,x94656)))+~P1(f333(f333(f335(f881(x94651,x94651)),f333(f333(f268(x94651,x94651),x94652),x94654)),x94656)) % 183.90/184.44 [9920]E(f333(f333(f268(x99201,x99202),f608(x99203,x99204,x99205,x99202,x99201,x99206)),f611(x99203,x99204,x99205,x99202,x99201,x99206)),x99206)+P1(f333(f333(f335(x99205),x99204),f333(f333(f272(x99201,x99202,f882(x99205,a870)),x99203),x99206))) % 183.90/184.44 [9926]E(f333(f333(f268(x99261,x99262),f609(x99263,x99264,x99262,x99261,x99265,x99266)),f610(x99263,x99264,x99262,x99261,x99265,x99266)),x99263)+~P1(f333(f333(f335(x99266),x99265),f333(f333(f272(x99261,x99262,f882(x99266,a870)),x99264),x99263))) % 183.90/184.44 [10084]P1(f333(f333(f335(x100841),x100842),f333(f333(x100843,f609(x100844,x100843,x100845,x100846,x100842,x100841)),f610(x100844,x100843,x100845,x100846,x100842,x100841))))+~P1(f333(f333(f335(x100841),x100842),f333(f333(f272(x100846,x100845,f882(x100841,a870)),x100843),x100844))) % 183.90/184.44 [10103]~P1(f333(f333(f335(x101031),x101032),f333(f333(x101035,f608(x101035,x101032,x101031,x101034,x101033,x101036)),f611(x101035,x101032,x101031,x101034,x101033,x101036))))+P1(f333(f333(f335(x101031),x101032),f333(f333(f272(x101033,x101034,f882(x101031,a870)),x101035),x101036))) % 183.90/184.44 [7860]P1(f333(f333(f335(x78601),x78604),x78606))+E(f190(x78601,x78602,f333(f333(f333(f71(x78601,f879(x78602)),x78603),x78604),x78605),x78606),f190(x78601,x78602,x78603,x78606)) % 183.90/184.44 [7937]P1(f333(f333(f335(x79371),x79374),x79376))+E(f333(f312(x79371,x79372,f333(f333(f333(f71(x79371,x79372),x79373),x79374),x79375)),x79376),f333(f312(x79371,x79372,x79373),x79376)) % 183.90/184.44 [7964]P1(f333(f333(f335(x79641),x79644),f333(f174(x79641),x79646)))+E(f333(f333(f155(x79641,x79642),f333(f333(f333(f71(x79641,x79642),x79643),x79644),x79645)),x79646),f333(f333(f155(x79641,x79642),x79643),x79646)) % 183.90/184.44 [8426]E(x84261,x84262)+E(f333(f333(f160(x84263,f333(f333(f160(x84263,x84264),x84261),x84265)),x84262),x84266),f333(f333(f160(x84263,f333(f333(f160(x84263,x84264),x84262),x84266)),x84261),x84265)) % 183.90/184.44 [8969]~P1(f333(f333(f335(x89693),x89696),x89695))+E(f333(f333(f311(x89691),x89692),f333(f312(x89693,x89691,x89694),f333(f333(f22(f882(x89693,a870)),x89695),f333(f333(f311(x89693),x89696),f196(f882(x89693,a870)))))),f333(f312(x89693,x89691,f333(f333(f333(f71(x89693,x89691),x89694),x89696),x89692)),x89695)) % 183.90/184.44 [9737]E(f189(x97371,x97372,x97373,f333(f333(f135(x97371),x97374),f333(f333(f152(x97371),x97375),f116(x97371))),x97376),f333(f333(f333(f71(x97371,f879(x97372)),f189(x97371,x97372,x97373,x97374,x97376)),x97375),f333(f240(x97372),f333(f333(f166(x97372),x97376),f333(f197(f876(x97371)),x97374)))))+~P1(f333(f333(f248(a875),f333(f197(f876(x97371)),x97374)),f333(f197(f876(x97372)),x97376))) % 183.90/184.44 [8747]~E(x87473,x87476)+E(f333(f333(f180(x87471,x87472),f333(f333(f152(f881(x87471,x87472)),f333(f333(f268(x87471,x87472),x87473),x87474)),x87475)),x87476),f333(f240(x87472),x87474)) % 183.90/184.44 [8774]E(x87741,x87742)+E(f333(f333(f180(x87743,x87744),f333(f333(f152(f881(x87743,x87744)),f333(f333(f268(x87743,x87744),x87741),x87745)),x87746)),x87742),f333(f333(f180(x87743,x87744),x87746),x87742)) % 183.90/184.44 [9045]~P1(f333(f333(x90454,x90455),x90456))+P1(f333(f333(f333(f333(f113(f882(x90451,f882(x90452,a870))),x90453),x90454),x90455),x90456)) % 183.90/184.44 [9047]~P1(f333(f333(x90473,x90475),x90476))+P1(f333(f333(f333(f333(f113(f882(x90471,f882(x90472,a870))),x90473),x90474),x90475),x90476)) % 183.90/184.44 [9331]P1(f333(f333(x93311,x93312),x93313))+~P1(f333(f333(f333(f333(f104(f882(x93314,f882(x93315,a870))),x93316),x93311),x93312),x93313)) % 183.90/184.44 [9332]P1(f333(f333(x93321,x93322),x93323))+~P1(f333(f333(f333(f333(f104(f882(x93324,f882(x93325,a870))),x93321),x93326),x93322),x93323)) % 183.90/184.44 [9759]~P66(x97592)+E(f333(f333(f6(x97591,x97592),f333(f333(f7(x97591,f882(x97593,a870),x97592),f333(f333(f8(f882(x97593,x97592),f882(f882(x97593,a870),x97592),x97591),f6(x97593,x97592)),x97594)),x97595)),x97596),f333(f333(f6(f881(x97591,x97593),x97592),f333(f272(x97591,x97593,x97592),x97594)),f333(f333(f270(x97591,x97593),x97596),f333(f16(f882(x97593,a870),x97591),x97595)))) % 183.90/184.44 [9760]~P73(x97602)+E(f333(f333(f9(x97601,x97602),f333(f333(f7(x97601,f882(x97603,a870),x97602),f333(f333(f8(f882(x97603,x97602),f882(f882(x97603,a870),x97602),x97601),f9(x97603,x97602)),x97604)),x97605)),x97606),f333(f333(f9(f881(x97601,x97603),x97602),f333(f272(x97601,x97603,x97602),x97604)),f333(f333(f270(x97601,x97603),x97606),f333(f16(f882(x97603,a870),x97601),x97605)))) % 183.90/184.44 [9903]~P66(x99032)+E(f333(f333(f6(x99031,x99032),f333(f333(f7(x99031,f882(x99033,a870),x99032),f333(f333(f8(f882(x99033,x99032),f882(f882(x99033,a870),x99032),x99031),f6(x99033,x99032)),f333(f7(x99033,x99031,x99032),x99034))),x99035)),x99036),f333(f333(f6(x99033,x99032),f333(f333(f7(x99033,f882(x99031,a870),x99032),f333(f333(f8(f882(x99031,x99032),f882(f882(x99031,a870),x99032),x99033),f6(x99031,x99032)),x99034)),x99036)),x99035)) % 183.90/184.44 [9601]~P1(f333(f333(f335(x96011),x96015),x96014))+E(f333(f333(f333(f71(x96011,f879(x96012)),f190(x96011,x96012,x96013,f333(f333(f22(f882(x96011,a870)),x96014),f333(f333(f311(x96011),x96015),f196(f882(x96011,a870)))))),x96015),x96016),f190(x96011,x96012,f333(f333(f333(f71(x96011,f879(x96012)),x96013),x96015),x96016),x96014)) % 183.90/184.44 [10181]~P1(f333(f333(f335(f881(x101811,x101812)),f333(f333(f268(x101811,x101812),x101815),x101816)),f333(f333(f113(f882(f881(x101811,x101812),a870)),x101813),x101814)))+P1(f333(f333(f333(f333(f113(f882(x101811,f882(x101812,a870))),f333(f333(f7(x101811,f882(f881(x101811,x101812),a870),f882(x101812,a870)),f333(f333(f8(f882(x101812,f882(f882(f881(x101811,x101812),a870),a870)),f882(f882(f881(x101811,x101812),a870),f882(x101812,a870)),x101811),f7(x101812,f882(f881(x101811,x101812),a870),a870)),f333(f333(f8(f882(x101812,f881(x101811,x101812)),f882(x101812,f882(f882(f881(x101811,x101812),a870),a870)),x101811),f333(f8(f881(x101811,x101812),f882(f882(f881(x101811,x101812),a870),a870),x101812),f335(f881(x101811,x101812)))),f268(x101811,x101812)))),x101813)),f333(f333(f7(x101811,f882(f881(x101811,x101812),a870),f882(x101812,a870)),f333(f333(f8(f882(x101812,f882(f882(f881(x101811,x101812),a870),a870)),f882(f882(f881(x101811,x101812),a870),f882(x101812,a870)),x101811),f7(x101812,f882(f881(x101811,x101812),a870),a870)),f333(f333(f8(f882(x101812,f881(x101811,x101812)),f882(x101812,f882(f882(f881(x101811,x101812),a870),a870)),x101811),f333(f8(f881(x101811,x101812),f882(f882(f881(x101811,x101812),a870),a870),x101812),f335(f881(x101811,x101812)))),f268(x101811,x101812)))),x101814)),x101815),x101816)) % 183.90/184.44 [10182]~P1(f333(f333(f335(f881(x101821,x101822)),f333(f333(f268(x101821,x101822),x101825),x101826)),f333(f333(f104(f882(f881(x101821,x101822),a870)),x101823),x101824)))+P1(f333(f333(f333(f333(f104(f882(x101821,f882(x101822,a870))),f333(f333(f7(x101821,f882(f881(x101821,x101822),a870),f882(x101822,a870)),f333(f333(f8(f882(x101822,f882(f882(f881(x101821,x101822),a870),a870)),f882(f882(f881(x101821,x101822),a870),f882(x101822,a870)),x101821),f7(x101822,f882(f881(x101821,x101822),a870),a870)),f333(f333(f8(f882(x101822,f881(x101821,x101822)),f882(x101822,f882(f882(f881(x101821,x101822),a870),a870)),x101821),f333(f8(f881(x101821,x101822),f882(f882(f881(x101821,x101822),a870),a870),x101822),f335(f881(x101821,x101822)))),f268(x101821,x101822)))),x101823)),f333(f333(f7(x101821,f882(f881(x101821,x101822),a870),f882(x101822,a870)),f333(f333(f8(f882(x101822,f882(f882(f881(x101821,x101822),a870),a870)),f882(f882(f881(x101821,x101822),a870),f882(x101822,a870)),x101821),f7(x101822,f882(f881(x101821,x101822),a870),a870)),f333(f333(f8(f882(x101822,f881(x101821,x101822)),f882(x101822,f882(f882(f881(x101821,x101822),a870),a870)),x101821),f333(f8(f881(x101821,x101822),f882(f882(f881(x101821,x101822),a870),a870),x101822),f335(f881(x101821,x101822)))),f268(x101821,x101822)))),x101824)),x101825),x101826)) % 183.90/184.44 [10188]P1(f333(f333(f335(f881(x101881,x101882)),f333(f333(f268(x101881,x101882),x101883),x101884)),f333(f333(f113(f882(f881(x101881,x101882),a870)),x101885),x101886)))+~P1(f333(f333(f333(f333(f113(f882(x101881,f882(x101882,a870))),f333(f333(f7(x101881,f882(f881(x101881,x101882),a870),f882(x101882,a870)),f333(f333(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)),f333(f333(f8(f882(x101882,f881(x101881,x101882)),f882(x101882,f882(f882(f881(x101881,x101882),a870),a870)),x101881),f333(f8(f881(x101881,x101882),f882(f882(f881(x101881,x101882),a870),a870),x101882),f335(f881(x101881,x101882)))),f268(x101881,x101882)))),x101885)),f333(f333(f7(x101881,f882(f881(x101881,x101882),a870),f882(x101882,a870)),f333(f333(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)),f333(f333(f8(f882(x101882,f881(x101881,x101882)),f882(x101882,f882(f882(f881(x101881,x101882),a870),a870)),x101881),f333(f8(f881(x101881,x101882),f882(f882(f881(x101881,x101882),a870),a870),x101882),f335(f881(x101881,x101882)))),f268(x101881,x101882)))),x101886)),x101883),x101884)) % 183.90/184.44 [10189]P1(f333(f333(f335(f881(x101891,x101892)),f333(f333(f268(x101891,x101892),x101893),x101894)),f333(f333(f104(f882(f881(x101891,x101892),a870)),x101895),x101896)))+~P1(f333(f333(f333(f333(f104(f882(x101891,f882(x101892,a870))),f333(f333(f7(x101891,f882(f881(x101891,x101892),a870),f882(x101892,a870)),f333(f333(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)),f333(f333(f8(f882(x101892,f881(x101891,x101892)),f882(x101892,f882(f882(f881(x101891,x101892),a870),a870)),x101891),f333(f8(f881(x101891,x101892),f882(f882(f881(x101891,x101892),a870),a870),x101892),f335(f881(x101891,x101892)))),f268(x101891,x101892)))),x101895)),f333(f333(f7(x101891,f882(f881(x101891,x101892),a870),f882(x101892,a870)),f333(f333(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)),f333(f333(f8(f882(x101892,f881(x101891,x101892)),f882(x101892,f882(f882(f881(x101891,x101892),a870),a870)),x101891),f333(f8(f881(x101891,x101892),f882(f882(f881(x101891,x101892),a870),a870),x101892),f335(f881(x101891,x101892)))),f268(x101891,x101892)))),x101896)),x101893),x101894)) % 183.90/184.44 [10175]~P1(f333(f333(f335(f881(x101752,x101753)),f333(f333(f268(x101752,x101753),x101755),x101756)),f333(f333(f41(x101751,f882(f881(x101752,x101753),a870)),f256(f882(x101751,a870))),x101754)))+P1(f333(f333(f333(f333(f41(x101751,f882(x101752,f882(x101753,a870))),f256(f882(x101751,a870))),f333(f333(f8(f882(f881(x101752,x101753),a870),f882(x101752,f882(x101753,a870)),x101751),f333(f7(x101752,f882(f881(x101752,x101753),a870),f882(x101753,a870)),f333(f333(f8(f882(x101753,f882(f882(f881(x101752,x101753),a870),a870)),f882(f882(f881(x101752,x101753),a870),f882(x101753,a870)),x101752),f7(x101753,f882(f881(x101752,x101753),a870),a870)),f333(f333(f8(f882(x101753,f881(x101752,x101753)),f882(x101753,f882(f882(f881(x101752,x101753),a870),a870)),x101752),f333(f8(f881(x101752,x101753),f882(f882(f881(x101752,x101753),a870),a870),x101753),f335(f881(x101752,x101753)))),f268(x101752,x101753))))),x101754)),x101755),x101756)) % 183.90/184.44 [10176]~P1(f333(f333(f335(f881(x101762,x101763)),f333(f333(f268(x101762,x101763),x101765),x101766)),f333(f333(f42(x101761,f882(f881(x101762,x101763),a870)),f256(f882(x101761,a870))),x101764)))+P1(f333(f333(f333(f333(f42(x101761,f882(x101762,f882(x101763,a870))),f256(f882(x101761,a870))),f333(f333(f8(f882(f881(x101762,x101763),a870),f882(x101762,f882(x101763,a870)),x101761),f333(f7(x101762,f882(f881(x101762,x101763),a870),f882(x101763,a870)),f333(f333(f8(f882(x101763,f882(f882(f881(x101762,x101763),a870),a870)),f882(f882(f881(x101762,x101763),a870),f882(x101763,a870)),x101762),f7(x101763,f882(f881(x101762,x101763),a870),a870)),f333(f333(f8(f882(x101763,f881(x101762,x101763)),f882(x101763,f882(f882(f881(x101762,x101763),a870),a870)),x101762),f333(f8(f881(x101762,x101763),f882(f882(f881(x101762,x101763),a870),a870),x101763),f335(f881(x101762,x101763)))),f268(x101762,x101763))))),x101764)),x101765),x101766)) % 183.90/184.44 [10185]P1(f333(f333(f335(f881(x101851,x101852)),f333(f333(f268(x101851,x101852),x101853),x101854)),f333(f333(f41(x101855,f882(f881(x101851,x101852),a870)),f256(f882(x101855,a870))),x101856)))+~P1(f333(f333(f333(f333(f41(x101855,f882(x101851,f882(x101852,a870))),f256(f882(x101855,a870))),f333(f333(f8(f882(f881(x101851,x101852),a870),f882(x101851,f882(x101852,a870)),x101855),f333(f7(x101851,f882(f881(x101851,x101852),a870),f882(x101852,a870)),f333(f333(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)),f333(f333(f8(f882(x101852,f881(x101851,x101852)),f882(x101852,f882(f882(f881(x101851,x101852),a870),a870)),x101851),f333(f8(f881(x101851,x101852),f882(f882(f881(x101851,x101852),a870),a870),x101852),f335(f881(x101851,x101852)))),f268(x101851,x101852))))),x101856)),x101853),x101854)) % 183.90/184.44 [10186]P1(f333(f333(f335(f881(x101861,x101862)),f333(f333(f268(x101861,x101862),x101863),x101864)),f333(f333(f42(x101865,f882(f881(x101861,x101862),a870)),f256(f882(x101865,a870))),x101866)))+~P1(f333(f333(f333(f333(f42(x101865,f882(x101861,f882(x101862,a870))),f256(f882(x101865,a870))),f333(f333(f8(f882(f881(x101861,x101862),a870),f882(x101861,f882(x101862,a870)),x101865),f333(f7(x101861,f882(f881(x101861,x101862),a870),f882(x101862,a870)),f333(f333(f8(f882(x101862,f882(f882(f881(x101861,x101862),a870),a870)),f882(f882(f881(x101861,x101862),a870),f882(x101862,a870)),x101861),f7(x101862,f882(f881(x101861,x101862),a870),a870)),f333(f333(f8(f882(x101862,f881(x101861,x101862)),f882(x101862,f882(f882(f881(x101861,x101862),a870),a870)),x101861),f333(f8(f881(x101861,x101862),f882(f882(f881(x101861,x101862),a870),a870),x101862),f335(f881(x101861,x101862)))),f268(x101861,x101862))))),x101866)),x101863),x101864)) % 183.90/184.44 [7409]E(f333(x74091,f333(x74092,x74093)),f333(x74094,x74093))+~E(f333(f72(x74095,x74096,x74097,x74091),x74092),x74094) % 183.90/184.44 [9631]~P22(x96313,x96314,x96311,x96315,x96316,x96317)+E(f333(f333(x96311,x96312),x96312),x96312) % 183.90/184.44 [10000]~E(f333(f242(f879(x100007),x100001,f209(x100007),x100005),f333(x100004,x100003)),f333(f240(x100007),x100002))+E(f333(f240(x100001),f768(x100002,x100003,x100004,x100005,x100006,x100007,x100001)),f333(x100004,x100003)) % 183.90/184.44 [10001]~E(f333(f242(f879(x100016),x100017,f209(x100016),x100011),f333(x100014,x100013)),f333(f240(x100016),x100012))+E(f333(x100011,f768(x100012,x100013,x100014,x100011,x100015,x100016,x100017)),f333(f240(x100016),x100012)) % 183.90/184.44 [5987]~E(f333(f333(f155(x59871,x59875),x59876),x59872),f333(f333(f155(x59873,x59875),x59877),x59874))+E(f333(f197(f876(x59871)),x59872),f333(f197(f876(x59873)),x59874)) % 183.90/184.44 [7487]E(x74871,x74872)+~E(f333(f333(f333(f71(x74873,f879(x74874)),x74875),x74876),f333(f240(x74874),x74871)),f333(f333(f333(f71(x74873,f879(x74874)),x74877),x74876),f333(f240(x74874),x74872))) % 183.90/184.44 [8465]E(f333(x84651,f333(x84652,x84653)),f333(x84654,x84653))+~E(f333(f72(x84655,x84656,x84657,x84651),x84652),f333(f72(x84656,x84656,x84657,f33(x84656)),x84654)) % 183.90/184.44 [8793]~P34(x87934,x87935,x87931,f333(f333(f152(x87934),x87932),x87936),f333(f333(f152(x87935),x87933),x87937))+P1(f333(f333(x87931,x87932),x87933)) % 183.90/184.44 [9177]P34(x91771,x91772,x91773,x91774,x91775)+~P34(x91771,x91772,x91773,f333(f333(f152(x91771),x91776),x91774),f333(f333(f152(x91772),x91777),x91775)) % 183.90/184.44 [9798]P1(f333(f333(x97981,x97982),f562(x97983,x97982,x97984,x97981)))+~P1(f333(f333(f269(x97985,x97986,x97987,x97981,x97984),x97982),x97983)) % 183.90/184.44 [9819]P1(f333(f333(x98191,f562(x98192,x98193,x98191,x98194)),x98192))+~P1(f333(f333(f269(x98195,x98196,x98197,x98194,x98191),x98193),x98192)) % 183.90/184.44 [6031]E(x60311,x60312)+~E(f333(f333(f333(f91(x60313),x60314),x60315),x60311),f333(f333(f333(f91(x60313),x60316),x60317),x60312)) % 183.90/184.44 [6032]E(x60321,x60322)+~E(f333(f333(f333(f91(x60323),x60324),x60321),x60325),f333(f333(f333(f91(x60323),x60326),x60322),x60327)) % 183.90/184.44 [6033]E(x60331,x60332)+~E(f333(f333(f333(f91(x60333),x60331),x60334),x60335),f333(f333(f333(f91(x60333),x60332),x60336),x60337)) % 183.90/184.44 [8914]~P20(x89146,x89141,x89143,x89147)+E(f333(f72(x89141,x89141,x89142,f333(x89143,x89144)),f333(f72(x89141,x89141,x89142,f333(x89143,x89144)),x89145)),f333(f72(x89141,x89141,x89142,f333(x89143,x89144)),x89145)) % 183.90/184.44 [9283]~P34(x92833,x92832,x92834,f333(f333(f155(x92831,x92833),x92835),x92836),x92837)+P34(x92831,x92832,f333(f333(f8(x92833,f882(x92832,a870),x92831),x92834),x92835),x92836,x92837) % 183.90/184.44 [9306]P34(x93061,x93062,x93063,f333(f333(f155(x93064,x93061),x93065),x93066),x93067)+~P34(x93064,x93062,f333(f333(f8(x93061,f882(x93062,a870),x93064),x93063),x93065),x93066,x93067) % 183.90/184.44 [9717]E(f189(x97171,x97172,f333(f333(f333(f71(x97171,f879(x97172)),x97173),x97174),f333(f240(x97172),x97175)),x97176,x97177),f333(f333(f333(f71(x97171,f879(x97172)),f189(x97171,x97172,x97173,x97176,x97177)),x97174),f333(f240(x97172),x97175)))+P1(f333(f333(f335(x97171),x97174),f333(f174(x97171),x97176))) % 183.90/184.44 [8913]~P1(f333(f333(f335(x89131),x89132),f333(f333(x89135,x89136),x89137)))+P1(f333(f333(f335(x89131),x89132),f333(f333(f272(x89133,x89134,f882(x89131,a870)),x89135),f333(f333(f268(x89133,x89134),x89136),x89137)))) % 183.90/184.44 [9203]P1(f333(f333(f333(x92031,x92032),x92033),x92034))+~P1(f333(f333(f333(f272(x92035,x92036,f882(x92037,a870)),x92031),f333(f333(f268(x92035,x92036),x92032),x92033)),x92034)) % 183.90/184.44 [9345]P1(f333(f333(f335(x93451),f333(f333(x93452,x93453),x93454)),f333(f312(f881(x93455,x93456),x93451,f333(f272(x93455,x93456,x93451),x93452)),x93457)))+~P1(f333(f333(f335(f881(x93455,x93456)),f333(f333(f268(x93455,x93456),x93453),x93454)),x93457)) % 183.90/184.44 [9678]P1(f333(f333(f335(f881(f876(x96781),f876(x96781))),f333(f333(f268(f876(x96781),f876(x96781)),f333(f333(f135(x96781),x96782),f333(f333(f152(x96781),x96783),x96784))),f333(f333(f135(x96781),x96782),f333(f333(f152(x96781),x96785),x96786)))),f148(x96781,x96787)))+~P1(f333(f333(f335(f881(x96781,x96781)),f333(f333(f268(x96781,x96781),x96783),x96785)),x96787)) % 183.90/184.44 [9739]~P34(x97391,x97393,x97394,x97396,f333(f333(f155(x97392,x97393),x97395),x97397))+P34(x97391,x97392,f333(f333(f7(x97391,f882(x97392,x97393),f882(x97392,a870)),f333(f333(f8(f882(x97393,a870),f882(f882(x97392,x97393),f882(x97392,a870)),x97391),f8(x97393,a870,x97392)),x97394)),x97395),x97396,x97397) % 183.90/184.44 [9823]P34(x98231,x98232,x98233,x98234,f333(f333(f155(x98235,x98232),x98236),x98237))+~P34(x98231,x98235,f333(f333(f7(x98231,f882(x98235,x98232),f882(x98235,a870)),f333(f333(f8(f882(x98232,a870),f882(f882(x98235,x98232),f882(x98235,a870)),x98231),f8(x98232,a870,x98235)),x98233)),x98236),x98234,x98237) % 183.90/184.44 [9195]E(x91951,x91952)+E(f333(f333(f333(f71(x91953,x91954),f333(f333(f333(f71(x91953,x91954),x91955),x91951),x91956)),x91952),x91957),f333(f333(f333(f71(x91953,x91954),f333(f333(f333(f71(x91953,x91954),x91955),x91952),x91957)),x91951),x91956)) % 183.90/184.44 [9439]E(f189(x94391,x94392,f333(f333(f333(f71(x94391,f879(x94392)),x94393),x94394),f333(f240(x94392),x94395)),x94396,x94397),f189(x94391,x94392,x94393,x94396,x94397))+~P1(f333(f333(f335(x94391),x94394),f333(f174(x94391),f333(f333(f177(x94391),f333(f197(f876(x94392)),x94397)),x94396)))) % 183.90/184.44 [9750]E(f189(x97501,x97502,f333(f333(f333(f71(x97501,f879(x97502)),x97503),x97504),f333(f240(x97502),x97505)),x97506,x97507),f333(f333(f333(f71(x97501,f879(x97502)),f189(x97501,x97502,x97503,x97506,x97507)),x97504),f333(f240(x97502),x97505)))+P1(f333(f333(f335(x97501),x97504),f333(f174(x97501),f333(f333(f177(x97501),f333(f197(f876(x97502)),x97507)),x97506)))) % 183.90/184.44 [10114]P1(f333(f333(f335(x101141),f845(x101142,x101143,x101144,x101145,x101146,x101147,x101141)),x101145))+P1(f333(f333(f333(f333(f42(x101141,f882(x101147,f882(x101146,a870))),x101145),x101144),x101143),x101142)) % 183.90/184.44 [10115]P1(f333(f333(f335(x101151),f841(x101152,x101153,x101154,x101155,x101156,x101157,x101151)),x101155))+~P1(f333(f333(f333(f333(f41(x101151,f882(x101157,f882(x101156,a870))),x101155),x101154),x101153),x101152)) % 183.90/184.44 [10140]P1(f333(f333(f333(x101401,f841(x101402,x101403,x101401,x101404,x101405,x101406,x101407)),x101403),x101402))+~P1(f333(f333(f333(f333(f41(x101407,f882(x101406,f882(x101405,a870))),x101404),x101401),x101403),x101402)) % 183.90/184.44 [10157]~P1(f333(f333(f333(x101575,f845(x101577,x101576,x101575,x101574,x101573,x101572,x101571)),x101576),x101577))+P1(f333(f333(f333(f333(f42(x101571,f882(x101572,f882(x101573,a870))),x101574),x101575),x101576),x101577)) % 183.90/184.44 [10174]~P1(f333(f333(f335(f881(x101741,x101743)),f333(f333(f268(x101741,x101743),x101746),x101747)),f333(f333(f290(x101741,x101742,x101743),x101744),x101745)))+P1(f333(f333(f269(x101741,x101742,x101743,f333(f333(f7(x101741,f882(f881(x101741,x101742),a870),f882(x101742,a870)),f333(f333(f8(f882(x101742,f882(f882(f881(x101741,x101742),a870),a870)),f882(f882(f881(x101741,x101742),a870),f882(x101742,a870)),x101741),f7(x101742,f882(f881(x101741,x101742),a870),a870)),f333(f333(f8(f882(x101742,f881(x101741,x101742)),f882(x101742,f882(f882(f881(x101741,x101742),a870),a870)),x101741),f333(f8(f881(x101741,x101742),f882(f882(f881(x101741,x101742),a870),a870),x101742),f335(f881(x101741,x101742)))),f268(x101741,x101742)))),x101744),f333(f333(f7(x101742,f882(f881(x101742,x101743),a870),f882(x101743,a870)),f333(f333(f8(f882(x101743,f882(f882(f881(x101742,x101743),a870),a870)),f882(f882(f881(x101742,x101743),a870),f882(x101743,a870)),x101742),f7(x101743,f882(f881(x101742,x101743),a870),a870)),f333(f333(f8(f882(x101743,f881(x101742,x101743)),f882(x101743,f882(f882(f881(x101742,x101743),a870),a870)),x101742),f333(f8(f881(x101742,x101743),f882(f882(f881(x101742,x101743),a870),a870),x101743),f335(f881(x101742,x101743)))),f268(x101742,x101743)))),x101745)),x101746),x101747)) % 183.90/184.44 [10184]P1(f333(f333(f335(f881(x101841,x101842)),f333(f333(f268(x101841,x101842),x101843),x101844)),f333(f333(f290(x101841,x101845,x101842),x101846),x101847)))+~P1(f333(f333(f269(x101841,x101845,x101842,f333(f333(f7(x101841,f882(f881(x101841,x101845),a870),f882(x101845,a870)),f333(f333(f8(f882(x101845,f882(f882(f881(x101841,x101845),a870),a870)),f882(f882(f881(x101841,x101845),a870),f882(x101845,a870)),x101841),f7(x101845,f882(f881(x101841,x101845),a870),a870)),f333(f333(f8(f882(x101845,f881(x101841,x101845)),f882(x101845,f882(f882(f881(x101841,x101845),a870),a870)),x101841),f333(f8(f881(x101841,x101845),f882(f882(f881(x101841,x101845),a870),a870),x101845),f335(f881(x101841,x101845)))),f268(x101841,x101845)))),x101846),f333(f333(f7(x101845,f882(f881(x101845,x101842),a870),f882(x101842,a870)),f333(f333(f8(f882(x101842,f882(f882(f881(x101845,x101842),a870),a870)),f882(f882(f881(x101845,x101842),a870),f882(x101842,a870)),x101845),f7(x101842,f882(f881(x101845,x101842),a870),a870)),f333(f333(f8(f882(x101842,f881(x101845,x101842)),f882(x101842,f882(f882(f881(x101845,x101842),a870),a870)),x101845),f333(f8(f881(x101845,x101842),f882(f882(f881(x101845,x101842),a870),a870),x101842),f335(f881(x101845,x101842)))),f268(x101845,x101842)))),x101847)),x101843),x101844)) % 183.90/184.44 [10124]~P134(x101242)+E(f333(f333(f6(x101241,x101242),f333(f333(f7(x101241,f882(x101243,a870),x101242),f333(f333(f8(f882(x101243,x101242),f882(f882(x101243,a870),x101242),x101241),f6(x101243,x101242)),f333(f333(f7(x101241,f882(x101243,x101242),f882(x101243,x101242)),f333(f333(f8(f882(x101242,x101242),f882(f882(x101243,x101242),f882(x101243,x101242)),x101241),f8(x101242,x101242,x101243)),f333(f333(f8(x101242,f882(x101242,x101242),x101241),f80(x101242)),x101244))),x101245))),x101246)),x101247),f333(f333(f80(x101242),f333(f333(f6(x101241,x101242),x101244),x101247)),f333(f333(f6(x101243,x101242),x101245),x101246))) % 183.90/184.44 [9236]~P19(x92367,x92361,x92363,x92368)+E(f333(f72(x92361,x92361,x92362,f333(x92363,x92364)),f333(f72(x92361,x92361,x92362,f333(x92363,x92365)),x92366)),f333(f72(x92361,x92361,x92362,f333(x92363,x92365)),f333(f72(x92361,x92361,x92362,f333(x92363,x92364)),x92366))) % 183.90/184.44 [10179]E(f333(f333(f268(x101791,x101792),f333(x101793,f586(x101794,x101795,x101793,x101796,x101797,x101798,x101792,x101791))),f333(x101795,f587(x101794,x101795,x101793,x101796,x101797,x101798,x101792,x101791))),x101798)+~P1(f333(f333(f335(f881(x101791,x101792)),x101798),f333(f312(f881(x101797,x101796),f881(x101791,x101792),f273(x101797,x101791,x101796,x101792,x101793,x101795)),x101794))) % 183.90/184.44 [10195]~P1(f333(f333(f335(f881(x101958,x101957)),x101956),f333(f312(f881(x101951,x101952),f881(x101958,x101957),f273(x101951,x101958,x101952,x101957,x101955,x101954)),x101953)))+P1(f333(f333(f335(f881(x101951,x101952)),f333(f333(f268(x101951,x101952),f586(x101953,x101954,x101955,x101952,x101951,x101956,x101957,x101958)),f587(x101953,x101954,x101955,x101952,x101951,x101956,x101957,x101958))),x101953)) % 183.90/184.44 [9668]P1(f333(f333(f335(f881(f881(x96681,x96682),f881(x96681,x96682))),f333(f333(f268(f881(x96681,x96682),f881(x96681,x96682)),f333(f333(f268(x96681,x96682),x96683),x96684)),f333(f333(f268(x96681,x96682),x96685),x96686))),f326(x96681,x96682,x96687,x96688)))+~P1(f333(f333(f335(f881(x96681,x96681)),f333(f333(f268(x96681,x96681),x96683),x96685)),x96687)) % 183.90/184.44 [10167]E(f333(f143(x101671,x101672,f333(f7(x101672,x101671,x101671),x101673),f333(x101674,x101675)),x101676),f333(x101674,f333(f143(x101677,x101672,f333(f7(x101672,x101677,x101677),x101678),x101675),x101676)))+P1(f333(f333(f335(x101672),f772(x101675,x101678,x101674,x101673,x101677,x101671,x101676,x101672)),f333(f174(x101672),x101676))) % 183.90/184.44 [10187]~E(f333(f72(x101871,x101871,x101877,f333(x101873,f772(x101875,x101878,x101874,x101873,x101877,x101871,x101876,x101872))),x101874),f333(f72(x101877,x101871,x101877,x101874),f333(x101878,f772(x101875,x101878,x101874,x101873,x101877,x101871,x101876,x101872))))+E(f333(f143(x101871,x101872,f333(f7(x101872,x101871,x101871),x101873),f333(x101874,x101875)),x101876),f333(x101874,f333(f143(x101877,x101872,f333(f7(x101872,x101877,x101877),x101878),x101875),x101876))) % 183.90/184.44 [8470]E(f333(x84701,f333(x84702,x84703)),f333(x84704,f333(x84705,x84703)))+~E(f333(f72(x84706,x84707,x84708,x84701),x84702),f333(f72(x84709,x84707,x84708,x84704),x84705)) % 183.90/184.44 [10053]P1(f333(f333(f335(f881(x100531,x100532)),f333(f333(f268(x100531,x100532),f333(x100533,x100534)),f333(x100535,x100536))),f333(f312(f881(x100537,x100538),f881(x100531,x100532),f273(x100537,x100531,x100538,x100532,x100533,x100535)),x100539)))+~P1(f333(f333(f335(f881(x100537,x100538)),f333(f333(f268(x100537,x100538),x100534),x100536)),x100539)) % 183.90/184.44 [8741]~E(f333(x87414,f333(x87415,x87416)),f333(x87419,f333(x874110,x874111)))+E(f333(f333(f72(x87411,x87412,x87413,x87414),x87415),x87416),f333(f333(f72(x87417,x87412,x87418,x87419),x874110),x874111)) % 183.90/184.44 [4591]~P99(x45911)+~P106(x45911)+E(f104(x45911),f245(x45911)) % 183.90/184.44 [4592]~P98(x45921)+~P106(x45921)+E(f113(x45921),f246(x45921)) % 183.90/184.44 [4837]~P114(x48371)+~P90(x48371)+E(f333(f74(x48371),f333(f106(x48371),a100)),f77(x48371)) % 183.90/184.44 [5112]E(x51121,f2(a1))+E(f81(a1,x51121),f333(f78(a1),f77(a1)))+P1(f333(f333(f248(a1),f2(a1)),x51121)) % 183.90/184.44 [5320]E(x53201,f2(a1))+E(f81(a1,x53201),f77(a1))+~P1(f333(f333(f248(a1),f2(a1)),x53201)) % 183.90/184.44 [7300]~P38(x73001)+P1(f333(f61(a1),x73001))+~P1(f333(f61(a875),f333(f312(a1,a875,a107),x73001))) % 183.90/184.44 [9630]E(x96301,f196(f882(f881(a875,a875),a870)))+~P1(f333(f61(f881(a875,a875)),x96301))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f196(f882(f881(a875,a875),a870))),x96301)),a36)) % 183.90/184.44 [9799]E(x97991,f2(a875))+E(x97991,f333(a115,f2(a875)))+~P1(f333(f333(f248(a875),x97991),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.44 [10081]E(x100811,f2(a102))+E(f333(f333(f79(a1),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(a20,f333(f333(f38(a102),x100811),f333(f106(a102),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))),f77(a1)),f333(a20,x100811))+E(f44(a102,x100811,f333(f106(a102),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f2(a102)) % 183.90/184.44 [9931]E(x99311,f2(a102))+~E(f44(a102,x99311,f333(f106(a102),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f2(a102))+E(f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(a20,f333(f333(f38(a102),x99311),f333(f106(a102),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f333(a20,x99311)) % 183.90/184.44 [4664]~P52(x46641,x46642)+P43(x46641,x46642)+~P44(a870) % 183.90/184.44 [4601]~P141(x46011)+P30(x46011,x46012)+~E(x46012,f2(x46011)) % 183.90/184.44 [4602]~P106(x46021)+P14(x46021,x46022)+~E(x46022,f116(x46021)) % 183.90/184.44 [4611]~P114(x46111)+~E(x46112,f2(x46111))+E(f81(x46111,x46112),f2(x46111)) % 183.90/184.44 [4612]~P87(x46121)+~E(x46122,f2(x46121))+E(f81(x46121,x46122),f2(x46121)) % 183.90/184.44 [4620]~P141(x46202)+~P30(x46202,x46201)+E(x46201,f2(x46202)) % 183.90/184.44 [4654]~P114(x46542)+~E(f81(x46542,x46541),f2(x46542))+E(x46541,f2(x46542)) % 183.90/184.44 [4671]~P3(x46712)+~P3(x46711)+P3(f882(x46711,x46712)) % 183.90/184.44 [4672]~P3(x46722)+~P3(x46721)+P3(f880(x46721,x46722)) % 183.90/184.44 [4673]~P3(x46732)+~P3(x46731)+P3(f881(x46731,x46732)) % 183.90/184.44 [4674]~P5(x46742)+~P5(x46741)+P5(f203(x46741,x46742)) % 183.90/184.44 [4675]~P57(x46752)+~P57(x46751)+P57(f882(x46751,x46752)) % 183.90/184.44 [4676]~P57(x46762)+~P57(x46761)+P57(f880(x46761,x46762)) % 183.90/184.44 [4677]~P57(x46772)+~P57(x46771)+P57(f881(x46771,x46772)) % 183.90/184.44 [4678]~P57(x46781)+~P92(x46782)+P92(f882(x46781,x46782)) % 183.90/184.44 [4679]~P142(x46792)+~P142(x46791)+P142(f881(x46791,x46792)) % 183.90/184.44 [4680]~P101(x46802)+~P101(x46801)+P101(f881(x46801,x46802)) % 183.90/184.44 [4808]~P106(x48081)+~P14(x48081,x48082)+P14(x48081,f153(x48081,x48082)) % 183.90/184.44 [5043]~P5(x50432)+~P5(x50431)+P5(f44(a1,x50431,x50432)) % 183.90/184.44 [4622]~P74(x46221)+~E(x46222,f2(x46221))+E(f333(f78(x46221),x46222),x46222) % 183.90/184.44 [4626]~P138(x46261)+~E(x46262,f2(a1))+E(f333(f105(x46261),x46262),f2(x46261)) % 183.90/184.44 [4627]~P89(x46271)+~E(x46272,f2(a1))+E(f333(f105(x46271),x46272),f2(x46271)) % 183.90/184.44 [4651]~P72(x46511)+~E(f2(x46511),x46512)+E(f333(f78(x46511),x46512),f2(x46511)) % 183.90/184.44 [4652]~P83(x46521)+~E(x46522,f2(x46521))+E(f333(f74(x46521),x46522),f2(x46521)) % 183.90/184.44 [4653]~P72(x46531)+~E(x46532,f2(x46531))+E(f333(f78(x46531),x46532),f2(x46531)) % 183.90/184.44 [4682]~P74(x46822)+E(x46821,f2(x46822))+~E(f333(f78(x46822),x46821),x46821) % 183.90/184.44 [4688]E(x46881,f333(a107,x46882))+~E(x46881,f2(a875))+~E(x46882,f333(f103(a1),x46881)) % 183.90/184.44 [4689]E(f333(a107,x46891),x46892)+~E(x46892,f2(a875))+~E(x46891,f333(f103(a1),x46892)) % 183.90/184.44 [4693]~P89(x46932)+E(x46931,f2(a1))+~E(f333(f105(x46932),x46931),f2(x46932)) % 183.90/184.44 [4698]~P83(x46982)+E(x46981,f2(x46982))+~E(f333(f74(x46982),x46981),f2(x46982)) % 183.90/184.44 [4699]~P72(x46992)+E(x46991,f2(x46992))+~E(f333(f78(x46992),x46991),f2(x46992)) % 183.90/184.44 [4700]~P72(x47001)+E(f2(x47001),x47002)+~E(f333(f78(x47001),x47002),f2(x47001)) % 183.90/184.44 [4883]~P106(x48831)+~P14(x48831,x48832)+P14(x48831,f333(f173(x48831),x48832)) % 183.90/184.44 [4908]~P1(x49082)+~P1(x49081)+P1(f333(f333(a331,x49081),x49082)) % 183.90/184.44 [4942]~E(f77(a875),f2(a875))+E(f333(f37(x49421),x49422),f2(a875))+~P1(f333(f61(x49421),x49422)) % 183.90/184.44 [4975]~P134(x49751)+~P111(x49751)+E(f333(f333(f258(x49751),f2(x49751)),f333(a115,x49752)),f2(x49751)) % 183.90/184.44 [5013]~P106(x50131)+P14(x50131,f140(x50131,x50132))+~P1(f333(f61(x50131),x50132)) % 183.90/184.44 [5014]~P106(x50141)+P14(x50141,f760(x50142,x50141))+~P1(f333(f61(x50141),x50142)) % 183.90/184.44 [5035]~P106(x50351)+E(f333(f174(x50351),f140(x50351,x50352)),x50352)+~P1(f333(f61(x50351),x50352)) % 183.90/184.44 [5036]~P106(x50361)+E(f333(f174(x50361),f760(x50362,x50361)),x50362)+~P1(f333(f61(x50361),x50362)) % 183.90/184.44 [5064]P1(x50641)+P1(x50642)+~P1(f333(f333(a332,x50642),x50641)) % 183.90/184.44 [5076]E(x50761,f196(f882(x50762,a870)))+~E(f333(f37(x50762),x50761),f2(a875))+~P1(f333(f61(x50762),x50761)) % 183.90/184.44 [5081]P1(x50811)+~P1(x50812)+~P1(f333(f333(a336,x50812),x50811)) % 183.90/184.44 [5130]~P71(x51301)+E(f333(f74(x51301),x51302),x51302)+P1(f333(f333(f248(x51301),x51302),f2(x51301))) % 183.90/184.44 [5193]~P57(x51932)+~P1(f333(f57(x51932),x51931))+P1(f333(x51931,f718(x51931,x51932))) % 183.90/184.44 [5194]~P57(x51942)+~P1(f333(f57(x51942),x51941))+P1(f333(x51941,f723(x51941,x51942))) % 183.90/184.44 [5230]E(x52301,f116(x52302))+P1(f333(f138(x52302),f117(x52302,x52301)))+~P1(f333(f138(x52302),x52301)) % 183.90/184.44 [5235]~P106(x52351)+~P1(f333(f61(x52351),x52352))+P1(f333(f138(x52351),f140(x52351,x52352))) % 183.90/184.44 [5236]~P106(x52361)+~P1(f333(f61(x52361),x52362))+P1(f333(f138(x52361),f760(x52362,x52361))) % 183.90/184.44 [5242]~P138(x52421)+E(f333(f103(x52421),f333(a107,x52422)),f333(f105(x52421),x52422))+P1(f333(f333(f248(a1),x52422),f2(a1))) % 183.90/184.44 [5270]P6(x52702,x52701)+E(f333(x52701,f485(x52701)),f333(x52701,f552(x52701)))+P1(f333(f333(x52701,f485(x52701)),f552(x52701))) % 183.90/184.44 [5285]E(f333(f103(a1),f404(x52851,x52852)),x52851)+P1(f333(x52852,f333(a107,x52851)))+~P1(f333(x52852,f2(a875))) % 183.90/184.44 [5297]~P57(x52971)+~P1(f333(x52972,f724(x52972,x52971)))+P1(f333(f58(x52971),x52972)) % 183.90/184.44 [5298]~P57(x52981)+~P1(f333(x52982,f726(x52982,x52981)))+P1(f333(f58(x52981),x52982)) % 183.90/184.44 [5313]~P57(x53132)+~P35(x53132,x53131,f55(x53132))+P1(f333(x53131,f775(x53131,x53132))) % 183.90/184.44 [5329]~P114(x53291)+~E(f81(x53291,x53292),f333(f78(x53291),f77(x53291)))+P1(f333(f333(f248(x53291),x53292),f2(x53291))) % 183.90/184.44 [5405]~E(x54052,f2(a1))+E(f227(x54051,x54052),f333(f333(f268(a1,a1),f2(a1)),f77(a1)))+P1(f333(f333(f248(a1),x54052),f2(a1))) % 183.90/184.44 [5406]~E(x54061,f2(a1))+E(f227(x54061,x54062),f333(f333(f268(a1,a1),f2(a1)),f77(a1)))+P1(f333(f333(f248(a1),x54062),f2(a1))) % 183.90/184.44 [5458]E(f333(f103(a1),f404(x54581,x54582)),x54581)+P1(f333(x54582,f333(a107,x54581)))+P1(f333(f333(f248(a1),x54581),f2(a1))) % 183.90/184.44 [5521]~P114(x55211)+E(f81(x55211,x55212),f333(f78(x55211),f77(x55211)))+~P1(f333(f333(f248(x55211),x55212),f2(x55211))) % 183.90/184.44 [5522]~P83(x55221)+E(f333(f74(x55221),x55222),f333(f78(x55221),x55222))+~P1(f333(f333(f248(x55221),x55222),f2(x55221))) % 183.90/184.44 [5523]~P83(x55231)+E(f333(f74(x55231),x55232),f333(f78(x55231),x55232))+~P1(f333(f333(f247(x55231),x55232),f2(x55231))) % 183.90/184.44 [5524]~P71(x55241)+E(f333(f74(x55241),x55242),f333(f78(x55241),x55242))+~P1(f333(f333(f248(x55241),x55242),f2(x55241))) % 183.90/184.44 [5621]~P1(f333(x56211,f404(x56212,x56211)))+P1(f333(x56211,f333(a107,x56212)))+~P1(f333(x56211,f2(a875))) % 183.90/184.44 [5628]E(x56281,f2(a875))+E(f333(a115,f358(x56282,x56281)),x56281)+~P1(f333(f333(f248(a875),x56281),f333(a115,x56282))) % 183.90/184.44 [5632]P6(x56321,x56322)+~E(f333(x56322,f485(x56322)),f333(x56322,f552(x56322)))+~P1(f333(f333(x56322,f485(x56322)),f552(x56322))) % 183.90/184.44 [5652]~P106(x56521)+P14(x56521,x56522)+P1(f333(f333(f247(a875),f743(x56522,x56521)),f744(x56522,x56521))) % 183.90/184.44 [5653]~P106(x56531)+P14(x56531,x56532)+P1(f333(f333(f247(a875),f751(x56532,x56531)),f755(x56532,x56531))) % 183.90/184.44 [5739]~P83(x57391)+~E(x57392,f2(x57391))+P1(f333(f333(f247(x57391),f333(f74(x57391),x57392)),f2(x57391))) % 183.90/184.44 [5818]~P57(x58182)+~P57(x58181)+E(f59(x58181,x58182,f55(x58181),f55(x58182)),f55(f881(x58181,x58182))) % 183.90/184.44 [5822]~P1(f333(x58221,f404(x58222,x58221)))+P1(f333(x58221,f333(a107,x58222)))+P1(f333(f333(f248(a1),x58222),f2(a1))) % 183.90/184.44 [5845]~P1(f333(x58451,f333(a107,x58452)))+P1(f333(x58451,f2(a875)))+~P1(f333(f333(f248(a1),x58452),f2(a1))) % 183.90/184.44 [6181]~P114(x61811)+~P1(f333(f333(f248(x61811),x61812),f2(x61811)))+P1(f333(f333(f248(x61811),f81(x61811,x61812)),f2(x61811))) % 183.90/184.44 [6295]~P114(x62951)+P1(f333(f333(f248(x62951),f333(f105(x62951),x62952)),f2(x62951)))+~P1(f333(f333(f248(a1),x62952),f2(a1))) % 183.90/184.44 [6296]~P114(x62961)+P1(f333(f333(f247(x62961),f333(f105(x62961),x62962)),f2(x62961)))+~P1(f333(f333(f247(a1),x62962),f2(a1))) % 183.90/184.44 [6303]~P83(x63032)+E(x63031,f2(x63032))+~P1(f333(f333(f247(x63032),f333(f74(x63032),x63031)),f2(x63032))) % 183.90/184.44 [6379]~P138(x63791)+~P1(f333(f333(f335(x63791),x63792),f112(x63791)))+P1(f333(f333(f335(x63791),f333(f78(x63791),x63792)),f112(x63791))) % 183.90/184.44 [6411]~P114(x64111)+~P1(f333(f333(f248(x64111),f81(x64111,x64112)),f2(x64111)))+P1(f333(f333(f248(x64111),x64112),f2(x64111))) % 183.90/184.44 [6580]~P114(x65802)+~P1(f333(f333(f248(x65802),f333(f105(x65802),x65801)),f2(x65802)))+P1(f333(f333(f248(a1),x65801),f2(a1))) % 183.90/184.44 [6581]~P114(x65812)+~P1(f333(f333(f247(x65812),f333(f105(x65812),x65811)),f2(x65812)))+P1(f333(f333(f247(a1),x65811),f2(a1))) % 183.90/184.44 [7087]~P114(x70871)+~P1(f333(f333(f248(x70871),x70872),f2(x70871)))+P1(f333(f333(f248(x70871),f333(f333(f79(x70871),x70872),x70872)),f2(x70871))) % 183.90/184.44 [7088]~P74(x70881)+~P1(f333(f333(f248(x70881),x70882),f2(x70881)))+P1(f333(f333(f248(x70881),f333(f333(f79(x70881),x70882),x70882)),f2(x70881))) % 183.90/184.44 [7089]~P74(x70891)+~P1(f333(f333(f247(x70891),x70892),f2(x70891)))+P1(f333(f333(f247(x70891),f333(f333(f79(x70891),x70892),x70892)),f2(x70891))) % 183.90/184.44 [7658]~P114(x76581)+~P1(f333(f333(f248(x76581),f333(f333(f79(x76581),x76582),x76582)),f2(x76581)))+P1(f333(f333(f248(x76581),x76582),f2(x76581))) % 183.90/184.44 [7659]~P74(x76591)+~P1(f333(f333(f248(x76591),f333(f333(f79(x76591),x76592),x76592)),f2(x76591)))+P1(f333(f333(f248(x76591),x76592),f2(x76591))) % 183.90/184.44 [7660]~P74(x76601)+~P1(f333(f333(f247(x76601),f333(f333(f79(x76601),x76602),x76602)),f2(x76601)))+P1(f333(f333(f247(x76601),x76602),f2(x76601))) % 183.90/184.44 [4738]~E(x47382,f2(a875))+~E(x47381,f2(a875))+E(f333(f333(f79(a875),x47381),x47382),f2(a875)) % 183.90/184.44 [4739]~E(x47392,f77(a875))+~E(x47391,f77(a875))+E(f333(f333(f80(a875),x47391),x47392),f77(a875)) % 183.90/184.44 [4740]~E(x47402,f77(a1))+~E(x47401,f77(a1))+E(f333(f333(f80(a1),x47401),x47402),f77(a1)) % 183.90/184.44 [4794]~P55(x47942)+E(x47941,f2(x47942))+E(f333(f333(f38(x47942),x47941),x47941),f77(x47942)) % 183.90/184.44 [4795]~P117(x47952)+E(x47951,f2(x47952))+E(f333(f333(f291(x47952),x47951),x47951),f77(x47952)) % 183.90/184.44 [4796]~P118(x47962)+E(x47961,f2(x47962))+E(f333(f333(f291(x47962),x47961),x47961),f77(x47962)) % 183.90/184.44 [4813]~P74(x48131)+~E(x48132,f2(x48131))+E(f333(f333(f79(x48131),x48132),x48132),f2(x48131)) % 183.90/184.44 [4816]~P137(x48161)+~E(x48162,f77(x48161))+E(f333(f333(f80(x48161),x48162),x48162),f77(x48161)) % 183.90/184.44 [4817]~P118(x48171)+~E(x48172,f2(x48171))+E(f333(f333(f291(x48171),x48172),x48172),f2(x48171)) % 183.90/184.44 [4862]~E(x48622,f2(a875))+~E(x48621,f2(a875))+E(f333(f78(a1),f333(f103(a1),x48621)),f333(f103(a1),x48622)) % 183.90/184.44 [4880]E(x48801,f77(a875))+E(x48802,f2(a875))+~E(f333(f333(f80(a875),x48802),x48801),x48802) % 183.90/184.44 [4890]E(x48901,f2(a875))+E(x48902,f2(a875))+~E(f333(f333(f80(a875),x48902),x48901),f2(a875)) % 183.90/184.44 [4917]~E(x49172,f2(a875))+~E(x49171,f333(a115,f2(a875)))+E(f333(f333(f79(a875),x49171),x49172),f333(a115,f2(a875))) % 183.90/184.44 [4918]~E(x49181,f2(a875))+~E(x49182,f333(a115,f2(a875)))+E(f333(f333(f79(a875),x49181),x49182),f333(a115,f2(a875))) % 183.90/184.44 [4925]E(x49251,f77(a1))+E(x49252,f333(f106(a1),a100))+~E(f333(f333(f80(a1),x49251),x49252),f77(a1)) % 183.90/184.44 [4926]E(x49261,f77(a1))+E(x49262,f333(f106(a1),a100))+~E(f333(f333(f80(a1),x49262),x49261),f77(a1)) % 183.90/184.44 [4927]E(x49271,f77(a1))+E(x49271,f333(f106(a1),a100))+~E(f333(f333(f80(a1),x49272),x49271),f77(a1)) % 183.90/184.44 [4929]E(x49291,f77(a1))+E(x49291,f333(f106(a1),a100))+~E(f333(f333(f80(a1),x49291),x49292),f77(a1)) % 183.90/184.44 [4946]~P74(x49462)+E(x49461,f2(x49462))+~E(f333(f333(f79(x49462),x49461),x49461),f2(x49462)) % 183.90/184.44 [4952]~E(x49521,f333(f106(a1),a100))+~E(x49522,f333(f106(a1),a100))+E(f333(f333(f80(a1),x49521),x49522),f77(a1)) % 183.90/184.44 [4964]E(x49641,f2(a875))+E(x49642,f2(a875))+~E(f333(f333(f79(a875),x49642),x49641),f333(a115,f2(a875))) % 183.90/184.44 [4974]~P58(x49741)+~P90(x49741)+E(f333(f333(f291(x49741),x49742),f333(f106(x49741),a82)),f2(x49741)) % 183.90/184.44 [4980]~P137(x49801)+~E(x49802,f333(f78(x49801),f77(x49801)))+E(f333(f333(f80(x49801),x49802),x49802),f77(x49801)) % 183.90/184.44 [4985]~P5(x49852)+~P5(x49851)+P5(f333(f333(f79(a1),x49851),x49852)) % 183.90/184.44 [4986]~P5(x49862)+~P5(x49861)+P5(f333(f333(f80(a1),x49861),x49862)) % 183.90/184.44 [4987]~P5(x49872)+~P5(x49871)+P5(f333(f333(f38(a1),x49871),x49872)) % 183.90/184.44 [4989]~E(x49892,f2(a1))+E(x49891,f2(a1))+E(f45(x49891,x49892),f333(f333(f268(a1,a1),f2(a1)),x49891)) % 183.90/184.44 [5011]~E(x50112,f333(a115,f2(a875)))+~E(x50111,f333(a115,f2(a875)))+E(f333(f333(f80(a875),x50111),x50112),f333(a115,f2(a875))) % 183.90/184.44 [5026]E(x50261,f2(a875))+E(x50262,f333(a115,f2(a875)))+~E(f333(f333(f258(a875),x50262),x50261),f333(a115,f2(a875))) % 183.90/184.44 [5027]E(x50271,f2(a875))+E(x50271,f333(a115,f2(a875)))+~E(f333(f333(f79(a875),x50272),x50271),f333(a115,f2(a875))) % 183.90/184.44 [5028]E(x50281,f2(a875))+E(x50281,f333(a115,f2(a875)))+~E(f333(f333(f79(a875),x50281),x50282),f333(a115,f2(a875))) % 183.90/184.44 [5037]~P58(x50371)+~P90(x50371)+E(f333(f333(f291(x50371),x50372),f333(f106(x50371),a100)),f333(f78(x50371),x50372)) % 183.90/184.44 [5056]E(x50561,f333(a107,x50562))+~E(x50561,f2(a875))+P1(f333(f333(f247(a1),f2(a1)),x50562)) % 183.90/184.44 [5057]E(f333(a107,x50571),x50572)+~E(x50572,f2(a875))+P1(f333(f333(f247(a1),f2(a1)),x50571)) % 183.90/184.44 [5072]E(x50721,f333(a115,f2(a875)))+E(x50722,f333(a115,f2(a875)))+~E(f333(f333(f79(a875),x50721),x50722),f333(a115,f2(a875))) % 183.90/184.44 [5083]~E(x50831,f333(a107,x50832))+E(x50831,f2(a875))+P1(f333(f333(f247(a1),f2(a1)),x50832)) % 183.90/184.44 [5084]~E(f333(a107,x50842),x50841)+E(x50841,f2(a875))+P1(f333(f333(f247(a1),f2(a1)),x50842)) % 183.90/184.44 [5106]~P62(x51061)+E(f333(f63(x51061,f113(x51061)),x51062),f13(x51061,x51062))+~P1(f333(f61(x51061),x51062)) % 183.90/184.44 [5107]~P62(x51071)+E(f333(f63(x51071,f104(x51071)),x51072),f10(x51071,x51072))+~P1(f333(f61(x51071),x51072)) % 183.90/184.44 [5108]~P106(x51081)+E(f333(f63(x51081,f245(x51081)),x51082),f14(x51081,x51082))+~P1(f333(f61(x51081),x51082)) % 183.90/184.44 [5109]~P106(x51091)+E(f333(f63(x51091,f246(x51091)),x51092),f15(x51091,x51092))+~P1(f333(f61(x51091),x51092)) % 183.90/184.44 [5111]~P57(x51111)+~P1(f333(x51112,f209(x51111)))+P1(f333(f57(f879(x51111)),x51112)) % 183.90/184.44 [5186]~P57(x51862)+P1(f333(x51861,f209(x51862)))+~P1(f333(f58(f879(x51862)),x51861)) % 183.90/184.44 [5187]E(x51871,x51872)+~E(f333(f333(f22(a875),x51872),x51871),f2(a875))+~E(f333(f333(f22(a875),x51871),x51872),f2(a875)) % 183.90/184.44 [5202]P5(x52021)+~P38(x52022)+~P1(f333(f333(f335(a1),x52021),x52022)) % 183.90/184.44 [5231]~P114(x52311)+~E(f81(x52311,x52312),f77(x52311))+P1(f333(f333(f248(x52311),f2(x52311)),x52312)) % 183.90/184.44 [5243]~P90(x52431)+E(f333(f103(x52431),f333(f106(a875),x52432)),f333(f106(x52431),x52432))+P1(f333(a201,f333(f106(a1),x52432))) % 183.90/184.44 [5249]~P43(x52491,x52492)+P44(a870)+P1(f333(f61(f881(x52491,x52491)),x52492)) % 183.90/184.44 [5322]~P106(x53221)+E(f333(f63(x53221,f245(x53221)),x53222),f11(x53221,f245(x53221),x53222))+~P1(f333(f61(x53221),x53222)) % 183.90/184.44 [5323]~P106(x53231)+E(f333(f63(x53231,f246(x53231)),x53232),f12(x53231,f246(x53231),x53232))+~P1(f333(f61(x53231),x53232)) % 183.90/184.44 [5336]E(x53361,x53362)+P1(f333(f333(f248(a875),x53362),x53361))+P1(f333(f333(f248(a875),x53361),x53362)) % 183.90/184.44 [5337]E(x53371,x53372)+P1(f333(f333(f248(a1),x53372),x53371))+P1(f333(f333(f248(a1),x53371),x53372)) % 183.90/184.44 [5392]~P90(x53921)+E(f333(f103(x53921),f333(f106(a875),x53922)),f2(x53921))+~P1(f333(a201,f333(f106(a1),x53922))) % 183.90/184.44 [5395]~E(x53952,f333(a107,x53951))+E(x53951,f333(f103(a1),x53952))+~P1(f333(f333(f247(a1),f2(a1)),x53951)) % 183.90/184.44 [5396]~E(f333(a107,x53961),x53962)+E(x53961,f333(f103(a1),x53962))+~P1(f333(f333(f247(a1),f2(a1)),x53961)) % 183.90/184.44 [5397]~E(x53971,f333(a107,x53972))+E(f333(f103(a1),x53971),x53972)+~P1(f333(f333(f247(a1),f2(a1)),x53972)) % 183.90/184.44 [5407]E(x54071,f333(a107,x54072))+~E(x54072,f333(f103(a1),x54071))+~P1(f333(f333(f247(a1),f2(a1)),x54072)) % 183.90/184.44 [5408]E(f333(a107,x54081),x54082)+~E(x54081,f333(f103(a1),x54082))+~P1(f333(f333(f247(a1),f2(a1)),x54081)) % 183.90/184.44 [5447]~P83(x54472)+E(x54471,f2(x54472))+P1(f333(f333(f248(x54472),f2(x54472)),f333(f74(x54472),x54471))) % 183.90/184.44 [5514]~P114(x55141)+E(f81(x55141,x55142),f77(x55141))+~P1(f333(f333(f248(x55141),f2(x55141)),x55142)) % 183.90/184.44 [5518]~P90(x55181)+E(f333(f103(x55181),f333(f106(a875),x55182)),f2(x55181))+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x55182))) % 183.90/184.44 [5525]~P83(x55251)+E(f333(f74(x55251),x55252),x55252)+~P1(f333(f333(f248(x55251),f2(x55251)),x55252)) % 183.90/184.44 [5526]~P83(x55261)+E(f333(f74(x55261),x55262),x55262)+~P1(f333(f333(f247(x55261),f2(x55261)),x55262)) % 183.90/184.44 [5535]E(x55351,f2(a875))+~E(f140(a875,f333(f303(a875,x55352),x55351)),f116(a875))+P1(f333(f333(f247(a875),x55351),x55352)) % 183.90/184.44 [5545]~P66(x55451)+E(f333(f333(f6(x55451,x55451),f5(x55451)),f333(f174(x55451),x55452)),f333(f167(x55451),x55452))+~P1(f333(f138(x55451),x55452)) % 183.90/184.44 [5548]~P138(x55481)+E(f333(f103(x55481),f333(a107,x55482)),f333(f105(x55481),x55482))+~P1(f333(f333(f247(a1),f2(a1)),x55482)) % 183.90/184.44 [5575]E(x55751,x55752)+P1(f333(f333(f248(a875),x55751),x55752))+~P1(f333(f333(f247(a875),x55751),x55752)) % 183.90/184.44 [5576]E(x55761,x55762)+P1(f333(f333(f248(a1),x55761),x55762))+~P1(f333(f333(f247(a1),x55761),x55762)) % 183.90/184.44 [5579]E(x55791,f77(a1))+~E(f333(f333(f80(a1),x55792),x55791),f77(a1))+~P1(f333(f333(f248(a1),f2(a1)),x55792)) % 183.90/184.44 [5580]E(x55801,f77(a1))+~E(f333(f333(f80(a1),x55801),x55802),f77(a1))+~P1(f333(f333(f248(a1),f2(a1)),x55801)) % 183.90/184.44 [5618]~P38(x56182)+P1(f333(f333(f247(a1),f2(a1)),x56181))+~P1(f333(f333(f335(a1),x56181),x56182)) % 183.90/184.44 [5637]~P52(x56371,x56372)+P37(x56371,x56372)+~P1(f333(f61(f881(x56371,x56371)),x56372)) % 183.90/184.44 [5639]~P52(x56391,x56392)+P43(x56391,x56392)+~P1(f333(f61(f881(x56391,x56391)),x56392)) % 183.90/184.44 [5683]E(x56831,f196(f882(x56832,a870)))+~P1(f333(f61(x56832),x56831))+P1(f333(f333(f248(a875),f2(a875)),f333(f37(x56832),x56831))) % 183.90/184.44 [5710]~P1(f333(x57101,x57102))+P1(f333(x57101,f2(a875)))+P1(f333(f333(f248(a875),f410(x57102,x57101)),x57102)) % 183.90/184.44 [5733]E(x57331,f2(a875))+~E(f333(f167(a875),x57332),f2(a875))+~P1(f333(f333(f335(a875),x57331),f333(f174(a875),x57332))) % 183.90/184.44 [5799]E(x57991,x57992)+~P1(f333(f333(f247(a875),x57992),x57991))+~P1(f333(f333(f247(a875),x57991),x57992)) % 183.90/184.44 [5800]E(x58001,x58002)+~P1(f333(f333(f247(a1),x58002),x58001))+~P1(f333(f333(f247(a1),x58001),x58002)) % 183.90/184.44 [5801]E(f333(f37(x58011),x58012),f2(a875))+~P1(f333(f61(x58011),x58012))+P1(f333(f333(f335(x58011),f521(x58012,x58011)),x58012)) % 183.90/184.44 [5810]E(f49(x58101,x58102),f45(x58101,x58102))+P1(f333(f333(f247(a1),f2(a1)),x58101))+~P1(f333(f333(f248(a1),f2(a1)),x58102)) % 183.90/184.44 [5834]~P1(f333(x58341,f402(x58341)))+P1(f333(x58341,f333(a107,x58342)))+~P1(f333(f333(f247(a1),f2(a1)),x58342)) % 183.90/184.44 [5836]P1(f333(f333(f248(a875),x58361),f345(x58362)))+~P1(f333(f61(a875),x58362))+~P1(f333(f333(f335(a875),x58361),x58362)) % 183.90/184.44 [5837]P1(f333(f333(f247(a875),x58371),f355(x58372)))+~P1(f333(f61(a875),x58372))+~P1(f333(f333(f335(a875),x58371),x58372)) % 183.90/184.44 [5866]E(x58661,x58662)+~P1(f333(f333(f248(a875),x58661),f333(a115,x58662)))+P1(f333(f333(f248(a875),x58661),x58662)) % 183.90/184.44 [5898]E(x58981,f333(a115,x58982))+~P1(f333(f333(f247(a875),x58981),f333(a115,x58982)))+P1(f333(f333(f247(a875),x58981),x58982)) % 183.90/184.44 [5911]P1(f333(x59111,f403(x59111)))+~P1(f333(x59111,f333(a107,x59112)))+~P1(f333(f333(f247(a1),f2(a1)),x59112)) % 183.90/184.44 [5925]~P1(f333(x59251,x59252))+~P1(f333(f333(f247(a1),f2(a1)),x59252))+P1(f333(x59251,f333(f103(a1),f376(x59251)))) % 183.90/184.44 [5940]~P83(x59402)+~E(x59401,f2(x59402))+~P1(f333(f333(f248(x59402),f2(x59402)),f333(f74(x59402),x59401))) % 183.90/184.44 [5967]~P52(x59671,x59672)+P37(x59671,f333(f288(x59671,x59671),x59672))+~P1(f333(f61(f881(x59671,x59671)),x59672)) % 183.90/184.44 [5975]~P90(x59751)+E(f333(f103(x59751),f333(f106(a875),x59752)),f333(f106(x59751),x59752))+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x59752))) % 183.90/184.44 [5979]E(f333(a115,x59791),x59792)+~P1(f333(f333(f248(a875),x59791),x59792))+P1(f333(f333(f248(a875),f333(a115,x59791)),x59792)) % 183.90/184.44 [5993]E(f333(f333(f38(a1),x59931),x59932),f2(a1))+~P1(f333(f333(f247(a1),x59931),f2(a1)))+~P1(f333(f333(f248(a1),x59932),x59931)) % 183.90/184.44 [6004]E(f44(a1,x60041,x60042),x60041)+~P1(f333(f333(f247(a1),x60041),f2(a1)))+~P1(f333(f333(f248(a1),x60042),x60041)) % 183.90/184.44 [6017]E(f46(x60171,x60172),f45(x60171,x60172))+~P1(f333(f333(f247(a1),f2(a1)),x60171))+~P1(f333(f333(f247(a1),f2(a1)),x60172)) % 183.90/184.44 [6025]E(f333(f333(f38(a1),x60251),x60252),f2(a1))+~P1(f333(f333(f247(a1),f2(a1)),x60251))+~P1(f333(f333(f248(a1),x60251),x60252)) % 183.90/184.44 [6037]E(f44(a875,f333(f106(a875),x60371),f333(f106(a875),x60372)),f333(f106(a875),x60371))+P1(f333(a201,f333(f106(a1),x60371)))+~P1(f333(a201,f333(f106(a1),x60372))) % 183.90/184.44 [6039]E(f44(a1,x60391,x60392),x60391)+~P1(f333(f333(f247(a1),f2(a1)),x60391))+~P1(f333(f333(f248(a1),x60391),x60392)) % 183.90/184.44 [6040]E(x60401,x60402)+~P1(f333(f333(f248(a875),x60401),f333(a115,x60402)))+~P1(f333(f333(f247(a875),x60402),x60401)) % 183.90/184.44 [6057]~P114(x60571)+~P1(f333(f333(f248(x60571),x60572),f2(x60571)))+P1(f333(f333(f248(x60571),x60572),f333(f78(x60571),x60572))) % 183.90/184.44 [6058]~P74(x60581)+~P1(f333(f333(f247(x60581),x60582),f2(x60581)))+P1(f333(f333(f247(x60581),x60582),f333(f78(x60581),x60582))) % 183.90/184.44 [6068]~P4(x60681)+E(f333(f333(f64(x60681,x60681,f104(x60681)),f256(x60681)),x60682),f40(x60681,x60682))+~P1(f333(f61(x60681),x60682)) % 183.90/184.44 [6069]~P4(x60691)+E(f333(f333(f64(x60691,x60691,f113(x60691)),f196(x60691)),x60692),f39(x60691,x60692))+~P1(f333(f61(x60691),x60692)) % 183.90/184.44 [6083]~P120(x60831)+~P1(f333(f333(f248(a875),f2(a875)),x60832))+P1(f333(f333(f248(x60831),f2(x60831)),f333(f103(x60831),x60832))) % 183.90/184.44 [6084]~P114(x60841)+~P1(f333(f333(f248(a1),f2(a1)),x60842))+P1(f333(f333(f248(x60841),f2(x60841)),f333(f105(x60841),x60842))) % 183.90/184.44 [6085]~P114(x60851)+~P1(f333(f333(f247(a1),f2(a1)),x60852))+P1(f333(f333(f247(x60851),f2(x60851)),f333(f105(x60851),x60852))) % 183.90/184.44 [6088]~P5(x60882)+~P5(x60881)+E(f333(f312(a875,a1,f103(a1)),f304(a875,f333(a107,x60881),f333(a107,x60882))),f304(a1,x60881,x60882)) % 183.90/184.44 [6094]P1(f333(x60941,x60942))+~P1(f333(f333(f247(a1),f2(a1)),x60942))+~P1(f333(x60941,f333(f103(a1),f385(x60941)))) % 183.90/184.44 [6119]E(f333(f333(f79(a875),f333(f106(a875),x61191)),f333(f106(a875),x61192)),f333(f106(a875),x61191))+P1(f333(f333(f248(a1),x61191),a82))+~P1(f333(f333(f248(a1),x61192),a82)) % 183.90/184.44 [6123]~P114(x61231)+P1(f333(f333(f248(x61231),f2(x61231)),f81(x61231,x61232)))+~P1(f333(f333(f248(x61231),f2(x61231)),x61232)) % 183.90/184.44 [6134]~P82(x61341)+~P1(f333(f333(f248(x61341),x61342),f2(x61341)))+P1(f333(f333(f248(x61341),f2(x61341)),f333(f78(x61341),x61342))) % 183.90/184.44 [6135]~P82(x61351)+~P1(f333(f333(f247(x61351),x61352),f2(x61351)))+P1(f333(f333(f247(x61351),f2(x61351)),f333(f78(x61351),x61352))) % 183.90/184.44 [6138]E(x61381,f256(f882(x61382,a870)))+~E(f333(f37(x61382),x61381),f333(f37(x61382),f256(f882(x61382,a870))))+~P1(f333(f61(x61382),f256(f882(x61382,a870)))) % 183.90/184.44 [6173]~P114(x61731)+P1(f333(f333(f248(x61731),x61732),f2(x61731)))+~P1(f333(f333(f248(x61731),x61732),f333(f78(x61731),x61732))) % 183.90/184.44 [6174]~P74(x61741)+P1(f333(f333(f247(x61741),x61742),f2(x61741)))+~P1(f333(f333(f247(x61741),x61742),f333(f78(x61741),x61742))) % 183.90/184.44 [6183]~P90(x61831)+P1(f333(f333(f335(x61831),f333(f106(x61831),x61832)),f194(x61831)))+~P1(f333(f333(f247(a1),a82),x61832)) % 183.90/184.44 [6214]E(x62141,f2(a875))+~P1(f333(f333(f248(a875),x62141),f333(a115,x62142)))+P1(f333(f333(f248(a875),f358(x62142,x62141)),x62142)) % 183.90/184.44 [6236]~P114(x62361)+~P1(f333(f333(f248(x62361),f2(x62361)),f81(x62361,x62362)))+P1(f333(f333(f248(x62361),f2(x62361)),x62362)) % 183.90/184.44 [6238]~E(f333(f106(a875),x62382),f333(f106(a875),x62381))+P1(f333(f333(f247(a1),f333(f106(a1),x62381)),f2(a1)))+~P1(f333(a201,f333(f106(a1),x62382))) % 183.90/184.44 [6268]E(f333(f267(a1,a1),f49(x62681,x62682)),f333(f333(f38(a1),x62681),x62682))+~P1(f333(f333(f248(a1),x62681),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x62682)) % 183.90/184.44 [6301]E(f333(f271(a1,a1),f49(x63011,x63012)),f44(a1,x63011,x63012))+~P1(f333(f333(f248(a1),x63011),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x63012)) % 183.90/184.44 [6304]~P120(x63042)+~P1(f333(f333(f248(x63042),f2(x63042)),f333(f103(x63042),x63041)))+P1(f333(f333(f248(a875),f2(a875)),x63041)) % 183.90/184.44 [6305]~P114(x63052)+~P1(f333(f333(f248(x63052),f2(x63052)),f333(f105(x63052),x63051)))+P1(f333(f333(f248(a1),f2(a1)),x63051)) % 183.90/184.44 [6306]~P114(x63062)+~P1(f333(f333(f247(x63062),f2(x63062)),f333(f105(x63062),x63061)))+P1(f333(f333(f247(a1),f2(a1)),x63061)) % 183.90/184.44 [6309]E(f333(f267(a1,a1),f46(x63091,x63092)),f333(f333(f38(a1),x63091),x63092))+~P1(f333(f333(f248(a1),f2(a1)),x63091))+~P1(f333(f333(f247(a1),f2(a1)),x63092)) % 183.90/184.44 [6324]E(f333(f271(a1,a1),f46(x63241,x63242)),f44(a1,x63241,x63242))+~P1(f333(f333(f248(a1),f2(a1)),x63241))+~P1(f333(f333(f247(a1),f2(a1)),x63242)) % 183.90/184.44 [6339]~P82(x63391)+P1(f333(f333(f248(x63391),x63392),f2(x63391)))+~P1(f333(f333(f248(x63391),f2(x63391)),f333(f78(x63391),x63392))) % 183.90/184.44 [6340]~P82(x63401)+P1(f333(f333(f247(x63401),x63402),f2(x63401)))+~P1(f333(f333(f247(x63401),f2(x63401)),f333(f78(x63401),x63402))) % 183.90/184.44 [6366]P1(f333(f48(x63661,x63662),f49(x63661,x63662)))+~P1(f333(f333(f248(a1),x63661),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x63662)) % 183.90/184.44 [6391]P1(f333(f48(x63911,x63912),f46(x63911,x63912)))+~P1(f333(f333(f248(a1),f2(a1)),x63912))+~P1(f333(f333(f247(a1),f2(a1)),x63911)) % 183.90/184.44 [6434]~P82(x64341)+P1(f333(f333(f248(x64341),f333(f78(x64341),x64342)),f2(x64341)))+~P1(f333(f333(f248(x64341),f2(x64341)),x64342)) % 183.90/184.44 [6435]~P82(x64351)+P1(f333(f333(f247(x64351),f333(f78(x64351),x64352)),f2(x64351)))+~P1(f333(f333(f247(x64351),f2(x64351)),x64352)) % 183.90/184.44 [6451]E(f333(f333(f22(a875),f333(a107,x64511)),f333(a107,x64512)),f333(a107,f203(x64511,x64512)))+~P1(f333(f333(f247(a1),f2(a1)),x64512))+~P1(f333(f333(f247(a1),f2(a1)),x64511)) % 183.90/184.44 [6468]P1(f333(f333(f247(a1),f2(a1)),f203(x64681,x64682)))+~P1(f333(f333(f247(a1),f2(a1)),x64682))+~P1(f333(f333(f247(a1),f2(a1)),x64681)) % 183.90/184.44 [6505]~P1(f333(x65051,x65052))+P1(f333(x65051,f2(a875)))+P1(f333(x65051,f333(f333(f79(a875),f410(x65052,x65051)),f77(a875)))) % 183.90/184.44 [6587]E(f333(f106(a875),x65871),f333(f106(a875),x65872))+~P1(f333(f333(f247(a1),f333(f106(a1),x65872)),f2(a1)))+~P1(f333(a201,f333(f106(a1),x65871))) % 183.90/184.44 [6597]~E(x65971,f2(a875))+~E(f691(x65972,x65971),f2(a875))+E(f333(f143(a875,a875,f79(a875),x65971),x65972),f2(a875)) % 183.90/184.44 [6623]~P1(f333(f61(x66231),f821(x66232,x66231)))+~P1(f333(f61(f882(x66231,a870)),x66232))+P1(f333(f61(x66231),f39(f882(x66231,a870),x66232))) % 183.90/184.44 [6629]E(x66291,x66292)+P1(f333(f333(f248(a1),x66291),x66292))+~P1(f333(f333(f248(a1),x66291),f333(f333(f79(a1),x66292),f77(a1)))) % 183.90/184.44 [6631]P1(f333(f333(f248(a875),f333(a107,x66311)),f333(a107,x66312)))+~P1(f333(f333(f248(a1),f2(a1)),x66312))+~P1(f333(f333(f248(a1),x66311),x66312)) % 183.90/184.44 [6632]P1(f333(f333(f248(a875),f333(a107,x66321)),f333(a107,x66322)))+~P1(f333(f333(f247(a1),f2(a1)),x66321))+~P1(f333(f333(f248(a1),x66321),x66322)) % 183.90/184.44 [6633]P1(f333(f333(f247(a875),f333(a107,x66331)),f333(a107,x66332)))+~P1(f333(f333(f248(a1),f2(a1)),x66331))+~P1(f333(f333(f247(a1),x66331),x66332)) % 183.90/184.44 [6634]P1(f333(f333(f247(a875),f333(a107,x66341)),f333(a107,x66342)))+~P1(f333(f333(f247(a1),f2(a1)),x66342))+~P1(f333(f333(f247(a1),x66341),x66342)) % 183.90/184.44 [6645]E(f44(a875,f333(a107,x66451),f333(a107,x66452)),f333(a107,f44(a1,x66451,x66452)))+~P1(f333(f333(f247(a1),f2(a1)),x66452))+~P1(f333(f333(f247(a1),f2(a1)),x66451)) % 183.90/184.44 [6667]~P82(x66671)+~P1(f333(f333(f248(x66671),f333(f78(x66671),x66672)),f2(x66671)))+P1(f333(f333(f248(x66671),f2(x66671)),x66672)) % 183.90/184.44 [6668]~P82(x66681)+~P1(f333(f333(f247(x66681),f333(f78(x66681),x66682)),f2(x66681)))+P1(f333(f333(f247(x66681),f2(x66681)),x66682)) % 183.90/184.44 [6683]~P1(f333(f333(f248(a1),a82),x66832))+~P1(f333(f333(f248(a1),x66831),x66832))+P1(f333(f333(f248(a875),f333(f106(a875),x66831)),f333(f106(a875),x66832))) % 183.90/184.44 [6774]~P1(f333(f333(f247(a1),f2(a1)),x67741))+P1(f333(f333(f248(a875),f333(a107,x67741)),x67742))+~P1(f333(f333(f248(a1),x67741),f333(f103(a1),x67742))) % 183.90/184.44 [6791]E(x67911,f2(a1))+E(f44(a1,x67912,x67911),f2(a1))+E(f333(f333(f22(a1),f333(f78(a1),f333(f333(f38(a1),x67912),x67911))),f77(a1)),f333(f333(f38(a1),x67912),f333(f78(a1),x67911))) % 183.90/184.44 [6807]~P1(f333(f333(f247(a1),f2(a1)),x68071))+~P1(f333(f333(f248(a875),f333(a107,x68071)),x68072))+P1(f333(f333(f248(a1),x68071),f333(f103(a1),x68072))) % 183.90/184.44 [6844]~P1(f333(f333(f247(a875),f333(a107,x68441)),f333(a107,x68442)))+~P1(f333(f333(f248(a1),f2(a1)),x68441))+P1(f333(f333(f247(a1),x68441),x68442)) % 183.90/184.44 [6845]~P1(f333(f333(f247(a875),f333(a107,x68451)),f333(a107,x68452)))+~P1(f333(f333(f247(a1),f2(a1)),x68452))+P1(f333(f333(f247(a1),x68451),x68452)) % 183.90/184.44 [6871]P1(f333(f333(f247(a1),x68711),x68712))+~P1(f333(f333(f247(a875),f333(f106(a875),x68711)),f333(f106(a875),x68712)))+P1(f333(f333(f247(a1),x68711),a82)) % 183.90/184.44 [6898]P1(f333(f333(f247(a1),f2(a1)),f44(a1,x68981,x68982)))+~P1(f333(f333(f247(a1),f2(a1)),x68982))+~P1(f333(f333(f247(a1),f2(a1)),x68981)) % 183.90/184.44 [6998]P1(f333(f333(f248(a1),a82),x69981))+~P1(f333(f333(f248(a1),x69982),x69981))+~P1(f333(f333(f248(a875),f333(f106(a875),x69982)),f333(f106(a875),x69981))) % 183.90/184.44 [7049]E(f333(f333(f268(a1,a1),f333(f333(f38(a1),x70491),x70492)),f44(a1,x70491,x70492)),f49(x70491,x70492))+~P1(f333(f333(f248(a1),x70491),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x70492)) % 183.90/184.44 [7070]E(f333(f333(f268(a1,a1),f333(f333(f38(a1),x70701),x70702)),f44(a1,x70701,x70702)),f46(x70701,x70702))+~P1(f333(f333(f247(a1),f2(a1)),x70702))+~P1(f333(f333(f247(a1),f2(a1)),x70701)) % 183.90/184.44 [7121]~P94(x71212)+E(x71211,f116(x71212))+E(f333(f143(x71212,x71212,f80(x71212),f333(f142(x71212),x71211)),f333(f173(x71212),x71211)),f333(f63(x71212,f80(x71212)),f333(f174(x71212),x71211))) % 183.90/184.44 [7233]~E(x72331,f2(a875))+E(f333(f143(a875,a875,f79(a875),x72331),x72332),f2(a875))+P1(f333(f333(f335(a875),f691(x72332,x72331)),f333(f174(a875),x72332))) % 183.90/184.44 [7280]~P1(f333(f333(f248(a1),x72802),f2(a1)))+P1(f333(f333(f248(a1),f333(f333(f38(a1),x72801),x72802)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x72801)) % 183.90/184.44 [7282]~P1(f333(f333(f248(a1),x72821),f2(a1)))+P1(f333(f333(f248(a1),f333(f333(f38(a1),x72821),x72822)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x72822)) % 183.90/184.44 [7283]~P1(f333(f333(f248(a1),x72832),f2(a1)))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x72831),x72832)),f2(a1)))+~P1(f333(f333(f247(a1),f2(a1)),x72831)) % 183.90/184.44 [7284]~P1(f333(f333(f247(a1),x72841),f2(a1)))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x72841),x72842)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x72842)) % 183.90/184.44 [7290]P1(f333(f333(f335(f882(x72901,a870)),f821(x72902,x72901)),x72902))+~P1(f333(f61(f882(x72901,a870)),x72902))+P1(f333(f61(x72901),f39(f882(x72901,a870),x72902))) % 183.90/184.44 [7387]P25(x73871,x73871,x73872,f256(f882(x73871,a870)))+~E(f333(f312(x73871,x73871,x73872),f256(f882(x73871,a870))),f256(f882(x73871,a870)))+~P1(f333(f61(x73871),f256(f882(x73871,a870)))) % 183.90/184.44 [7515]~P25(x75151,x75151,x75152,f256(f882(x75151,a870)))+E(f333(f312(x75151,x75151,x75152),f256(f882(x75151,a870))),f256(f882(x75151,a870)))+~P1(f333(f61(x75151),f256(f882(x75151,a870)))) % 183.90/184.44 [7652]E(f333(f333(f38(a1),x76521),x76522),f333(f106(a1),a100))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x76521),x76522)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x76521)) % 183.90/184.44 [7713]~P1(f333(f333(f248(a1),x77132),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f38(a1),x77131),x77132)),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x77131)) % 183.90/184.44 [7718]E(f333(f333(f79(a1),x77181),x77182),f44(a1,x77181,x77182))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),x77181),x77182)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x77181)) % 183.90/184.44 [7721]P1(f333(f333(f248(a1),x77211),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f38(a1),x77211),x77212)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x77212)) % 183.90/184.44 [8118]~P57(x81181)+~P1(f333(f58(f879(x81181)),x81182))+P1(f333(f58(x81181),f333(f333(f8(f879(x81181),a870,x81181),x81182),f240(x81181)))) % 183.90/184.44 [8431]~P106(x84311)+P14(x84311,x84312)+~P1(f333(f333(f247(x84311),f333(f333(f166(x84311),x84312),f743(x84312,x84311))),f333(f333(f166(x84311),x84312),f744(x84312,x84311)))) % 183.90/184.44 [8432]~P106(x84321)+P14(x84321,x84322)+~P1(f333(f333(f247(x84321),f333(f333(f166(x84321),x84322),f751(x84322,x84321))),f333(f333(f166(x84321),x84322),f755(x84322,x84321)))) % 183.90/184.44 [8584]~P57(x85841)+P1(f333(f57(f879(x85841)),x85842))+~P1(f333(f57(x85841),f333(f333(f8(f879(x85841),a870,x85841),x85842),f240(x85841)))) % 183.90/184.44 [9747]~P57(x97471)+~P57(x97472)+E(f333(f333(f155(f876(x97471),f882(x97472,x97471)),f333(f333(f8(f882(x97472,f879(x97471)),f882(x97472,x97471),f876(x97471)),f72(f879(x97471),x97471,x97472,f244(x97471))),f333(f333(f8(f876(f881(x97472,x97471)),f882(x97472,f879(x97471)),f876(x97471)),f180(x97472,x97471)),f333(f184(x97472,x97471),f55(x97472))))),f54(x97471,f333(f197(f876(x97472)),f55(x97472)),f55(x97471))),f55(f882(x97472,x97471))) % 183.90/184.44 [5676]E(x56761,f2(a1))+~E(f44(a1,x56762,x56761),f2(a1))+E(f333(f333(f38(a1),x56762),f333(f78(a1),x56761)),f333(f78(a1),f333(f333(f38(a1),x56762),x56761))) % 183.90/184.44 [5694]~P38(x56942)+~P38(x56941)+P38(f333(f333(f113(f882(a1,a870)),x56941),x56942)) % 183.90/184.44 [5695]~P38(x56952)+~P38(x56951)+P38(f333(f333(f104(f882(a1,a870)),x56951),x56952)) % 183.90/184.44 [5713]~P58(x57131)+~P90(x57131)+E(f333(f78(x57131),f333(f333(f291(x57131),f77(x57131)),x57132)),f333(f333(f291(x57131),f333(f106(x57131),a100)),x57132)) % 183.90/184.44 [5826]E(x58261,f2(a1))+~E(f44(a1,x58262,x58261),f2(a1))+E(f333(f333(f38(a1),f333(f78(a1),x58262)),x58261),f333(f78(a1),f333(f333(f38(a1),x58262),x58261))) % 183.90/184.44 [5961]~P106(x59611)+P14(x59611,x59612)+P1(f333(f333(f248(a875),f744(x59612,x59611)),f333(f197(f876(x59611)),x59612))) % 183.90/184.44 [5962]~P106(x59621)+P14(x59621,x59622)+P1(f333(f333(f248(a875),f755(x59622,x59621)),f333(f197(f876(x59621)),x59622))) % 183.90/184.44 [6115]~P90(x61151)+~E(f333(f106(x61151),x61152),f2(x61151))+P30(x61151,f333(f106(x61151),f333(f333(f79(a1),x61152),f333(f78(a1),a82)))) % 183.90/184.44 [6116]~P90(x61161)+~E(f333(f106(x61161),x61162),f2(x61161))+P30(x61161,f333(f106(x61161),f333(f333(f79(a1),a82),f333(f78(a1),x61162)))) % 183.90/184.44 [6118]E(f333(a50,f46(f333(f78(a1),x61181),f333(f78(a1),x61182))),f45(x61181,x61182))+P1(f333(f333(f248(a1),f2(a1)),x61182))+P1(f333(f333(f247(a1),f2(a1)),x61181)) % 183.90/184.44 [6244]~E(x62442,f2(a875))+~E(x62441,f2(a875))+P1(f333(f333(f247(a1),f333(f103(a1),x62441)),f333(f78(a1),f333(f103(a1),x62442)))) % 183.90/184.44 [6272]E(f333(f333(f79(a875),f333(f106(a875),x62721)),f333(f106(a875),x62722)),f333(f106(a875),f333(f333(f79(a1),x62721),x62722)))+P1(f333(f333(f248(a1),x62721),a82))+P1(f333(f333(f248(a1),x62722),a82)) % 183.90/184.44 [6400]~P74(x64001)+~P1(f333(f333(f248(x64001),f2(x64001)),x64002))+P1(f333(f333(f248(x64001),f333(f78(x64001),x64002)),x64002)) % 183.90/184.44 [6401]~P74(x64011)+~P1(f333(f333(f247(x64011),f2(x64011)),x64012))+P1(f333(f333(f247(x64011),f333(f78(x64011),x64012)),x64012)) % 183.90/184.44 [6573]E(f333(f333(f22(a875),f333(a107,x65731)),f333(a107,x65732)),f333(a107,f333(f333(f22(a1),x65731),x65732)))+~P1(f333(f333(f247(a1),f2(a1)),x65732))+~P1(f333(f333(f247(a1),x65732),x65731)) % 183.90/184.44 [6606]E(f333(a107,f44(a1,f333(f106(a1),x66061),f333(f106(a1),x66062))),f44(a875,f333(f106(a875),x66061),f333(f106(a875),x66062)))+P1(f333(a201,f333(f106(a1),x66061)))+P1(f333(a201,f333(f106(a1),x66062))) % 183.90/184.44 [6624]~P74(x66241)+P1(f333(f333(f248(x66241),f2(x66241)),x66242))+~P1(f333(f333(f248(x66241),f333(f78(x66241),x66242)),x66242)) % 183.90/184.44 [6625]~P74(x66251)+P1(f333(f333(f247(x66251),f2(x66251)),x66252))+~P1(f333(f333(f247(x66251),f333(f78(x66251),x66252)),x66252)) % 183.90/184.44 [6636]~P74(x66361)+~P1(f333(f333(f248(x66361),f2(x66361)),x66362))+P1(f333(f333(f248(x66361),f2(x66361)),f333(f333(f79(x66361),x66362),x66362))) % 183.90/184.44 [6639]~P74(x66391)+~P1(f333(f333(f247(x66391),f2(x66391)),x66392))+P1(f333(f333(f247(x66391),f2(x66391)),f333(f333(f79(x66391),x66392),x66392))) % 183.90/184.44 [6650]E(f333(f333(f79(a875),f333(a107,x66501)),f333(a107,x66502)),f333(a107,f333(f333(f79(a1),x66501),x66502)))+~P1(f333(f333(f247(a1),f2(a1)),x66502))+~P1(f333(f333(f247(a1),f2(a1)),x66501)) % 183.90/184.44 [6662]E(x66621,f2(a875))+P1(f333(f333(f248(a875),f2(a875)),x66622))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f258(a875),x66622),x66621))) % 183.90/184.44 [6692]~P90(x66921)+E(f333(f106(x66921),x66922),f2(x66921))+~P30(x66921,f333(f106(x66921),f333(f333(f79(a1),a82),f333(f78(a1),x66922)))) % 183.90/184.44 [6693]~P90(x66931)+E(f333(f106(x66931),x66932),f2(x66931))+~P30(x66931,f333(f106(x66931),f333(f333(f79(a1),x66932),f333(f78(a1),a82)))) % 183.90/184.44 [6752]~P1(f333(f61(x67521),x67522))+~P1(f333(f61(x67521),f256(f882(x67521,a870))))+P1(f333(f61(x67521),f333(f78(f882(x67521,a870)),x67522))) % 183.90/184.44 [6775]~P1(f333(f333(f248(a1),f2(a1)),x67752))+~P1(f333(f333(f247(a1),x67752),x67751))+P1(f333(f333(f248(a1),f2(a1)),f333(f333(f38(a1),x67751),x67752))) % 183.90/184.44 [6776]~P1(f333(f333(f248(a1),x67762),f2(a1)))+~P1(f333(f333(f247(a1),x67761),f2(a1)))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f38(a1),x67761),x67762))) % 183.90/184.44 [6815]~P1(f333(f333(f248(a875),f2(a875)),x68152))+~P1(f333(f333(f248(a875),f2(a875)),x68151))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f80(a875),x68151),x68152))) % 183.90/184.44 [6816]~P1(f333(f333(f247(a1),f2(a1)),x68162))+~P1(f333(f333(f247(a1),f2(a1)),x68161))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),x68161),x68162))) % 183.90/184.44 [6817]~P1(f333(f333(f247(a1),f2(a1)),x68172))+~P1(f333(f333(f247(a1),f2(a1)),x68171))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f80(a1),x68171),x68172))) % 183.90/184.44 [6818]~P1(f333(f333(f248(a1),f2(a1)),x68182))+~P1(f333(f333(f247(a1),f2(a1)),x68181))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f38(a1),x68181),x68182))) % 183.90/184.44 [6819]~P1(f333(f333(f247(a1),f2(a1)),x68192))+~P1(f333(f333(f247(a1),f2(a1)),x68191))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f38(a1),x68191),x68192))) % 183.90/184.44 [6884]E(x68841,f2(a1))+E(f44(a1,x68842,x68841),f2(a1))+E(f333(f333(f22(a1),f333(f78(a1),f333(f333(f38(a1),x68842),x68841))),f77(a1)),f333(f333(f38(a1),f333(f78(a1),x68842)),x68841)) % 183.90/184.44 [6939]P1(f333(f333(f248(a875),f2(a875)),x69391))+P1(f333(f333(f248(a875),f2(a875)),x69392))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f79(a875),x69392),x69391))) % 183.90/184.44 [6943]~P74(x69431)+P1(f333(f333(f248(x69431),f2(x69431)),x69432))+~P1(f333(f333(f248(x69431),f2(x69431)),f333(f333(f79(x69431),x69432),x69432))) % 183.90/184.44 [6944]~P74(x69441)+P1(f333(f333(f247(x69441),f2(x69441)),x69442))+~P1(f333(f333(f247(x69441),f2(x69441)),f333(f333(f79(x69441),x69442),x69442))) % 183.90/184.44 [6999]~P1(f333(f61(x69991),x69992))+P1(f333(f61(x69991),f256(f882(x69991,a870))))+~P1(f333(f61(x69991),f333(f78(f882(x69991,a870)),x69992))) % 183.90/184.44 [7062]P1(f333(f333(f247(a1),x70621),f2(a1)))+~P1(f333(f333(f248(a1),x70622),f2(a1)))+~P1(f333(f333(f247(a1),f2(a1)),f333(f333(f38(a1),x70621),x70622))) % 183.90/184.44 [7068]~P1(f333(f333(f248(a1),f2(a1)),x70681))+P1(f333(f333(f247(a1),x70681),x70682))+~P1(f333(f333(f248(a1),f2(a1)),f333(f333(f38(a1),x70682),x70681))) % 183.90/184.44 [7069]~P1(f333(f333(f247(a1),f2(a1)),x70692))+P1(f333(f333(f247(a1),x70691),x70692))+~P1(f333(f333(f248(a1),f2(a1)),f333(f333(f38(a1),x70692),x70691))) % 183.90/184.44 [7098]P1(f333(f333(f248(a1),f2(a1)),x70981))+~P1(f333(f333(f247(a1),f2(a1)),x70982))+~P1(f333(f333(f248(a1),f2(a1)),f333(f333(f38(a1),x70982),x70981))) % 183.90/184.44 [7099]P1(f333(f333(f247(a1),f2(a1)),x70991))+~P1(f333(f333(f248(a1),f2(a1)),x70992))+~P1(f333(f333(f247(a1),f2(a1)),f333(f333(f38(a1),x70991),x70992))) % 183.90/184.44 [7546]~P1(f333(f61(x75462),f256(f882(x75462,a870))))+~P1(f333(f61(x75461),f256(f882(x75461,a870))))+P1(f333(f61(f880(x75461,x75462)),f256(f882(f880(x75461,x75462),a870)))) % 183.90/184.44 [7547]~P1(f333(f61(x75472),f256(f882(x75472,a870))))+~P1(f333(f61(x75471),f256(f882(x75471,a870))))+P1(f333(f61(f881(x75471,x75472)),f256(f882(f881(x75471,x75472),a870)))) % 183.90/184.44 [7616]~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x76161))+~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x76162))+P1(f333(f333(f248(a875),x76161),f333(f333(f80(a875),x76162),x76161))) % 183.90/184.44 [7617]~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x76171))+~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x76172))+P1(f333(f333(f248(a875),x76171),f333(f333(f80(a875),x76171),x76172))) % 183.90/184.44 [7651]E(f333(f37(x76511),f256(f882(x76511,a870))),f333(a115,f2(a875)))+P1(f333(f61(x76512),f256(f882(x76512,a870))))+~P1(f333(f61(f882(x76512,x76511)),f256(f882(f882(x76512,x76511),a870)))) % 183.90/184.44 [7784]~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x77842))+~P1(f333(f333(f248(a875),f333(a115,f2(a875))),x77841))+P1(f333(f333(f248(a875),f333(a115,f2(a875))),f333(f333(f80(a875),x77841),x77842))) % 183.90/184.44 [7785]~P1(f333(f333(f247(a875),f333(a115,f2(a875))),x77851))+~P1(f333(f333(f247(a875),f333(a115,f2(a875))),x77852))+P1(f333(f333(f247(a875),f333(a115,f2(a875))),f333(f333(f80(a875),x77851),x77852))) % 183.90/184.44 [8481]E(x84811,f116(x84812))+~P1(f333(f138(x84812),x84811))+E(f179(x84812,f333(f333(f8(a870,a870,x84812),a328),f333(f333(f7(x84812,x84812,a870),a330),f145(x84812,x84811))),x84811),f117(x84812,x84811)) % 183.90/184.44 [8575]~P38(x85752)+~P38(x85751)+E(f333(f312(a875,a1,f103(a1)),f333(f333(f113(f882(a875,a870)),f333(f312(a1,a875,a107),x85751)),f333(f312(a1,a875,a107),x85752))),f333(f333(f113(f882(a1,a870)),x85751),x85752)) % 183.90/184.44 [8576]~P38(x85762)+~P38(x85761)+E(f333(f312(a875,a1,f103(a1)),f333(f333(f104(f882(a875,a870)),f333(f312(a1,a875,a107),x85761)),f333(f312(a1,a875,a107),x85762))),f333(f333(f104(f882(a1,a870)),x85761),x85762)) % 183.90/184.44 [9230]~P90(x92301)+~E(f333(f106(x92301),x92302),f77(x92301))+P30(x92301,f333(f106(x92301),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f78(a1),x92302)))) % 183.90/184.44 [9463]~P90(x94631)+E(f333(f106(x94631),x94632),f77(x94631))+~P30(x94631,f333(f106(x94631),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f78(a1),x94632)))) % 183.90/184.44 [10192]E(x101921,f2(a1))+E(x101922,f2(a1))+E(f333(f273(a1,a1,a1,a1,f33(a1),f333(f80(a1),f81(a1,x101922))),f333(f333(f333(f99(f881(a1,a1)),f333(f333(a330,f81(a1,x101921)),f81(a1,x101922))),f52(x101921,x101922)),f333(f333(f272(a1,a1,f881(a1,a1)),f333(f333(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f333(f333(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))),f333(f333(f8(f881(a1,a1),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f333(f7(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f333(f333(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f99(f881(a1,a1))),f333(f333(f7(a1,a1,a870),a330),f2(a1))))),f333(f333(f7(a1,a1,f881(a1,a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f78(a1))),f2(a1))))),f333(f333(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f333(f333(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f882(a1,a1),a1),f22(a1)),f78(a1))),f77(a1))))),f333(f22(a1),f333(f74(a1),x101922))))),f52(x101921,x101922)))),f45(x101921,x101922)) % 183.90/184.44 [10193]E(x101931,f2(a1))+E(x101932,f2(a1))+E(f333(f273(a1,a1,a1,a1,f33(a1),f333(f80(a1),f81(a1,x101932))),f333(f333(f333(f99(f881(a1,a1)),f333(f333(a332,f333(f333(a331,f333(f333(f248(a1),f2(a1)),x101932)),f333(f333(f247(a1),f2(a1)),x101931))),f333(f333(a331,f333(f333(f248(a1),x101932),f2(a1))),f333(f333(f248(a1),x101931),f2(a1))))),f52(x101931,x101932)),f333(f333(f272(a1,a1,f881(a1,a1)),f333(f333(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f333(f333(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))),f333(f333(f8(f881(a1,a1),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f333(f7(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f333(f333(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f99(f881(a1,a1))),f333(f333(f7(a1,a1,a870),a330),f2(a1))))),f333(f333(f7(a1,a1,f881(a1,a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f78(a1))),f2(a1))))),f333(f333(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f333(f333(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f882(a1,a1),a1),f22(a1)),f78(a1))),f77(a1))))),f333(f22(a1),f333(f74(a1),x101932))))),f52(x101931,x101932)))),f45(x101931,x101932)) % 183.90/184.44 [10194]~P29(a5000)+P24(a872,x101941,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),a330),x101942),f202(x101942))),f196(f882(f874(a872),a870))))+~P24(a872,x101941,f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),f333(f333(f8(f882(a872,f882(a872,a870)),f882(a872,a870),a872),f333(f8(f882(a872,a870),a870,a872),f87(a872))),f333(f333(f8(f882(a872,a870),f882(a872,f882(a872,a870)),a872),f333(f7(a872,f882(a872,a870),f882(a872,a870)),f333(f333(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870)),f333(f333(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f333(f8(a870,f882(a870,a870),a872),a336)),f202(x101942))))),a330))),x101942),a330)),f196(f882(f874(a872),a870)))) % 183.90/184.44 [5702]~P114(x57021)+~P90(x57021)+E(f333(f74(x57021),f333(f333(f258(x57021),f333(f106(x57021),a100)),x57022)),f77(x57021)) % 183.90/184.44 [6184]~P138(x61841)+~P1(f333(f333(f248(a1),x61842),f2(a1)))+E(f333(f78(x61841),f333(f103(x61841),f333(a107,f333(f78(a1),x61842)))),f333(f105(x61841),x61842)) % 183.90/184.44 [6384]P1(f333(f333(f247(a102),x63841),f77(a102)))+E(f333(f333(f79(a102),f77(a102)),f281(x63841,f333(f333(f38(a102),x63842),x63841))),f281(x63841,x63842))+P1(f333(f333(f248(a102),x63842),x63841)) % 183.90/184.44 [6984]~P89(x69841)+~P1(f333(f333(f335(x69841),x69842),f112(x69841)))+~E(f333(f333(f79(x69841),f333(f333(f79(x69841),f77(x69841)),x69842)),x69842),f2(x69841)) % 183.90/184.44 [7100]~P1(f333(f333(f248(a1),x71001),f2(a1)))+~P1(f333(f333(f247(a1),x71002),f2(a1)))+E(f333(f267(a1,a1),f333(a50,f46(f333(f78(a1),x71001),f333(f78(a1),x71002)))),f333(f333(f38(a1),x71001),x71002)) % 183.90/184.44 [7117]~P1(f333(f333(f248(a1),x71171),f2(a1)))+~P1(f333(f333(f247(a1),x71172),f2(a1)))+E(f333(f271(a1,a1),f333(a50,f46(f333(f78(a1),x71171),f333(f78(a1),x71172)))),f44(a1,x71171,x71172)) % 183.90/184.44 [7123]~P1(f333(f333(f248(a1),x71232),f2(a1)))+E(f333(f267(a1,a1),f333(a50,f49(f333(f78(a1),x71231),f333(f78(a1),x71232)))),f333(f333(f38(a1),x71231),x71232))+~P1(f333(f333(f248(a1),f2(a1)),x71231)) % 183.90/184.44 [7141]~P1(f333(f333(f248(a1),x71412),f2(a1)))+E(f333(f271(a1,a1),f333(a50,f49(f333(f78(a1),x71411),f333(f78(a1),x71412)))),f44(a1,x71411,x71412))+~P1(f333(f333(f248(a1),f2(a1)),x71411)) % 183.90/184.44 [7194]E(f333(f333(f38(a1),f333(f333(f258(a1),x71941),x71942)),x71941),f333(f333(f258(a1),x71941),f333(f333(f22(a875),x71942),f333(a115,f2(a875)))))+~P1(f333(f333(f248(a875),f2(a875)),x71942))+~P1(f333(f333(f248(a1),f2(a1)),x71941)) % 183.90/184.44 [7287]~P1(f333(f333(f248(a875),f2(a875)),x72871))+~P1(f333(f333(f248(a875),f2(a875)),x72872))+P1(f333(f333(f248(a875),f333(f333(f22(a875),x72871),x72872)),x72871)) % 183.90/184.44 [7288]~P1(f333(f333(f248(a875),f2(a875)),x72881))+~P1(f333(f333(f248(a875),f77(a875)),x72882))+P1(f333(f333(f248(a875),f333(f333(f38(a875),x72881),x72882)),x72881)) % 183.90/184.44 [7289]~P1(f333(f333(f248(a1),f2(a1)),x72891))+~P1(f333(f333(f248(a1),f77(a1)),x72892))+P1(f333(f333(f248(a1),f333(f333(f38(a1),x72891),x72892)),x72891)) % 183.90/184.44 [7437]E(x74371,f2(a875))+~E(x74372,f2(a1))+~P1(f333(f333(f248(a1),f2(a1)),f333(f333(f258(a1),f333(f74(a1),x74372)),x74371))) % 183.90/184.44 [7863]~E(x78632,f116(f876(x78631)))+E(f333(f197(f876(f876(x78631))),f182(x78631,x78632)),f2(a875))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x78631),a875),f197(f876(x78631))),x78632))) % 183.90/184.44 [8117]P1(f333(x81171,x81172))+~P1(f333(x81171,f333(a109,f591(x81171,x81172))))+~P1(f333(f333(f335(f882(f881(a875,a875),a870)),x81172),a101)) % 183.90/184.44 [8136]E(x81361,f116(f876(x81362)))+E(f333(f197(f876(x81362)),f333(f333(f166(f876(x81362)),x81361),f2(a875))),f333(f197(f876(f876(x81362))),f182(x81362,x81361)))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x81362),a875),f197(f876(x81362))),x81361))) % 183.90/184.44 [8837]~P1(f333(f61(x88371),f333(f253(x88371),x88372)))+~P1(f333(f61(x88371),f256(f882(x88371,a870))))+P1(f333(f61(x88371),f333(f253(x88371),f333(f333(f8(a870,a870,x88371),a328),x88372)))) % 183.90/184.44 [8900]E(f333(f333(f268(a875,a875),f333(a115,f333(f333(f38(a875),f333(f333(f22(a875),x89001),x89002)),x89002))),f44(a875,f333(f333(f22(a875),x89001),x89002),x89002)),f84(f881(a875,a875),f47(x89001,x89002)))+~P1(f333(f333(f248(a875),f2(a875)),x89002))+~P1(f333(f333(f247(a875),x89002),x89001)) % 183.90/184.44 [9193]~P1(f333(f61(x91931),f333(f253(x91931),x91932)))+P1(f333(f61(x91931),f256(f882(x91931,a870))))+~P1(f333(f61(x91931),f333(f253(x91931),f333(f333(f8(a870,a870,x91931),a328),x91932)))) % 183.90/184.44 [9914]P26(x99141,x99142)+~P37(x99141,f333(f267(f882(f881(x99141,x99141),a870),f882(f881(x99141,x99141),a870)),x99142))+~P1(f333(f333(f247(f882(f881(x99141,x99141),a870)),f333(f333(f290(x99141,x99141,x99141),f333(f267(f882(f881(x99141,x99141),a870),f882(f881(x99141,x99141),a870)),x99142)),f333(f271(f882(f881(x99141,x99141),a870),f882(f881(x99141,x99141),a870)),x99142))),f333(f267(f882(f881(x99141,x99141),a870),f882(f881(x99141,x99141),a870)),x99142))) % 183.90/184.44 [7220]~P1(f333(f333(f248(a875),f2(a875)),x72202))+P1(f333(f333(f248(a875),x72201),x72202))+E(f333(a115,f333(f333(f38(a875),f333(f333(f22(a875),x72201),x72202)),x72202)),f333(f333(f38(a875),x72201),x72202)) % 183.90/184.44 [7357]~P1(f333(f333(f248(a875),f2(a875)),x73572))+~P1(f333(f333(f247(a875),x73572),x73571))+E(f333(a115,f333(f333(f38(a875),f333(f333(f22(a875),x73571),x73572)),x73572)),f333(f333(f38(a875),x73571),x73572)) % 183.90/184.44 [8346]~P90(x83461)+~P89(x83461)+~P30(x83461,f333(f106(x83461),f333(f333(f22(a1),f333(f333(f79(a1),x83462),x83462)),a100))) % 183.90/184.44 [9100]E(x91001,f2(a875))+E(f333(f333(f272(a875,a875,f881(a875,a875)),f333(f333(f8(a875,f882(a875,f881(a875,a875)),a875),f268(a875,a875)),a115)),f84(f881(a875,a875),f47(f333(f333(f22(a875),x91002),x91001),x91001))),f84(f881(a875,a875),f47(x91002,x91001)))+P1(f333(f333(f248(a875),x91002),x91001)) % 183.90/184.44 [9526]P1(f333(x95262,f657(x95262,x95261)))+P1(f333(x95261,f657(x95262,x95261)))+E(f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95261)),f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95262))) % 183.90/184.44 [9530]~P1(f333(x95302,f657(x95302,x95301)))+~P1(f333(x95301,f657(x95302,x95301)))+E(f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95301)),f333(f253(a1),f333(f333(f18(a1,a870,a870),f333(f333(f8(a870,f882(a870,a870),a1),a331),f333(f247(a1),f2(a1)))),x95302))) % 183.90/184.44 [7574]~P59(x75741)+~P90(x75741)+E(f333(f333(f291(x75741),x75742),f333(f106(x75741),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))),x75742) % 183.90/184.44 [9229]~P90(x92291)+~E(f333(f106(x92291),x92292),f77(x92291))+P30(x92291,f333(f106(x92291),f333(f333(f79(a1),x92292),f333(f78(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.44 [9406]~P137(x94061)+~E(x94062,f77(x94061))+E(f333(f333(f258(x94061),x94062),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(x94061)) % 183.90/184.44 [9407]~P137(x94071)+~E(x94072,f2(x94071))+E(f333(f333(f258(x94071),x94072),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f2(x94071)) % 183.90/184.44 [9420]~P137(x94201)+~E(x94202,f333(f78(x94201),f77(x94201)))+E(f333(f333(f258(x94201),x94202),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(x94201)) % 183.90/184.44 [9464]~P90(x94641)+E(f333(f106(x94641),x94642),f77(x94641))+~P30(x94641,f333(f106(x94641),f333(f333(f79(a1),x94642),f333(f78(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.44 [9848]~P114(x98482)+E(x98481,f2(x98482))+P1(f333(f333(f248(x98482),f2(x98482)),f333(f333(f258(x98482),x98481),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.44 [9913]~P114(x99132)+~E(x99131,f2(x99132))+~P1(f333(f333(f248(x99132),f2(x99132)),f333(f333(f258(x99132),x99131),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.44 [9939]P1(f333(f333(f247(a1),x99391),f2(a1)))+P1(f333(f333(f248(a1),x99392),x99391))+E(f333(f43(x99391),f46(x99392,f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99391))),f46(x99392,x99391)) % 183.90/184.44 [9940]~P1(f333(f333(f248(a1),f2(a1)),x99401))+P1(f333(f333(f248(a1),x99402),x99401))+E(f333(f43(x99401),f46(x99402,f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99401))),f46(x99402,x99401)) % 183.90/184.44 [9941]P1(f333(f333(f247(a1),x99411),f2(a1)))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),x99412),x99411)))+E(f333(f43(x99411),f49(x99412,f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99411))),f49(x99412,x99411)) % 183.90/184.44 [9942]~P1(f333(f333(f248(a1),f2(a1)),x99421))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),x99422),x99421)))+E(f333(f43(x99421),f49(x99422,f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99421))),f49(x99422,x99421)) % 183.90/184.44 [9943]~P141(x99431)+~P1(f333(f333(f247(a1),f2(a1)),x99432))+E(f333(f103(x99431),f333(a107,f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x99432))),f333(f333(f79(x99431),f333(f103(x99431),f333(a107,x99432))),f333(f103(x99431),f333(a107,x99432)))) % 183.90/184.44 [5044]~P143(x50441,x50443,x50442)+~E(x50443,f2(a1))+P1(f333(x50441,x50442)) % 183.90/184.44 [5165]~P106(x51651)+~P14(x51651,x51653)+P14(x51651,f172(x51651,x51652,x51653)) % 183.90/184.44 [5166]~P106(x51661)+~P14(x51661,x51663)+P14(x51661,f179(x51661,x51662,x51663)) % 183.90/184.44 [4749]~P72(x47492)+~E(x47493,f333(f78(x47492),x47491))+E(x47491,f333(f78(x47492),x47493)) % 183.90/184.44 [4751]~P72(x47511)+~E(f333(f78(x47511),x47513),x47512)+E(f333(f78(x47511),x47512),x47513) % 183.90/184.44 [4827]~P106(x48273)+E(x48271,x48272)+~E(f333(f254(x48273),x48271),f333(f254(x48273),x48272)) % 183.90/184.44 [4828]~P100(x48283)+E(x48281,x48282)+~E(f333(f103(x48283),x48281),f333(f103(x48283),x48282)) % 183.90/184.44 [4829]~P106(x48293)+E(x48291,x48292)+~E(f333(f305(x48293),x48291),f333(f305(x48293),x48292)) % 183.90/184.44 [4830]~P106(x48303)+E(x48301,x48302)+~E(f333(f255(x48303),x48301),f333(f255(x48303),x48302)) % 183.90/184.44 [4831]~P106(x48313)+E(x48311,x48312)+~E(f333(f302(x48313),x48311),f333(f302(x48313),x48312)) % 183.90/184.44 [4832]~P72(x48323)+E(x48321,x48322)+~E(f333(f78(x48323),x48321),f333(f78(x48323),x48322)) % 183.90/184.44 [4833]~P93(x48333)+E(x48331,x48332)+~E(f333(f78(x48333),x48331),f333(f78(x48333),x48332)) % 183.90/184.44 [4834]~P89(x48343)+E(x48341,x48342)+~E(f333(f105(x48343),x48341),f333(f105(x48343),x48342)) % 183.90/184.44 [4933]~P57(x49331)+~P1(f333(x49332,x49333))+P1(f333(f57(x49331),x49332)) % 183.90/184.44 [4966]~P57(x49663)+P1(f333(x49661,x49662))+~P1(f333(f58(x49663),x49661)) % 183.90/184.44 [5063]~P144(x50631,x50632,x50633)+~E(x50632,f2(a1))+P1(f333(x50631,f2(a1))) % 183.90/184.44 [5101]~E(x51011,f2(a875))+E(f342(x51011,x51012,x51013),f196(f882(x51013,a870)))+~E(f333(f37(x51013),x51012),f333(a115,x51011)) % 183.90/184.44 [5248]~E(x52482,f2(a875))+E(f333(f267(a875,a875),x52481),f2(a875))+~P1(f333(f47(x52483,x52482),x52481)) % 183.90/184.44 [5294]P1(f333(x52941,x52942))+~E(x52943,f333(f103(a1),x52942))+~P1(f333(x52941,f333(a107,x52943))) % 183.90/184.44 [5765]~E(x57653,f2(a875))+~P1(f333(x57651,x57652))+P1(f333(x57651,f44(a875,x57652,x57653))) % 183.90/184.44 [5926]~P57(x59263)+~P10(x59263,x59261,x59262)+P1(f333(x59261,f719(x59262,x59261,x59263))) % 183.90/184.44 [5988]~P101(x59882)+~P101(x59881)+E(f132(x59881,x59882,f133(x59881,x59883),f133(x59882,x59883)),f133(f881(x59881,x59882),x59883)) % 183.90/184.44 [6166]~E(x61663,f2(a875))+P1(f333(x61661,x61662))+~P1(f333(x61661,f44(a875,x61662,x61663))) % 183.90/184.44 [6315]~P57(x63151)+P11(x63151,x63152,x63153)+~P1(f333(x63152,f722(x63153,x63152,x63151))) % 183.90/184.44 [6841]E(x68411,f2(a875))+~P1(f333(x68412,f468(x68411,x68413,x68412)))+P1(f333(x68412,f44(a875,x68413,x68411))) % 183.90/184.44 [6949]~P4(x69491)+~P1(f333(f333(f247(x69491),x69492),f863(x69493,x69492,x69491)))+P1(f333(f333(f247(x69491),x69492),f40(x69491,x69493))) % 183.90/184.44 [6951]~P1(f333(x69511,x69512))+~P1(f333(x69511,f468(x69513,x69512,x69511)))+P1(f333(x69511,f44(a875,x69512,x69513))) % 183.90/184.44 [7055]E(x70551,f116(x70552))+E(f333(f333(f152(x70552),f706(x70553,x70551,x70552)),f709(x70553,x70551,x70552)),x70551)+~P1(f333(f333(f335(f876(x70552)),x70551),f162(x70552,x70553))) % 183.90/184.44 [7086]~P138(x70861)+~P1(f333(f333(f335(x70861),x70862),f112(x70861)))+P1(f333(f333(f335(x70861),f333(f333(f258(x70861),x70862),x70863)),f112(x70861))) % 183.90/184.44 [7406]P37(x74061,x74062)+~P1(f333(f333(f335(x74061),x74063),f630(x74062,x74061)))+P1(f333(f333(f335(x74061),f656(x74062,x74061,x74063)),f630(x74062,x74061))) % 183.90/184.44 [7679]E(x76791,f116(x76792))+~P1(f333(f333(f335(f876(x76792)),x76791),f162(x76792,x76793)))+P1(f333(f333(f335(f876(x76792)),f709(x76793,x76791,x76792)),f162(x76792,x76793))) % 183.90/184.44 [7733]E(x77331,f2(a875))+E(f333(f333(f79(a875),f333(f333(f80(a875),x77331),f469(x77331,x77332,x77333))),f468(x77331,x77332,x77333)),x77332)+P1(f333(x77333,f44(a875,x77332,x77331))) % 183.90/184.44 [7779]~P1(f333(x77793,x77792))+E(f333(f333(f79(a875),f333(f333(f80(a875),x77791),f469(x77791,x77792,x77793))),f468(x77791,x77792,x77793)),x77792)+P1(f333(x77793,f44(a875,x77792,x77791))) % 183.90/184.44 [7919]P1(f333(f333(f248(a1),x79191),f461(x79192,x79193,x79191)))+P1(f333(f333(x79193,f333(f333(f38(a1),x79192),x79191)),f44(a1,x79192,x79191)))+~P1(f333(f333(f248(a1),x79191),f2(a1))) % 183.90/184.44 [8198]P1(f333(f333(x81982,f333(f333(f38(a1),x81981),x81983)),f44(a1,x81981,x81983)))+~P1(f333(f333(f248(a1),x81983),f2(a1)))+P1(f333(f333(f247(a1),f461(x81981,x81982,x81983)),f2(a1))) % 183.90/184.44 [8379]E(f333(f333(f79(a1),f333(f333(f80(a1),x83791),f462(x83792,x83793,x83791))),f461(x83792,x83793,x83791)),x83792)+P1(f333(f333(x83793,f333(f333(f38(a1),x83792),x83791)),f44(a1,x83792,x83791)))+~P1(f333(f333(f248(a1),x83791),f2(a1))) % 183.90/184.44 [8621]~P1(f333(f333(x86211,f462(x86212,x86211,x86213)),f461(x86212,x86211,x86213)))+P1(f333(f333(x86211,f333(f333(f38(a1),x86212),x86213)),f44(a1,x86212,x86213)))+~P1(f333(f333(f248(a1),x86213),f2(a1))) % 183.90/184.44 [8847]~P106(x88471)+~P14(x88471,x88473)+P14(x88471,f150(x88471,x88471,f5(x88471),x88472,x88473)) % 183.90/184.44 [9355]~P122(x93552)+E(x93551,f2(x93552))+~P1(f333(f333(f247(x93552),f333(f333(f79(x93552),f333(f333(f80(x93552),x93553),x93553)),f333(f333(f80(x93552),x93551),x93551))),f2(x93552))) % 183.90/184.44 [9356]~P122(x93562)+E(x93561,f2(x93562))+~P1(f333(f333(f247(x93562),f333(f333(f79(x93562),f333(f333(f80(x93562),x93561),x93561)),f333(f333(f80(x93562),x93563),x93563))),f2(x93562))) % 183.90/184.44 [10130]~P114(x101301)+~P1(f333(f333(f248(x101301),x101302),f2(x101301)))+P1(f333(f333(f248(x101301),f333(f333(f258(x101301),x101302),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x101303)))),f2(x101301))) % 183.90/184.44 [10138]~P114(x101382)+E(x101381,f2(x101382))+~P1(f333(f333(f247(x101382),f333(f333(f79(x101382),f333(f333(f258(x101382),x101383),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101382),x101381),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f2(x101382))) % 183.90/184.44 [10139]~P114(x101392)+E(x101391,f2(x101392))+~P1(f333(f333(f247(x101392),f333(f333(f79(x101392),f333(f333(f258(x101392),x101391),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101392),x101393),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f2(x101392))) % 183.90/184.44 [4783]~E(x47832,x47833)+~P65(x47831)+E(f333(f333(f22(x47831),x47832),x47833),f2(x47831)) % 183.90/184.44 [4784]~E(x47842,x47843)+~P72(x47841)+E(f333(f333(f22(x47841),x47842),x47843),f2(x47841)) % 183.90/184.44 [4797]~P139(x47971)+~E(x47973,f2(x47971))+E(f333(f333(f79(x47971),x47972),x47973),x47972) % 183.90/184.44 [4814]~P136(x48141)+~E(x48143,f2(x48141))+E(f333(f333(f80(x48141),x48142),x48143),f2(x48141)) % 183.90/184.44 [4815]~P136(x48151)+~E(x48152,f2(x48151))+E(f333(f333(f80(x48151),x48152),x48153),f2(x48151)) % 183.90/184.44 [4836]~E(x48363,f116(x48361))+~E(x48362,f116(x48361))+E(f333(f333(f135(x48361),x48362),x48363),f116(x48361)) % 183.90/184.44 [4923]~P139(x49232)+E(x49231,f2(x49232))+~E(f333(f333(f79(x49232),x49233),x49231),x49233) % 183.90/184.44 [4924]~P72(x49241)+~E(x49242,f333(f78(x49241),x49243))+E(f333(f333(f79(x49241),x49242),x49243),f2(x49241)) % 183.90/184.44 [4931]E(x49311,f116(x49312))+E(x49313,f2(a875))+~E(f333(f333(f177(x49312),x49313),x49311),f116(x49312)) % 183.90/184.44 [4937]~P65(x49373)+E(x49371,x49372)+~E(f333(f333(f22(x49373),x49371),x49372),f2(x49373)) % 183.90/184.44 [4938]~P72(x49383)+E(x49381,x49382)+~E(f333(f333(f22(x49383),x49381),x49382),f2(x49383)) % 183.90/184.44 [4947]~P137(x49472)+E(x49471,f2(x49472))+~E(f333(f333(f258(x49472),x49471),x49473),f2(x49472)) % 183.90/184.44 [4948]~P63(x49482)+E(x49481,f196(x49482))+~E(f333(f333(f113(x49482),x49483),x49481),f196(x49482)) % 183.90/184.44 [4949]~P63(x49492)+E(x49491,f196(x49492))+~E(f333(f333(f113(x49492),x49491),x49493),f196(x49492)) % 183.90/184.44 [4950]~P97(x49502)+E(x49501,f256(x49502))+~E(f333(f333(f104(x49502),x49503),x49501),f256(x49502)) % 183.90/184.44 [4951]~P97(x49512)+E(x49511,f256(x49512))+~E(f333(f333(f104(x49512),x49511),x49513),f256(x49512)) % 183.90/184.44 [5017]~P72(x50172)+E(x50171,f333(f78(x50172),x50173))+~E(f333(f333(f79(x50172),x50171),x50173),f2(x50172)) % 183.90/184.44 [5018]~P72(x50181)+E(f333(f78(x50181),x50182),x50183)+~E(f333(f333(f79(x50181),x50182),x50183),f2(x50181)) % 183.90/184.44 [5020]~E(x50202,x50203)+~P105(x50201)+P1(f333(f333(f247(x50201),x50202),x50203)) % 183.90/184.44 [5022]~E(x50222,x50223)+~P108(x50221)+P1(f333(f333(f247(x50221),x50222),x50223)) % 183.90/184.44 [5023]~E(x50232,x50233)+~P92(x50231)+P1(f333(f333(f90(x50231),x50232),x50233)) % 183.90/184.44 [5117]~P116(x51171)+~E(x51172,f333(f78(x51171),x51173))+E(f333(f333(f80(x51171),x51172),x51172),f333(f333(f80(x51171),x51173),x51173)) % 183.90/184.44 [5125]~P106(x51251)+~P14(x51251,x51253)+P14(x51251,f333(f333(f177(x51251),x51252),x51253)) % 183.90/184.44 [5126]~P106(x51261)+~P14(x51261,x51263)+P14(x51261,f333(f333(f139(x51261),x51262),x51263)) % 183.90/184.44 [5163]E(x51631,x51632)+E(x51633,f2(a875))+~E(f333(f333(f80(a875),x51633),x51631),f333(f333(f80(a875),x51633),x51632)) % 183.90/184.44 [5164]E(x51641,x51642)+E(x51643,f2(a875))+~E(f333(f333(f80(a875),x51641),x51643),f333(f333(f80(a875),x51642),x51643)) % 183.90/184.44 [5239]~E(x52392,x52393)+~P108(x52391)+E(f304(x52391,x52392,x52393),f333(f333(f311(x52391),x52392),f196(f882(x52391,a870)))) % 183.90/184.44 [5281]E(x52811,x52812)+~P92(x52813)+~P1(f333(f333(f90(x52813),x52811),x52812)) % 183.90/184.44 [5292]~E(x52921,x52922)+~P106(x52923)+~P1(f333(f333(f248(x52923),x52921),x52922)) % 183.90/184.44 [5293]~E(x52931,x52932)+~P108(x52933)+~P1(f333(f333(f248(x52933),x52931),x52932)) % 183.90/184.44 [5303]~P108(x53031)+E(f333(f303(x53031,x53032),x53033),f196(f882(x53031,a870)))+P1(f333(f333(f248(x53031),x53032),x53033)) % 183.90/184.44 [5350]~P108(x53501)+E(f306(x53501,x53502,x53503),f196(f882(x53501,a870)))+P1(f333(f333(f248(x53501),x53502),x53503)) % 183.90/184.44 [5351]~P108(x53511)+E(f304(x53511,x53512,x53513),f196(f882(x53511,a870)))+P1(f333(f333(f247(x53511),x53512),x53513)) % 183.90/184.44 [5352]~P108(x53521)+E(f196(f882(x53521,a870)),f306(x53521,x53522,x53523))+P1(f333(f333(f248(x53521),x53522),x53523)) % 183.90/184.44 [5353]~P108(x53531)+E(f196(f882(x53531,a870)),f304(x53531,x53532,x53533))+P1(f333(f333(f247(x53531),x53532),x53533)) % 183.90/184.44 [5361]~P98(x53611)+~E(f333(f333(f113(x53611),x53612),x53613),x53613)+P1(f333(f333(f247(x53611),x53612),x53613)) % 183.90/184.44 [5362]~P99(x53621)+~E(f333(f333(f104(x53621),x53622),x53623),x53622)+P1(f333(f333(f247(x53621),x53622),x53623)) % 183.90/184.44 [5363]~P106(x53631)+~E(f333(f333(f245(x53631),x53632),x53633),x53632)+P1(f333(f333(f247(x53631),x53632),x53633)) % 183.90/184.44 [5364]~P106(x53641)+~E(f333(f333(f246(x53641),x53642),x53643),x53643)+P1(f333(f333(f247(x53641),x53642),x53643)) % 183.90/184.44 [5384]~P106(x53841)+P14(x53841,x53842)+~P14(x53841,f333(f333(f152(x53841),x53843),x53842)) % 183.90/184.44 [5385]~P106(x53851)+P14(x53851,x53852)+~P14(x53851,f333(f333(f135(x53851),x53853),x53852)) % 183.90/184.44 [5386]~P106(x53861)+P14(x53861,x53862)+~P14(x53861,f333(f333(f135(x53861),x53862),x53863)) % 183.90/184.44 [5454]~P106(x54541)+P1(f333(f333(f247(x54541),x54543),x54542))+P1(f333(f333(f248(x54541),x54542),x54543)) % 183.90/184.44 [5456]~P106(x54561)+P1(f333(f333(f247(x54561),x54563),x54562))+P1(f333(f333(f247(x54561),x54562),x54563)) % 183.90/184.44 [5494]~P98(x54941)+E(f333(f333(f113(x54941),x54942),x54943),x54942)+~P1(f333(f333(f247(x54941),x54943),x54942)) % 183.90/184.44 [5496]~P98(x54961)+E(f333(f333(f113(x54961),x54962),x54963),x54963)+~P1(f333(f333(f247(x54961),x54962),x54963)) % 183.90/184.44 [5497]~P99(x54971)+E(f333(f333(f104(x54971),x54972),x54973),x54973)+~P1(f333(f333(f247(x54971),x54973),x54972)) % 183.90/184.44 [5499]~P99(x54991)+E(f333(f333(f104(x54991),x54992),x54993),x54992)+~P1(f333(f333(f247(x54991),x54992),x54993)) % 183.90/184.44 [5500]~P106(x55001)+E(f333(f333(f245(x55001),x55002),x55003),x55003)+~P1(f333(f333(f247(x55001),x55003),x55002)) % 183.90/184.44 [5502]~P106(x55021)+E(f333(f333(f245(x55021),x55022),x55023),x55022)+~P1(f333(f333(f247(x55021),x55022),x55023)) % 183.90/184.44 [5503]~P106(x55031)+E(f333(f333(f246(x55031),x55032),x55033),x55032)+~P1(f333(f333(f247(x55031),x55033),x55032)) % 183.90/184.44 [5505]~P106(x55051)+E(f333(f333(f246(x55051),x55052),x55053),x55053)+~P1(f333(f333(f247(x55051),x55052),x55053)) % 183.90/184.44 [5512]~P117(x55122)+E(x55121,f2(x55122))+E(f333(f333(f291(x55122),f333(f78(x55122),x55123)),f333(f78(x55122),x55121)),f333(f333(f291(x55122),x55123),x55121)) % 183.90/184.44 [5559]~P108(x55591)+E(f333(f303(x55591,x55592),x55593),f196(f882(x55591,a870)))+~P1(f333(f333(f247(x55591),x55593),x55592)) % 183.90/184.44 [5591]~P108(x55911)+E(f307(x55911,x55912,x55913),f196(f882(x55911,a870)))+~P1(f333(f333(f247(x55911),x55913),x55912)) % 183.90/184.44 [5592]~P108(x55921)+E(f306(x55921,x55922,x55923),f196(f882(x55921,a870)))+~P1(f333(f333(f247(x55921),x55923),x55922)) % 183.90/184.44 [5593]~P108(x55931)+E(f304(x55931,x55932,x55933),f196(f882(x55931,a870)))+~P1(f333(f333(f248(x55931),x55933),x55932)) % 183.90/184.44 [5644]~E(f333(f333(f22(a875),x56441),x56443),x56442)+E(x56441,f333(f333(f79(a875),x56442),x56443))+~P1(f333(f333(f247(a875),x56443),x56441)) % 183.90/184.44 [5645]~E(x56451,f333(f333(f79(a875),x56453),x56452))+E(f333(f333(f22(a875),x56451),x56452),x56453)+~P1(f333(f333(f247(a875),x56452),x56451)) % 183.90/184.44 [5691]~P1(f333(x56911,x56913))+P1(f333(x56911,f383(x56911,x56912)))+~P1(f333(f333(f248(a875),x56913),x56912)) % 183.90/184.44 [5692]~P1(f333(x56921,x56923))+P1(f333(x56921,f408(x56921,x56922)))+~P1(f333(f333(f247(a875),x56923),x56922)) % 183.90/184.44 [5700]~P108(x57001)+~E(f333(f303(x57001,x57002),x57003),f196(f882(x57001,a870)))+~P1(f333(f333(f248(x57001),x57002),x57003)) % 183.90/184.44 [5705]~P105(x57051)+~P1(f333(f333(f248(x57051),x57052),x57053))+P1(f333(f333(f247(x57051),x57052),x57053)) % 183.90/184.44 [5707]~P108(x57071)+~P1(f333(f333(f248(x57071),x57072),x57073))+P1(f333(f333(f247(x57071),x57072),x57073)) % 183.90/184.44 [5813]~P108(x58131)+~E(f306(x58131,x58132,x58133),f196(f882(x58131,a870)))+~P1(f333(f333(f248(x58131),x58132),x58133)) % 183.90/184.44 [5814]~P108(x58141)+~E(f304(x58141,x58142,x58143),f196(f882(x58141,a870)))+~P1(f333(f333(f247(x58141),x58142),x58143)) % 183.90/184.44 [5815]~P108(x58151)+~E(f196(f882(x58151,a870)),f306(x58151,x58152,x58153))+~P1(f333(f333(f248(x58151),x58152),x58153)) % 183.90/184.44 [5816]~P108(x58161)+~E(f196(f882(x58161,a870)),f304(x58161,x58162,x58163))+~P1(f333(f333(f247(x58161),x58162),x58163)) % 183.90/184.44 [5824]P1(f333(x58241,x58242))+~P1(f333(x58241,f388(x58241,x58243)))+~P1(f333(f333(f248(a875),x58242),x58243)) % 183.90/184.44 [5825]P1(f333(x58251,x58252))+~P1(f333(x58251,f411(x58251,x58253)))+~P1(f333(f333(f247(a875),x58252),x58253)) % 183.90/184.44 [5833]~E(x58331,f333(a115,x58333))+P1(f333(f333(f248(a875),x58331),f333(a115,x58332)))+~P1(f333(f333(f248(a875),x58333),x58332)) % 183.90/184.44 [5849]E(x58491,x58492)+~E(f333(f333(f80(a875),x58493),x58491),f333(f333(f80(a875),x58493),x58492))+~P1(f333(f333(f248(a875),f2(a875)),x58493)) % 183.90/184.44 [5905]E(f333(x59051,f359(x59051,x59052,x59053)),f77(a875))+~E(f333(f333(f6(x59053,a875),x59051),x59052),f77(a875))+~P1(f333(f61(x59053),x59052)) % 183.90/184.44 [5917]~P4(x59171)+P1(f333(f333(f247(x59171),x59172),f39(x59171,x59173)))+~P1(f333(f333(f335(x59171),x59172),x59173)) % 183.90/184.44 [5947]~P105(x59471)+~P1(f333(f333(f248(x59471),x59473),x59472))+~P1(f333(f333(f248(x59471),x59472),x59473)) % 183.90/184.44 [5948]~P105(x59481)+~P1(f333(f333(f247(x59481),x59483),x59482))+~P1(f333(f333(f248(x59481),x59482),x59483)) % 183.90/184.44 [5949]~P106(x59491)+~P1(f333(f333(f248(x59491),x59493),x59492))+~P1(f333(f333(f248(x59491),x59492),x59493)) % 183.90/184.44 [5952]~P106(x59521)+~P1(f333(f333(f247(x59521),x59523),x59522))+~P1(f333(f333(f248(x59521),x59522),x59523)) % 183.90/184.44 [5953]~P108(x59531)+~P1(f333(f333(f248(x59531),x59533),x59532))+~P1(f333(f333(f248(x59531),x59532),x59533)) % 183.90/184.44 [5982]~E(f333(x59822,f360(x59822,x59823,x59821)),f2(a875))+E(f333(f333(f6(x59821,a875),x59822),x59823),f2(a875))+~P1(f333(f61(x59821),x59823)) % 183.90/184.44 [5983]~E(f333(x59832,f807(x59832,x59833,x59831)),f77(a875))+E(f333(f333(f9(x59831,a875),x59832),x59833),f77(a875))+~P1(f333(f61(x59831),x59833)) % 183.90/184.44 [5997]~P107(x59971)+~P1(f333(f333(f248(x59971),x59973),x59972))+P1(f333(f333(f335(x59971),x59972),f333(f305(x59971),x59973))) % 183.90/184.44 [5998]~P107(x59981)+~P1(f333(f333(f247(x59981),x59983),x59982))+P1(f333(f333(f335(x59981),x59982),f333(f255(x59981),x59983))) % 183.90/184.44 [5999]~P107(x59991)+~P1(f333(f333(f248(x59991),x59992),x59993))+P1(f333(f333(f335(x59991),x59992),f333(f254(x59991),x59993))) % 183.90/184.44 [6000]~P107(x60001)+~P1(f333(f333(f247(x60001),x60002),x60003))+P1(f333(f333(f335(x60001),x60002),f333(f302(x60001),x60003))) % 183.90/184.44 [6012]E(f333(x60121,f361(x60121,x60122,x60123)),f333(a115,f2(a875)))+~E(f333(f333(f6(x60123,a875),x60121),x60122),f333(a115,f2(a875)))+~P1(f333(f61(x60123),x60122)) % 183.90/184.44 [6095]~P4(x60951)+~P1(f333(f333(f335(x60951),x60953),x60952))+P1(f333(f333(f247(x60951),f40(x60951,x60952)),x60953)) % 183.90/184.44 [6112]~P1(f333(f333(f247(a875),x61121),x61123))+P1(f333(f333(f247(a875),x61121),x61122))+~P1(f333(f333(f247(a875),x61123),x61122)) % 183.90/184.44 [6113]~P1(f333(f333(f247(a1),x61131),x61133))+P1(f333(f333(f247(a1),x61131),x61132))+~P1(f333(f333(f247(a1),x61133),x61132)) % 183.90/184.44 [6130]~P107(x61301)+~P1(f333(f333(f335(x61301),x61303),f333(f305(x61301),x61302)))+P1(f333(f333(f248(x61301),x61302),x61303)) % 183.90/184.44 [6131]~P107(x61311)+~P1(f333(f333(f335(x61311),x61312),f333(f254(x61311),x61313)))+P1(f333(f333(f248(x61311),x61312),x61313)) % 183.90/184.44 [6132]~P107(x61321)+~P1(f333(f333(f335(x61321),x61323),f333(f255(x61321),x61322)))+P1(f333(f333(f247(x61321),x61322),x61323)) % 183.90/184.44 [6133]~P107(x61331)+~P1(f333(f333(f335(x61331),x61332),f333(f302(x61331),x61333)))+P1(f333(f333(f247(x61331),x61332),x61333)) % 183.90/184.44 [6250]P1(f333(x62501,x62502))+~P1(f333(x62501,f596(x62501)))+~P1(f333(f333(f335(x62503),x62502),f256(f882(x62503,a870)))) % 183.90/184.44 [6349]~P60(x63491)+P1(f333(f333(f248(x63491),f2(x63491)),f455(x63493,x63492,x63491)))+P1(f333(f333(f247(x63491),x63492),x63493)) % 183.90/184.44 [6350]~P61(x63501)+P1(f333(f333(f248(x63501),f2(x63501)),f808(x63503,x63502,x63501)))+P1(f333(f333(f247(x63501),x63502),x63503)) % 183.90/184.44 [6417]~P82(x64171)+~P1(f333(f333(f248(x64171),x64173),f333(f78(x64171),x64172)))+P1(f333(f333(f248(x64171),x64172),f333(f78(x64171),x64173))) % 183.90/184.44 [6419]~P82(x64191)+~P1(f333(f333(f247(x64191),x64193),f333(f78(x64191),x64192)))+P1(f333(f333(f247(x64191),x64192),f333(f78(x64191),x64193))) % 183.90/184.44 [6431]~P1(f333(f333(f248(a875),x64311),x64313))+~P1(f333(f333(f248(a875),x64313),x64312))+P1(f333(f333(f248(a875),f333(a115,x64311)),x64312)) % 183.90/184.44 [6457]~P114(x64571)+P1(f333(f333(f248(x64571),f333(f105(x64571),x64572)),f333(f105(x64571),x64573)))+~P1(f333(f333(f248(a1),x64572),x64573)) % 183.90/184.44 [6458]~P120(x64581)+P1(f333(f333(f248(x64581),f333(f103(x64581),x64582)),f333(f103(x64581),x64583)))+~P1(f333(f333(f248(a875),x64582),x64583)) % 183.90/184.44 [6459]~P120(x64591)+P1(f333(f333(f247(x64591),f333(f103(x64591),x64592)),f333(f103(x64591),x64593)))+~P1(f333(f333(f247(a875),x64592),x64593)) % 183.90/184.44 [6460]~P114(x64601)+P1(f333(f333(f247(x64601),f333(f105(x64601),x64602)),f333(f105(x64601),x64603)))+~P1(f333(f333(f247(a1),x64602),x64603)) % 183.90/184.44 [6466]~P106(x64661)+E(f333(f333(f113(f882(x64661,a870)),f333(f254(x64661),x64662)),f333(f303(x64661,x64662),x64663)),f333(f254(x64661),x64663))+~P1(f333(f333(f247(x64661),x64662),x64663)) % 183.90/184.44 [6495]~P82(x64951)+~P1(f333(f333(f248(x64951),x64953),x64952))+P1(f333(f333(f248(x64951),f333(f78(x64951),x64952)),f333(f78(x64951),x64953))) % 183.90/184.44 [6497]~P82(x64971)+~P1(f333(f333(f247(x64971),x64973),x64972))+P1(f333(f333(f247(x64971),f333(f78(x64971),x64972)),f333(f78(x64971),x64973))) % 183.90/184.44 [6499]~P93(x64991)+~P1(f333(f333(f247(x64991),x64993),x64992))+P1(f333(f333(f247(x64991),f333(f78(x64991),x64992)),f333(f78(x64991),x64993))) % 183.90/184.44 [6531]~P106(x65311)+E(f333(f333(f113(f882(x65311,a870)),f333(f254(x65311),x65312)),f304(x65311,x65312,x65313)),f333(f302(x65311),x65313))+~P1(f333(f333(f247(x65311),x65312),x65313)) % 183.90/184.44 [6532]~P106(x65321)+E(f333(f333(f113(f882(x65321,a870)),f333(f302(x65321),x65322)),f307(x65321,x65322,x65323)),f333(f254(x65321),x65323))+~P1(f333(f333(f248(x65321),x65322),x65323)) % 183.90/184.44 [6533]~P106(x65331)+E(f333(f333(f113(f882(x65331,a870)),f333(f302(x65331),x65332)),f306(x65331,x65332,x65333)),f333(f302(x65331),x65333))+~P1(f333(f333(f247(x65331),x65332),x65333)) % 183.90/184.44 [6568]~P106(x65681)+E(f333(f333(f113(f882(x65681,a870)),f333(f303(x65681,x65682),x65683)),f333(f255(x65681),x65683)),f333(f255(x65681),x65682))+~P1(f333(f333(f247(x65681),x65682),x65683)) % 183.90/184.44 [6723]~P106(x67231)+E(f333(f333(f113(f882(x67231,a870)),f307(x67231,x67232,x67233)),f333(f255(x67231),x67233)),f333(f305(x67231),x67232))+~P1(f333(f333(f248(x67231),x67232),x67233)) % 183.90/184.44 [6724]~P106(x67241)+E(f333(f333(f113(f882(x67241,a870)),f306(x67241,x67242,x67243)),f333(f305(x67241),x67243)),f333(f305(x67241),x67242))+~P1(f333(f333(f247(x67241),x67242),x67243)) % 183.90/184.44 [6725]~P106(x67251)+E(f333(f333(f113(f882(x67251,a870)),f304(x67251,x67252,x67253)),f333(f305(x67251),x67253)),f333(f255(x67251),x67252))+~P1(f333(f333(f247(x67251),x67252),x67253)) % 183.90/184.44 [6743]P1(f333(x67431,x67432))+~P1(f333(f333(f247(a875),x67432),x67433))+P1(f333(f333(f335(a875),f411(x67431,x67433)),f304(a875,f2(a875),x67433))) % 183.90/184.44 [6777]E(x67771,x67772)+~E(f333(f333(f166(x67773),x67771),f654(x67773,x67772,x67771)),f333(f333(f166(x67773),x67772),f654(x67773,x67772,x67771)))+~E(f333(f197(f876(x67773)),x67771),f333(f197(f876(x67773)),x67772)) % 183.90/184.44 [6782]~E(x67823,f333(f333(f38(a875),x67821),x67822))+~P1(f333(f333(f248(a875),f2(a875)),x67822))+P1(f333(f333(f248(a875),x67821),f333(f333(f80(a875),x67822),f333(a115,x67823)))) % 183.90/184.44 [6799]~P1(f333(x67991,x67993))+~P1(f333(f333(f247(a875),x67993),x67992))+P1(f333(f333(f335(a875),f408(x67991,x67992)),f304(a875,f2(a875),x67992))) % 183.90/184.44 [6838]~P1(f333(x68381,x68383))+P1(f333(x68381,f412(x68381,x68382)))+~P1(f333(f333(f335(a875),x68383),f304(a875,f2(a875),x68382))) % 183.90/184.44 [6858]~P120(x68583)+~P1(f333(f333(f248(x68583),f333(f103(x68583),x68581)),f333(f103(x68583),x68582)))+P1(f333(f333(f248(a875),x68581),x68582)) % 183.90/184.44 [6859]~P114(x68593)+~P1(f333(f333(f248(x68593),f333(f105(x68593),x68591)),f333(f105(x68593),x68592)))+P1(f333(f333(f248(a1),x68591),x68592)) % 183.90/184.44 [6860]~P120(x68603)+~P1(f333(f333(f247(x68603),f333(f103(x68603),x68601)),f333(f103(x68603),x68602)))+P1(f333(f333(f247(a875),x68601),x68602)) % 183.90/184.44 [6861]~P114(x68613)+~P1(f333(f333(f247(x68613),f333(f105(x68613),x68611)),f333(f105(x68613),x68612)))+P1(f333(f333(f247(a1),x68611),x68612)) % 183.90/184.44 [6878]~P120(x68781)+~P1(f333(f333(f248(x68781),f77(x68781)),x68782))+P1(f333(f333(f248(x68781),f77(x68781)),f333(f333(f258(x68781),x68782),f333(a115,x68783)))) % 183.90/184.44 [6880]~P82(x68801)+~P1(f333(f333(f248(x68801),f333(f78(x68801),x68803)),f333(f78(x68801),x68802)))+P1(f333(f333(f248(x68801),x68802),x68803)) % 183.90/184.44 [6881]~P82(x68811)+~P1(f333(f333(f247(x68811),f333(f78(x68811),x68813)),f333(f78(x68811),x68812)))+P1(f333(f333(f247(x68811),x68812),x68813)) % 183.90/184.44 [6882]~P93(x68821)+~P1(f333(f333(f247(x68821),f333(f78(x68821),x68823)),f333(f78(x68821),x68822)))+P1(f333(f333(f247(x68821),x68822),x68823)) % 183.90/184.44 [6908]P1(f333(x69081,x69082))+~P1(f333(x69081,f413(x69081,x69083)))+~P1(f333(f333(f335(a875),x69082),f304(a875,f2(a875),x69083))) % 183.90/184.44 [6927]~P60(x69271)+P1(f333(f333(f248(x69271),f455(x69273,x69272,x69271)),f77(x69271)))+P1(f333(f333(f247(x69271),x69272),x69273)) % 183.90/184.44 [6946]~E(f44(a875,x69463,x69462),f44(a875,x69461,x69462))+E(f333(f333(f79(a875),x69461),f333(f333(f80(a875),x69462),f518(x69461,x69462,x69463))),x69463)+~P1(f333(f333(f247(a875),x69461),x69463)) % 183.90/184.44 [6965]E(f333(x69651,f762(x69651,x69652,x69653)),f209(x69652))+~P1(f333(f61(x69653),f186(x69653,x69652,x69651)))+P1(f333(f61(x69653),f256(f882(x69653,a870)))) % 183.90/184.44 [7006]E(f333(f333(f6(x70061,a875),x70062),x70063),f2(a875))+~P1(f333(f61(x70061),x70063))+P1(f333(f333(f335(x70061),f360(x70062,x70063,x70061)),x70063)) % 183.90/184.44 [7007]E(f333(f333(f9(x70071,a875),x70072),x70073),f77(a875))+~P1(f333(f61(x70071),x70073))+P1(f333(f333(f335(x70071),f807(x70072,x70073,x70071)),x70073)) % 183.90/184.44 [7029]~P106(x70291)+~P1(f333(f333(f248(x70291),x70292),x70293))+P1(f333(f333(f248(f882(x70291,a870)),f333(f254(x70291),x70292)),f333(f254(x70291),x70293))) % 183.90/184.44 [7030]~P106(x70301)+~P1(f333(f333(f247(x70301),x70302),x70303))+P1(f333(f333(f247(f882(x70301,a870)),f333(f254(x70301),x70302)),f333(f254(x70301),x70303))) % 183.90/184.44 [7031]~P106(x70311)+~P1(f333(f333(f247(x70311),x70313),x70312))+P1(f333(f333(f247(f882(x70311,a870)),f333(f305(x70311),x70312)),f333(f305(x70311),x70313))) % 183.90/184.44 [7032]~P108(x70321)+~P1(f333(f333(f247(x70321),x70323),x70322))+P1(f333(f333(f247(f882(x70321,a870)),f333(f255(x70321),x70322)),f333(f255(x70321),x70323))) % 183.90/184.44 [7033]~P108(x70331)+~P1(f333(f333(f247(x70331),x70332),x70333))+P1(f333(f333(f247(f882(x70331,a870)),f333(f302(x70331),x70332)),f333(f302(x70331),x70333))) % 183.90/184.44 [7041]~P4(x70411)+P1(f333(f333(f247(x70411),x70412),f40(x70411,x70413)))+P1(f333(f333(f335(x70411),f863(x70413,x70412,x70411)),x70413)) % 183.90/184.44 [7047]~P82(x70471)+P1(f333(f333(f248(x70471),f333(f333(f22(x70471),x70472),x70473)),f2(x70471)))+~P1(f333(f333(f248(x70471),x70472),x70473)) % 183.90/184.44 [7048]~P82(x70481)+P1(f333(f333(f247(x70481),f333(f333(f22(x70481),x70482),x70483)),f2(x70481)))+~P1(f333(f333(f247(x70481),x70482),x70483)) % 183.90/184.44 [7090]P1(f333(x70901,x70902))+P1(f333(f333(f247(a875),f413(x70901,x70903)),x70903))+~P1(f333(f333(f335(a875),x70902),f304(a875,f2(a875),x70903))) % 183.90/184.44 [7130]~E(f333(f333(f6(x71301,a875),x71302),x71303),f77(a875))+~P1(f333(f61(x71301),x71303))+P1(f333(f333(f335(x71301),f359(x71302,x71303,x71301)),x71303)) % 183.90/184.44 [7131]~P1(f333(x71311,x71313))+P1(f333(f333(f247(a875),f412(x71311,x71312)),x71312))+~P1(f333(f333(f335(a875),x71313),f304(a875,f2(a875),x71312))) % 183.90/184.44 [7171]~P4(x71711)+P1(f333(f333(f335(x71711),f864(x71713,x71712,x71711)),x71712))+P1(f333(f333(f247(x71711),f39(x71711,x71712)),x71713)) % 183.90/184.44 [7202]~E(f333(f333(f6(x72021,a875),x72022),x72023),f333(a115,f2(a875)))+~P1(f333(f61(x72021),x72023))+P1(f333(f333(f335(x72021),f361(x72022,x72023,x72021)),x72023)) % 183.90/184.44 [7213]E(x72131,f2(a875))+P1(f333(x72132,f44(a875,x72133,x72131)))+P1(f333(f333(f248(a875),f468(x72131,x72133,x72132)),x72131)) % 183.90/184.44 [7318]~P1(f333(x73181,x73182))+P1(f333(x73181,f44(a875,x73182,x73183)))+P1(f333(f333(f248(a875),f468(x73183,x73182,x73181)),x73183)) % 183.90/184.44 [7441]E(x74411,f116(x74412))+~P1(f333(f333(f335(f876(x74412)),x74411),f162(x74412,x74413)))+P1(f333(f333(f335(x74412),f706(x74413,x74411,x74412)),x74413)) % 183.90/184.44 [7463]~P106(x74631)+E(f333(f333(f113(f882(x74631,a870)),f333(f333(f311(x74631),x74632),f196(f882(x74631,a870)))),f307(x74631,x74632,x74633)),f333(f303(x74631,x74632),x74633))+~P1(f333(f333(f248(x74631),x74632),x74633)) % 183.90/184.44 [7489]~P106(x74891)+E(f333(f333(f113(f882(x74891,a870)),f333(f333(f311(x74891),x74892),f196(f882(x74891,a870)))),f306(x74891,x74892,x74893)),f304(x74891,x74892,x74893))+~P1(f333(f333(f247(x74891),x74892),x74893)) % 183.90/184.44 [7596]~P106(x75961)+P1(f333(f333(f248(x75961),x75962),x75963))+~P1(f333(f333(f248(f882(x75961,a870)),f333(f254(x75961),x75962)),f333(f254(x75961),x75963))) % 183.90/184.44 [7597]~P106(x75971)+P1(f333(f333(f247(x75971),x75972),x75973))+~P1(f333(f333(f247(f882(x75971,a870)),f333(f305(x75971),x75973)),f333(f305(x75971),x75972))) % 183.90/184.44 [7598]~P108(x75981)+P1(f333(f333(f247(x75981),x75982),x75983))+~P1(f333(f333(f247(f882(x75981,a870)),f333(f255(x75981),x75983)),f333(f255(x75981),x75982))) % 183.90/184.44 [7599]~P106(x75991)+P1(f333(f333(f247(x75991),x75992),x75993))+~P1(f333(f333(f247(f882(x75991,a870)),f333(f254(x75991),x75992)),f333(f254(x75991),x75993))) % 183.90/184.44 [7600]~P108(x76001)+P1(f333(f333(f247(x76001),x76002),x76003))+~P1(f333(f333(f247(f882(x76001,a870)),f333(f302(x76001),x76002)),f333(f302(x76001),x76003))) % 183.90/184.44 [7623]~P82(x76231)+~P1(f333(f333(f248(x76231),f333(f333(f22(x76231),x76232),x76233)),f2(x76231)))+P1(f333(f333(f248(x76231),x76232),x76233)) % 183.90/184.44 [7624]~P82(x76241)+~P1(f333(f333(f247(x76241),f333(f333(f22(x76241),x76242),x76243)),f2(x76241)))+P1(f333(f333(f247(x76241),x76242),x76243)) % 183.90/184.44 [7786]E(x77861,f2(a875))+~E(f333(f143(a875,a875,f79(a875),x77862),x77863),f2(a875))+~P1(f333(f333(f335(a875),x77861),f333(f174(a875),x77863))) % 183.90/184.44 [7790]~P4(x77901)+~P1(f333(f333(f247(x77901),f864(x77903,x77902,x77901)),x77903))+P1(f333(f333(f247(x77901),f39(x77901,x77902)),x77903)) % 183.90/184.44 [7945]P1(f333(f333(f247(a1),f2(a1)),f465(x79451,x79452,x79453)))+P1(f333(f333(x79452,f333(f333(f38(a1),x79451),x79453)),f44(a1,x79451,x79453)))+~P1(f333(f333(f248(a1),f2(a1)),x79453)) % 183.90/184.44 [8040]E(x80401,x80402)+~E(f333(f197(f876(x80403)),x80401),f333(f197(f876(x80403)),x80402))+~P1(f333(f333(f272(x80403,x80403,a870),a330),f683(x80403,x80401,x80402))) % 183.90/184.44 [8108]~P37(x81082,x81083)+E(x81081,f196(f882(x81082,a870)))+~P1(f333(f333(f247(f882(x81082,a870)),x81081),f333(f287(x81082,x81082,x81083),x81081))) % 183.90/184.44 [8138]~P61(x81381)+~P1(f333(f333(f247(x81381),x81382),f333(f333(f79(x81381),x81383),f808(x81383,x81382,x81381))))+P1(f333(f333(f247(x81381),x81382),x81383)) % 183.90/184.44 [8179]P39(x81791,x81792,x81793)+P1(f333(f333(f335(x81791),f592(x81793,x81792,x81791)),x81792))+P1(f333(f333(f335(f881(x81791,x81791)),f593(x81793,x81792,x81791)),x81793)) % 183.90/184.44 [8202]P1(f333(f333(x82022,f333(f333(f38(a1),x82021),x82023)),f44(a1,x82021,x82023)))+~P1(f333(f333(f248(a1),f2(a1)),x82023))+P1(f333(f333(f248(a1),f465(x82021,x82022,x82023)),x82023)) % 183.90/184.44 [8226]E(f333(f312(a875,a875,f333(f333(f7(a875,a875,a875),f22(a875)),x82261)),f333(f303(a875,x82262),x82263)),f196(f882(a875,a870)))+P1(f333(f333(f248(a875),x82261),x82263))+P1(f333(f333(f248(a875),x82262),x82263)) % 183.90/184.44 [8332]E(f333(f312(a875,a875,f333(f333(f7(a875,a875,a875),f22(a875)),x83321)),f333(f303(a875,x83322),x83323)),f333(f333(f311(a875),f2(a875)),f196(f882(a875,a870))))+P1(f333(f333(f248(a875),x83321),x83323))+~P1(f333(f333(f248(a875),x83322),x83323)) % 183.90/184.44 [8349]~P106(x83491)+E(f150(x83491,x83491,f5(x83491),x83492,x83493),x83493)+~P1(f333(f333(f335(x83491),x83492),f333(f174(x83491),x83493))) % 183.90/184.44 [8363]P25(x83631,x83631,x83632,x83633)+~P1(f333(f61(x83631),x83633))+~P1(f333(f333(f247(f882(x83631,a870)),x83633),f333(f312(x83631,x83631,x83632),x83633))) % 183.90/184.44 [8386]E(f333(f333(f79(a1),f333(f333(f80(a1),x83861),f464(x83862,x83863,x83861))),f465(x83862,x83863,x83861)),x83862)+P1(f333(f333(x83863,f333(f333(f38(a1),x83862),x83861)),f44(a1,x83862,x83861)))+~P1(f333(f333(f248(a1),f2(a1)),x83861)) % 183.90/184.44 [8627]~P1(f333(f333(x86271,f464(x86272,x86271,x86273)),f465(x86272,x86271,x86273)))+P1(f333(f333(x86271,f333(f333(f38(a1),x86272),x86273)),f44(a1,x86272,x86273)))+~P1(f333(f333(f248(a1),f2(a1)),x86273)) % 183.90/184.44 [9493]~P1(f333(f61(x94931),x94932))+~P1(f333(f333(f335(x94931),x94933),x94932))+P1(f333(f333(f248(a875),f333(f37(x94931),f333(f333(f22(f882(x94931,a870)),x94932),f333(f333(f311(x94931),x94933),f196(f882(x94931,a870)))))),f333(f37(x94931),x94932))) % 183.90/184.44 [10091]P39(x100911,x100912,x100913)+~P1(f333(f333(f272(x100911,x100911,a870),f333(f333(f7(x100911,f882(x100911,a870),f882(x100911,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x100911,a870),f882(x100911,a870)),x100911),f8(a870,a870,x100911)),f333(f333(f8(a870,f882(a870,a870),x100911),a331),f333(f333(f7(x100911,f882(x100911,a870),a870),f335(x100911)),x100912)))),f333(f333(f7(x100911,f882(x100911,a870),a870),f335(x100911)),x100912))),f593(x100913,x100912,x100911)))+P1(f333(f333(f335(x100911),f592(x100913,x100912,x100911)),x100912)) % 183.90/184.44 [5473]~P117(x54732)+E(x54731,f2(x54732))+E(f333(f333(f291(x54732),x54733),f333(f78(x54732),x54731)),f333(f78(x54732),f333(f333(f291(x54732),x54733),x54731))) % 183.90/184.44 [5607]~E(x56073,f196(f882(x56071,a870)))+~E(x56072,f196(f882(x56071,a870)))+E(f333(f333(f113(f882(x56071,a870)),x56072),x56073),f196(f882(x56071,a870))) % 183.90/184.44 [5665]~E(x56653,f2(a875))+~P1(f333(x56651,f2(a875)))+P1(f333(x56651,f333(f333(f38(a875),x56652),x56653))) % 183.90/184.44 [5805]~P61(x58052)+E(x58051,f2(x58052))+E(f333(f333(f291(x58052),f333(f74(x58052),x58053)),f333(f74(x58052),x58051)),f333(f74(x58052),f333(f333(f291(x58052),x58053),x58051))) % 183.90/184.44 [5971]~P1(f333(f61(x59711),x59713))+E(f333(f37(x59711),f333(f333(f311(x59711),x59712),x59713)),f333(a115,f333(f37(x59711),x59713)))+P1(f333(f333(f335(x59711),x59712),x59713)) % 183.90/184.44 [6044]~E(x60442,f2(a875))+P1(f333(x60441,f2(a875)))+~P1(f333(x60441,f333(f333(f38(a875),x60443),x60442))) % 183.90/184.44 [6063]~P1(f333(f61(x60631),x60633))+E(f333(f37(x60631),f333(f333(f311(x60631),x60632),x60633)),f333(f37(x60631),x60633))+~P1(f333(f333(f335(x60631),x60632),x60633)) % 183.90/184.44 [6097]~P1(f333(f61(x60971),x60973))+E(f333(f37(x60971),f333(f333(f311(x60971),x60972),x60973)),f333(f333(f79(a875),f77(a875)),f333(f37(x60971),x60973)))+P1(f333(f333(f335(x60971),x60972),x60973)) % 183.90/184.44 [6212]E(f333(f333(f79(a875),x62121),f362(x62121,x62122,x62123)),x62122)+~P1(f333(x62123,f2(a875)))+P1(f333(x62123,f333(f333(f22(a875),x62122),x62121))) % 183.90/184.44 [6213]E(f333(f333(f79(a875),x62131),f363(x62131,x62132,x62133)),x62132)+~P1(f333(x62133,f2(a875)))+P1(f333(x62133,f333(f333(f22(a875),x62132),x62131))) % 183.90/184.44 [6260]~P4(x62601)+~P1(f333(f61(x62601),x62603))+E(f333(f333(f64(x62601,x62601,f113(x62601)),x62602),x62603),f333(f333(f113(x62601),x62602),f39(x62601,x62603))) % 183.90/184.44 [6261]~P4(x62611)+~P1(f333(f61(x62611),x62613))+E(f333(f333(f64(x62611,x62611,f104(x62611)),x62612),x62613),f333(f333(f104(x62611),x62612),f40(x62611,x62613))) % 183.90/184.44 [6267]~P90(x62671)+~E(f333(f106(x62671),x62672),f333(f106(x62671),x62673))+P30(x62671,f333(f106(x62671),f333(f333(f79(a1),x62672),f333(f78(a1),x62673)))) % 183.90/184.44 [6274]~P138(x62741)+E(f333(f333(f22(x62741),f333(f103(x62741),x62742)),f333(f103(x62741),x62743)),f333(f103(x62741),f333(f333(f22(a875),x62742),x62743)))+~P1(f333(f333(f247(a875),x62743),x62742)) % 183.90/184.44 [6360]E(f333(f333(f79(a875),x63601),f362(x63601,x63602,x63603)),x63602)+P1(f333(f333(f248(a875),x63602),x63601))+P1(f333(x63603,f333(f333(f22(a875),x63602),x63601))) % 183.90/184.44 [6361]E(f333(f333(f79(a875),x63611),f363(x63611,x63612,x63613)),x63612)+P1(f333(f333(f248(a875),x63612),x63611))+P1(f333(x63613,f333(f333(f22(a875),x63612),x63611))) % 183.90/184.44 [6376]~P114(x63761)+E(f333(f333(f80(x63761),f333(f74(x63761),x63762)),x63763),f333(f74(x63761),f333(f333(f80(x63761),x63762),x63763)))+~P1(f333(f333(f247(x63761),f2(x63761)),x63763)) % 183.90/184.44 [6377]~P60(x63771)+E(f333(f333(f291(x63771),f333(f74(x63771),x63772)),x63773),f333(f74(x63771),f333(f333(f291(x63771),x63772),x63773)))+~P1(f333(f333(f248(x63771),f2(x63771)),x63773)) % 183.90/184.44 [6385]~P62(x63851)+~P1(f333(f61(x63851),x63853))+E(f333(f333(f64(x63851,x63851,f113(x63851)),x63852),x63853),f13(x63851,f333(f333(f311(x63851),x63852),x63853))) % 183.90/184.44 [6386]~P62(x63861)+~P1(f333(f61(x63861),x63863))+E(f333(f333(f64(x63861,x63861,f104(x63861)),x63862),x63863),f10(x63861,f333(f333(f311(x63861),x63862),x63863))) % 183.90/184.44 [6387]~P106(x63871)+~P1(f333(f61(x63871),x63873))+E(f333(f333(f64(x63871,x63871,f245(x63871)),x63872),x63873),f14(x63871,f333(f333(f311(x63871),x63872),x63873))) % 183.90/184.44 [6388]~P106(x63881)+~P1(f333(f61(x63881),x63883))+E(f333(f333(f64(x63881,x63881,f246(x63881)),x63882),x63883),f15(x63881,f333(f333(f311(x63881),x63882),x63883))) % 183.90/184.44 [6433]E(x64331,f116(x64332))+~E(f182(x64332,x64333),f116(f876(x64332)))+~P1(f333(f333(f335(f876(x64332)),x64331),f333(f174(f876(x64332)),x64333))) % 183.90/184.44 [6474]~P1(f333(f138(x64741),x64743))+P1(f333(f333(f335(x64741),x64742),f333(f174(x64741),x64743)))+P1(f333(f138(x64741),f333(f333(f152(x64741),x64742),x64743))) % 183.90/184.44 [6485]~P94(x64851)+~P1(f333(f61(x64851),x64853))+E(f333(f63(x64851,f80(x64851)),f333(f333(f311(x64851),x64852),x64853)),f333(f333(f64(x64851,x64851,f80(x64851)),x64852),x64853)) % 183.90/184.44 [6507]~P106(x65071)+~P1(f333(f61(x65071),x65073))+E(f11(x65071,f245(x65071),f333(f333(f311(x65071),x65072),x65073)),f333(f333(f64(x65071,x65071,f245(x65071)),x65072),x65073)) % 183.90/184.44 [6508]~P106(x65081)+~P1(f333(f61(x65081),x65083))+E(f12(x65081,f246(x65081),f333(f333(f311(x65081),x65082),x65083)),f333(f333(f64(x65081,x65081,f246(x65081)),x65082),x65083)) % 183.90/184.44 [6510]P1(f333(x65101,f2(a875)))+~P1(f333(f333(f248(a875),x65102),x65103))+~P1(f333(x65101,f333(f333(f22(a875),x65102),x65103))) % 183.90/184.44 [6528]~P114(x65281)+P1(f333(f333(f248(x65281),x65282),x65283))+~P1(f333(f333(f248(x65281),f333(f74(x65281),x65282)),x65283)) % 183.90/184.44 [6530]~P83(x65301)+P1(f333(f333(f247(x65301),x65302),x65303))+~P1(f333(f333(f247(x65301),f333(f74(x65301),x65302)),x65303)) % 183.90/184.44 [6547]E(x65471,f116(x65472))+E(f333(f142(x65472),f333(f333(f139(x65472),x65473),x65471)),f333(f333(f166(x65472),x65471),x65473))+~P1(f333(f333(f248(a875),x65473),f333(f197(f876(x65472)),x65471))) % 183.90/184.44 [6599]~P1(f333(x65991,x65993))+P1(f333(x65991,f389(x65991,x65992)))+~P1(f333(f333(f335(a875),x65993),f333(f303(a875,f2(a875)),x65992))) % 183.90/184.44 [6621]P1(f333(x66211,x66212))+~P1(f333(f333(f248(a875),x66212),x66213))+P1(f333(f333(f335(a875),f388(x66211,x66213)),f333(f303(a875,f2(a875)),x66213))) % 183.90/184.44 [6637]~P120(x66371)+~P1(f333(f333(f248(x66371),f2(x66371)),x66372))+P1(f333(f333(f248(x66371),f2(x66371)),f333(f333(f258(x66371),x66372),x66373))) % 183.90/184.44 [6638]~P120(x66381)+~P1(f333(f333(f247(x66381),f77(x66381)),x66382))+P1(f333(f333(f247(x66381),f77(x66381)),f333(f333(f258(x66381),x66382),x66383))) % 183.90/184.44 [6640]~P120(x66401)+~P1(f333(f333(f247(x66401),f2(x66401)),x66402))+P1(f333(f333(f247(x66401),f2(x66401)),f333(f333(f258(x66401),x66402),x66403))) % 183.90/184.44 [6664]~P1(f333(x66641,x66643))+~P1(f333(f333(f248(a875),x66643),x66642))+P1(f333(f333(f335(a875),f383(x66641,x66642)),f333(f303(a875,f2(a875)),x66642))) % 183.90/184.44 [6671]P1(f333(f61(x66711),x66712))+~P1(f333(f61(x66711),x66713))+~P1(f333(f333(f247(f882(x66711,a870)),x66712),x66713)) % 183.90/184.44 [6679]P1(f333(x66791,x66792))+~P1(f333(x66791,f390(x66791,x66793)))+~P1(f333(f333(f335(a875),x66792),f333(f303(a875,f2(a875)),x66793))) % 183.90/184.44 [6690]E(x66901,f2(a875))+P1(f333(x66902,f391(x66901,x66903,x66902)))+~P1(f333(x66902,f333(f333(f38(a875),x66903),x66901))) % 183.90/184.44 [6698]~P122(x66982)+E(x66981,f2(x66982))+~E(f333(f333(f79(x66982),f333(f333(f80(x66982),x66983),x66983)),f333(f333(f80(x66982),x66981),x66981)),f2(x66982)) % 183.90/184.44 [6699]~P122(x66992)+E(x66991,f2(x66992))+~E(f333(f333(f79(x66992),f333(f333(f80(x66992),x66991),x66991)),f333(f333(f80(x66992),x66993),x66993)),f2(x66992)) % 183.90/184.44 [6744]E(x67441,f2(a875))+~P1(f333(x67442,f392(x67441,x67443,x67442)))+P1(f333(x67442,f333(f333(f38(a875),x67443),x67441))) % 183.90/184.44 [6749]~P106(x67491)+~P14(x67491,x67493)+P14(x67491,f333(f333(f149(x67491,x67491,f5(x67491)),x67492),x67493)) % 183.90/184.44 [6792]P1(f333(x67921,f391(x67922,x67923,x67921)))+P1(f333(x67921,f2(a875)))+~P1(f333(x67921,f333(f333(f38(a875),x67923),x67922))) % 183.90/184.44 [6798]~P90(x67981)+E(f333(f106(x67981),x67982),f333(f106(x67981),x67983))+~P30(x67981,f333(f106(x67981),f333(f333(f79(a1),x67982),f333(f78(a1),x67983)))) % 183.90/184.44 [6864]E(x68641,f2(a1))+E(x68642,f2(a1))+~P1(f333(f48(x68642,x68642),f333(f333(f268(a1,a1),x68643),x68641))) % 183.90/184.44 [6865]E(x68651,f77(a1))+E(x68652,f2(a1))+~P1(f333(f48(x68652,x68652),f333(f333(f268(a1,a1),x68651),x68653))) % 183.90/184.44 [6879]P1(f333(x68791,x68792))+P1(f333(f333(f248(a875),f390(x68791,x68793)),x68793))+~P1(f333(f333(f335(a875),x68792),f333(f303(a875,f2(a875)),x68793))) % 183.90/184.44 [6903]~P1(f333(x69031,f362(x69033,x69032,x69031)))+~P1(f333(x69031,f2(a875)))+P1(f333(x69031,f333(f333(f22(a875),x69032),x69033))) % 183.90/184.44 [6904]~P1(f333(x69041,f363(x69043,x69042,x69041)))+~P1(f333(x69041,f2(a875)))+P1(f333(x69041,f333(f333(f22(a875),x69042),x69043))) % 183.90/184.44 [6905]~P1(f333(x69051,f392(x69053,x69052,x69051)))+~P1(f333(x69051,f2(a875)))+P1(f333(x69051,f333(f333(f38(a875),x69052),x69053))) % 183.90/184.44 [6923]~P1(f333(x69231,x69233))+P1(f333(f333(f248(a875),f389(x69231,x69232)),x69232))+~P1(f333(f333(f335(a875),x69233),f333(f303(a875,f2(a875)),x69232))) % 183.90/184.44 [6924]E(f333(f333(f22(a875),f333(f333(f22(a875),x69241),x69242)),f333(f333(f22(a875),x69243),x69242)),f333(f333(f22(a875),x69241),x69243))+~P1(f333(f333(f247(a875),x69242),x69241))+~P1(f333(f333(f247(a875),x69242),x69243)) % 183.90/184.44 [6959]~P82(x69591)+~P1(f333(f333(f248(x69591),f333(f78(x69591),x69593)),x69592))+P1(f333(f333(f248(x69591),f333(f78(x69591),x69592)),x69593)) % 183.90/184.44 [6960]~P114(x69601)+~P1(f333(f333(f248(x69601),f333(f74(x69601),x69602)),x69603))+P1(f333(f333(f248(x69601),f333(f78(x69601),x69602)),x69603)) % 183.90/184.44 [6962]~P82(x69621)+~P1(f333(f333(f247(x69621),f333(f78(x69621),x69623)),x69622))+P1(f333(f333(f247(x69621),f333(f78(x69621),x69622)),x69623)) % 183.90/184.44 [6964]~P83(x69641)+~P1(f333(f333(f247(x69641),f333(f74(x69641),x69642)),x69643))+P1(f333(f333(f247(x69641),f333(f78(x69641),x69642)),x69643)) % 183.90/184.44 [7000]~P1(f333(x70003,f362(x70002,x70001,x70003)))+P1(f333(f333(f248(a875),x70001),x70002))+P1(f333(x70003,f333(f333(f22(a875),x70001),x70002))) % 183.90/184.44 [7001]~P1(f333(x70013,f363(x70012,x70011,x70013)))+P1(f333(f333(f248(a875),x70011),x70012))+P1(f333(x70013,f333(f333(f22(a875),x70011),x70012))) % 183.90/184.44 [7051]~E(f822(x70513,x70512,x70511),f823(x70513,x70512,x70511))+E(f333(f333(f104(f882(x70511,a870)),x70512),f39(f882(x70511,a870),x70513)),f196(f882(x70511,a870)))+P1(f333(f333(f335(f882(x70511,a870)),x70512),x70513)) % 183.90/184.44 [7060]~P1(f333(f61(x70601),x70603))+P1(f333(f61(x70601),f40(f882(x70601,a870),x70602)))+~P1(f333(f333(f335(f882(x70601,a870)),x70603),x70602)) % 183.90/184.44 [7119]~P106(x71191)+E(f333(f333(f113(f882(x71191,a870)),f333(f303(x71191,x71192),x71193)),f333(f333(f311(x71191),x71193),f196(f882(x71191,a870)))),f304(x71191,x71192,x71193))+~P1(f333(f333(f247(x71191),x71192),x71193)) % 183.90/184.44 [7120]E(x71201,f2(a875))+P1(f333(f333(f248(a875),f396(x71201,x71203,x71202)),x71201))+P1(f333(x71202,f333(f333(f38(a875),x71203),x71201))) % 183.90/184.44 [7155]E(x71551,x71552)+~P1(f333(f333(f247(f882(x71553,a870)),x71551),x71552))+P1(f333(f333(f248(f882(x71553,a870)),x71551),x71552)) % 183.90/184.44 [7168]E(x71681,x71682)+~E(f333(f197(f876(x71683)),x71681),f333(f197(f876(x71683)),x71682))+P1(f333(f333(f248(a875),f654(x71683,x71681,x71682)),f333(f197(f876(x71683)),x71682))) % 183.90/184.44 [7214]P7(x72141,x72142,x72143)+~E(f333(f266(x72141,x72141),x72143),x72142)+~E(f333(f333(f290(x72141,x72141,x72141),f333(f288(x72141,x72141),x72143)),x72143),x72143) % 183.90/184.44 [7286]~P1(f333(x72861,f2(a875)))+P1(f333(f333(f248(a875),f396(x72863,x72862,x72861)),x72863))+P1(f333(x72861,f333(f333(f38(a875),x72862),x72863))) % 183.90/184.44 [7295]~P106(x72951)+E(f333(f333(f113(f882(x72951,a870)),f307(x72951,x72952,x72953)),f333(f333(f311(x72951),x72953),f196(f882(x72951,a870)))),f306(x72951,x72952,x72953))+~P1(f333(f333(f248(x72951),x72952),x72953)) % 183.90/184.44 [7395]~P1(f333(f61(x73951),x73953))+P1(f333(f333(f248(a875),f333(f37(x73951),x73952)),f333(f37(x73951),x73953)))+~P1(f333(f333(f248(f882(x73951,a870)),x73952),x73953)) % 183.90/184.44 [7396]~P1(f333(f61(x73961),x73963))+P1(f333(f333(f247(a875),f333(f37(x73961),x73962)),f333(f37(x73961),x73963)))+~P1(f333(f333(f247(f882(x73961,a870)),x73962),x73963)) % 183.90/184.44 [7434]~P1(f333(x74343,x74342))+P1(f333(f333(f202(x74341),x74342),f847(x74342,x74341,x74343)))+~P1(f333(f333(f202(f31(x74343,x74341)),x74342),x74342)) % 183.90/184.44 [7534]E(x75341,x75342)+~P1(f333(f333(f247(f882(x75343,a870)),x75342),x75341))+~P1(f333(f333(f247(f882(x75343,a870)),x75341),x75342)) % 183.90/184.44 [7537]~P106(x75371)+P14(x75371,x75372)+~P14(x75371,f333(f333(f149(x75371,x75371,f5(x75371)),x75373),x75372)) % 183.90/184.44 [7603]~P1(f333(f333(f248(a875),x76033),x76032))+~P1(f333(f333(f248(a875),x76033),x76031))+P1(f333(f333(f248(a875),f333(f333(f22(a875),x76031),x76032)),f333(f333(f22(a875),x76031),x76033))) % 183.90/184.44 [7604]~P1(f333(f333(f248(a875),x76041),x76043))+~P1(f333(f333(f247(a875),x76042),x76041))+P1(f333(f333(f248(a875),f333(f333(f22(a875),x76041),x76042)),f333(f333(f22(a875),x76043),x76042))) % 183.90/184.44 [7621]~P1(f333(f333(f248(a1),x76212),f2(a1)))+~P1(f333(f333(f247(a1),x76213),x76211))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x76211),x76212)),f333(f333(f38(a1),x76213),x76212))) % 183.90/184.44 [7641]~P1(f333(f333(f248(a875),f2(a875)),x76412))+~P1(f333(f333(f248(a875),x76411),x76413))+P1(f333(f333(f248(a875),f333(f333(f80(a875),x76411),x76412)),f333(f333(f80(a875),x76413),x76412))) % 183.90/184.44 [7642]~P1(f333(f333(f248(a875),f2(a875)),x76421))+~P1(f333(f333(f248(a875),x76422),x76423))+P1(f333(f333(f248(a875),f333(f333(f80(a875),x76421),x76422)),f333(f333(f80(a875),x76421),x76423))) % 183.90/184.44 [7643]~P1(f333(f333(f248(a1),f2(a1)),x76431))+~P1(f333(f333(f248(a1),x76432),x76433))+P1(f333(f333(f248(a1),f333(f333(f80(a1),x76431),x76432)),f333(f333(f80(a1),x76431),x76433))) % 183.90/184.44 [7645]~P1(f333(f333(f248(a875),f2(a875)),x76453))+~P1(f333(f333(f247(a875),x76453),x76452))+P1(f333(f333(f247(a875),f333(f333(f38(a875),x76451),x76452)),f333(f333(f38(a875),x76451),x76453))) % 183.90/184.44 [7646]~P1(f333(f333(f248(a1),f2(a1)),x76462))+~P1(f333(f333(f247(a1),x76461),x76463))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x76461),x76462)),f333(f333(f38(a1),x76463),x76462))) % 183.90/184.44 [7697]E(x76971,f2(a875))+E(f333(f333(f79(a875),f333(f333(f80(a875),x76971),f392(x76971,x76972,x76973))),f396(x76971,x76972,x76973)),x76972)+P1(f333(x76973,f333(f333(f38(a875),x76972),x76971))) % 183.90/184.44 [7758]E(f333(f333(f79(a875),f333(f333(f80(a875),x77581),f392(x77581,x77582,x77583))),f396(x77581,x77582,x77583)),x77582)+~P1(f333(x77583,f2(a875)))+P1(f333(x77583,f333(f333(f38(a875),x77582),x77581))) % 183.90/184.44 [7777]~P1(f333(f61(x77771),x77773))+P1(f333(f333(f335(x77771),f368(x77772,x77773,x77771)),x77773))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f9(x77771,a875),x77772),x77773))) % 183.90/184.44 [7778]~P1(f333(f61(x77781),x77783))+P1(f333(f333(f335(x77781),f471(x77782,x77783,x77781)),x77783))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f9(x77781,a875),x77782),x77783))) % 183.90/184.44 [8073]E(x80731,f196(f882(x80732,a870)))+E(x80731,f333(f333(f311(x80732),x80733),f196(f882(x80732,a870))))+~P1(f333(f333(f247(f882(x80732,a870)),x80731),f333(f333(f311(x80732),x80733),f196(f882(x80732,a870))))) % 183.90/184.44 [8091]~P57(x80911)+P11(x80911,x80912,x80913)+P1(f333(f333(f335(f876(x80911)),f722(x80913,x80912,x80911)),f333(f174(f876(x80911)),f54(x80911,x80913,f55(x80911))))) % 183.90/184.44 [8110]~P1(f333(f333(f248(a875),f2(a875)),x81103))+P1(f333(f333(f248(a875),x81101),x81102))+~P1(f333(f333(f248(a875),f333(f333(f258(a875),x81103),x81101)),f333(f333(f258(a875),x81103),x81102))) % 183.90/184.44 [8112]~P1(f333(f333(f248(a875),f2(a875)),x81123))+P1(f333(f333(f247(a875),x81121),x81122))+~P1(f333(f333(f247(a875),f333(f333(f80(a875),x81123),x81121)),f333(f333(f80(a875),x81123),x81122))) % 183.90/184.44 [8113]~P1(f333(f333(f248(a875),f2(a875)),x81133))+P1(f333(f333(f247(a875),x81131),x81132))+~P1(f333(f333(f247(a875),f333(f333(f80(a875),x81131),x81133)),f333(f333(f80(a875),x81132),x81133))) % 183.90/184.44 [8140]~P57(x81401)+~P10(x81401,x81403,x81402)+P1(f333(f333(f335(f876(x81401)),f719(x81402,x81403,x81401)),f333(f174(f876(x81401)),f54(x81401,x81402,f55(x81401))))) % 183.90/184.44 [8148]~P1(f333(x81481,x81483))+P1(f333(f333(f202(f31(x81481,x81482)),f847(x81483,x81482,x81481)),x81483))+~P1(f333(f333(f202(f31(x81481,x81482)),x81483),x81483)) % 183.90/184.44 [8157]~E(f333(f333(f104(f882(x81571,a870)),f823(x81573,x81572,x81571)),f822(x81573,x81572,x81571)),f196(f882(x81571,a870)))+E(f333(f333(f104(f882(x81571,a870)),x81572),f39(f882(x81571,a870),x81573)),f196(f882(x81571,a870)))+P1(f333(f333(f335(f882(x81571,a870)),x81572),x81573)) % 183.90/184.44 [8174]E(x81741,f116(x81742))+~E(f333(f143(f876(x81742),f876(x81742),f135(x81742),f116(x81742)),x81743),f116(x81742))+~P1(f333(f333(f335(f876(x81742)),x81741),f333(f174(f876(x81742)),x81743))) % 183.90/184.44 [8231]E(x82311,f196(f882(f882(x82312,a870),a870)))+P1(f333(f333(f335(f882(x82312,a870)),f466(x82313,x82311,x82312)),x82311))+P1(f333(f333(f247(f882(x82312,a870)),f40(f882(x82312,a870),x82311)),x82313)) % 183.90/184.44 [8238]~P66(x82381)+~P73(x82381)+E(f333(f333(f6(a1,x82381),f333(f333(f8(a875,x82381,a1),x82382),a107)),f333(f312(a875,a1,f103(a1)),x82383)),f333(f333(f6(a875,x82381),x82382),x82383)) % 183.90/184.44 [8239]~P66(x82391)+~P73(x82391)+E(f333(f333(f9(a1,x82391),f333(f333(f8(a875,x82391,a1),x82392),a107)),f333(f312(a875,a1,f103(a1)),x82393)),f333(f333(f9(a875,x82391),x82392),x82393)) % 183.90/184.44 [8278]~P1(f333(f61(x82781),x82783))+~P1(f333(f333(f248(a875),f2(a875)),f333(x82782,f368(x82782,x82783,x82781))))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f9(x82781,a875),x82782),x82783))) % 183.90/184.44 [8279]~P1(f333(f61(x82791),x82793))+~P1(f333(f333(f248(a875),f2(a875)),f333(x82792,f471(x82792,x82793,x82791))))+P1(f333(f333(f248(a875),f2(a875)),f333(f333(f9(x82791,a875),x82792),x82793))) % 183.90/184.44 [8314]~P59(x83142)+E(x83141,f77(x83142))+E(f333(f333(f291(x83142),f333(f333(f22(x83142),f333(f333(f258(x83142),x83141),x83143)),f77(x83142))),f333(f333(f22(x83142),x83141),f77(x83142))),f333(f333(f6(a875,x83142),f333(f258(x83142),x83141)),f333(f303(a875,f2(a875)),x83143))) % 183.90/184.44 [8372]E(x83721,f2(a875))+~P1(f333(x83723,f333(f333(f38(a875),x83722),x83721)))+P1(f333(f333(f248(a875),x83722),f333(f333(f80(a875),x83721),f333(a115,f391(x83721,x83722,x83723))))) % 183.90/184.44 [8391]P1(f333(x83911,f2(a875)))+~P1(f333(x83911,f333(f333(f38(a875),x83912),x83913)))+P1(f333(f333(f248(a875),x83912),f333(f333(f80(a875),x83913),f333(a115,f391(x83913,x83912,x83911))))) % 183.90/184.44 [8433]E(x84331,f2(a875))+~P1(f333(x84333,f333(f333(f38(a875),x84332),x84331)))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x84331),f391(x84331,x84332,x84333))),x84332)) % 183.90/184.44 [8472]P1(f333(x84721,f2(a875)))+~P1(f333(x84721,f333(f333(f38(a875),x84723),x84722)))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x84722),f391(x84722,x84723,x84721))),x84723)) % 183.90/184.44 [8475]~P106(x84751)+E(f333(f333(f149(x84751,x84751,f5(x84751)),x84752),x84753),f150(x84751,x84751,f5(x84751),x84752,x84753))+P1(f333(f333(f335(x84751),x84752),f333(f174(x84751),x84753))) % 183.90/184.44 [8513]~E(f333(x85133,f602(x85132,x85133,x85131)),f333(x85133,f604(x85132,x85133,x85131)))+~P54(x85131,f333(x85133,f603(x85132,x85133,x85131)))+P54(x85131,f333(f333(f41(x85132,f882(x85131,f882(x85131,a870))),f256(f882(x85132,a870))),x85133)) % 183.90/184.44 [8521]E(x85211,f196(f882(f882(x85212,a870),a870)))+~P1(f333(f333(f247(f882(x85212,a870)),f466(x85213,x85211,x85212)),x85213))+P1(f333(f333(f247(f882(x85212,a870)),f40(f882(x85212,a870),x85211)),x85213)) % 183.90/184.44 [8578]~P61(x85781)+~P1(f333(f333(f248(x85781),x85782),x85783))+P1(f333(f333(f248(x85781),x85782),f333(f333(f291(x85781),f333(f333(f79(x85781),x85782),x85783)),f333(f333(f79(x85781),f77(x85781)),f77(x85781))))) % 183.90/184.44 [8633]~P1(f333(f333(x86331,f537(x86331,x86333,x86332)),f544(x86331,x86333,x86332)))+P1(f333(f333(x86331,x86332),x86333))+~P1(f333(f321(f881(a1,a1),a51),f333(f333(f268(a1,a1),x86332),x86333))) % 183.90/184.44 [8634]~P1(f333(f333(x86341,f545(x86341,x86343,x86342)),f546(x86341,x86343,x86342)))+P1(f333(f333(x86341,x86342),x86343))+~P1(f333(f321(f881(a1,a1),a56),f333(f333(f268(a1,a1),x86342),x86343))) % 183.90/184.44 [8635]~P1(f333(f333(x86351,f547(x86351,x86353,x86352)),f548(x86351,x86353,x86352)))+P1(f333(f333(x86351,x86352),x86353))+~P1(f333(f321(f881(a1,a1),a236),f333(f333(f268(a1,a1),x86352),x86353))) % 183.90/184.44 [8636]~P1(f333(f333(x86361,f550(x86361,x86363,x86362)),f551(x86361,x86363,x86362)))+P1(f333(f333(x86361,x86362),x86363))+~P1(f333(f321(f881(a875,a875),a231),f333(f333(f268(a875,a875),x86362),x86363))) % 183.90/184.44 [8637]~P1(f333(f333(x86371,f694(x86371,x86373,x86372)),f696(x86371,x86373,x86372)))+P1(f333(f333(x86371,x86372),x86373))+~P1(f333(f321(f881(a1,a1),a185),f333(f333(f268(a1,a1),x86372),x86373))) % 183.90/184.44 [8890]P1(f333(f333(x88901,x88902),x88903))+P1(f333(f321(f881(a875,a875),a231),f333(f333(f268(a875,a875),f550(x88901,x88903,x88902)),f551(x88901,x88903,x88902))))+~P1(f333(f321(f881(a875,a875),a231),f333(f333(f268(a875,a875),x88902),x88903))) % 183.90/184.44 [8891]P1(f333(f333(x88911,x88912),x88913))+P1(f333(f321(f881(a1,a1),a51),f333(f333(f268(a1,a1),f537(x88911,x88913,x88912)),f544(x88911,x88913,x88912))))+~P1(f333(f321(f881(a1,a1),a51),f333(f333(f268(a1,a1),x88912),x88913))) % 183.90/184.44 [8892]P1(f333(f333(x88921,x88922),x88923))+P1(f333(f321(f881(a1,a1),a56),f333(f333(f268(a1,a1),f545(x88921,x88923,x88922)),f546(x88921,x88923,x88922))))+~P1(f333(f321(f881(a1,a1),a56),f333(f333(f268(a1,a1),x88922),x88923))) % 183.90/184.44 [8893]P1(f333(f333(x88931,x88932),x88933))+P1(f333(f321(f881(a1,a1),a236),f333(f333(f268(a1,a1),f547(x88931,x88933,x88932)),f548(x88931,x88933,x88932))))+~P1(f333(f321(f881(a1,a1),a236),f333(f333(f268(a1,a1),x88932),x88933))) % 183.90/184.44 [8894]P1(f333(f333(x88941,x88942),x88943))+P1(f333(f321(f881(a1,a1),a185),f333(f333(f268(a1,a1),f694(x88941,x88943,x88942)),f696(x88941,x88943,x88942))))+~P1(f333(f321(f881(a1,a1),a185),f333(f333(f268(a1,a1),x88942),x88943))) % 183.90/184.44 [9240]~P1(f333(f61(x92401),x92403))+P1(f333(f333(f335(f881(f882(x92401,a870),f882(x92401,a870))),f333(f333(f268(f882(x92401,a870),f882(x92401,a870)),x92402),x92403)),f308(x92401)))+~P1(f333(f333(f248(f882(x92401,a870)),x92402),x92403)) % 183.90/184.44 [9311]~P54(x93111,f333(x93113,f603(x93112,x93113,x93111)))+P54(x93111,f333(f333(f41(x93112,f882(x93111,f882(x93111,a870))),f256(f882(x93112,a870))),x93113))+~E(f333(f333(f104(f882(x93111,a870)),f262(x93111,x93111,f333(x93113,f602(x93112,x93113,x93111)))),f263(x93111,x93111,f333(x93113,f604(x93112,x93113,x93111)))),f196(f882(x93111,a870))) % 183.90/184.44 [9382]~P28(a872,f196(f882(f874(a872),a870)),f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),x93821),x93822),x93823)),f196(f882(f874(a872),a870))))+~P24(a872,f196(f882(f874(a872),a870)),f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),a330),x93822),f202(x93822))),f196(f882(f874(a872),a870))))+P24(a872,f196(f882(f874(a872),a870)),f333(f333(f311(f874(a872)),f333(f333(f333(f91(a872),x93821),x93822),x93823)),f196(f882(f874(a872),a870)))) % 183.90/184.44 [9508]P39(x95081,x95082,x95083)+P1(f333(f333(f335(f881(x95081,x95081)),f593(x95083,x95082,x95081)),x95083))+~P1(f333(f333(f335(f881(x95081,x95081)),f333(f333(f268(x95081,x95081),f592(x95083,x95082,x95081)),f592(x95083,x95082,x95081))),x95083)) % 183.90/184.44 [10092]P39(x100921,x100922,x100923)+~P1(f333(f333(f272(x100921,x100921,a870),f333(f333(f7(x100921,f882(x100921,a870),f882(x100921,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x100921,a870),f882(x100921,a870)),x100921),f8(a870,a870,x100921)),f333(f333(f8(a870,f882(a870,a870),x100921),a331),f333(f333(f7(x100921,f882(x100921,a870),a870),f335(x100921)),x100922)))),f333(f333(f7(x100921,f882(x100921,a870),a870),f335(x100921)),x100922))),f593(x100923,x100922,x100921)))+~P1(f333(f333(f335(f881(x100921,x100921)),f333(f333(f268(x100921,x100921),f592(x100923,x100922,x100921)),f592(x100923,x100922,x100921))),x100923)) % 183.90/184.44 [5646]~P55(x56462)+E(x56461,f2(x56462))+E(f333(f333(f38(x56462),f333(f333(f80(x56462),x56463),x56461)),x56461),x56463) % 183.90/184.44 [5647]~P55(x56472)+E(x56471,f2(x56472))+E(f333(f333(f38(x56472),f333(f333(f80(x56472),x56471),x56473)),x56471),x56473) % 183.90/184.44 [6432]~P66(x64321)+~E(f333(x64322,f2(a875)),f2(x64321))+E(f333(f333(f6(a875,x64321),x64322),f333(f303(a875,f333(a115,f2(a875))),x64323)),f333(f333(f6(a875,x64321),x64322),f333(f303(a875,f2(a875)),x64323))) % 183.90/184.44 [6560]~P55(x65602)+E(x65601,f2(x65602))+E(f333(f333(f38(x65602),f333(f333(f79(x65602),x65603),x65601)),x65601),f333(f333(f79(x65602),f333(f333(f38(x65602),x65603),x65601)),f77(x65602))) % 183.90/184.44 [6561]~P55(x65612)+E(x65611,f2(x65612))+E(f333(f333(f38(x65612),f333(f333(f79(x65612),x65611),x65613)),x65611),f333(f333(f79(x65612),f333(f333(f38(x65612),x65613),x65611)),f77(x65612))) % 183.90/184.44 [6780]~P1(f333(x67803,f2(a1)))+P1(f333(f333(f247(a875),x67801),x67802))+P1(f333(x67803,f333(f103(a1),f333(f333(f22(a875),x67802),x67801)))) % 183.90/184.44 [6885]P1(f333(f333(f247(a875),x68852),x68851))+P1(f333(f333(f248(a875),x68851),x68852))+P1(f333(x68853,f333(f103(a1),f333(f333(f22(a875),x68851),x68852)))) % 183.90/184.44 [6957]E(f333(f333(f79(a875),f333(f106(a875),x69571)),f333(f333(f79(a875),f333(f106(a875),x69572)),x69573)),f333(f333(f79(a875),f333(f106(a875),x69571)),x69573))+P1(f333(a201,f333(f106(a1),x69571)))+~P1(f333(a201,f333(f106(a1),x69572))) % 183.90/184.44 [7038]~E(x70382,f333(f333(f38(a875),x70383),x70381))+~P1(f333(f333(f248(a875),f2(a875)),x70381))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x70381),x70382)),x70383)) % 183.90/184.44 [7152]~P1(f333(f61(x71521),x71523))+~P1(f333(f61(x71521),x71522))+P1(f333(f61(x71521),f333(f333(f113(f882(x71521,a870)),x71522),x71523))) % 183.90/184.44 [7447]~P106(x74471)+~P1(f333(f61(x74471),x74472))+E(f140(x74471,f333(f333(f22(f882(x74471,a870)),x74472),f333(f333(f311(x74471),x74473),f196(f882(x74471,a870))))),f172(x74471,x74473,f140(x74471,x74472))) % 183.90/184.44 [7513]P1(f333(x75131,f2(a1)))+~P1(f333(f333(f248(a875),x75132),x75133))+~P1(f333(x75131,f333(f103(a1),f333(f333(f22(a875),x75132),x75133)))) % 183.90/184.44 [7531]~P1(f333(f61(x75311),x75312))+E(f333(f37(x75311),f333(f333(f22(f882(x75311,a870)),x75312),f333(f333(f311(x75311),x75313),f196(f882(x75311,a870))))),f333(f37(x75311),x75312))+P1(f333(f333(f335(x75311),x75313),x75312)) % 183.90/184.44 [7661]~P120(x76611)+~P1(f333(f333(f248(x76611),f77(x76611)),x76612))+P1(f333(f333(f248(x76611),f77(x76611)),f333(f333(f80(x76611),x76612),f333(f333(f258(x76611),x76612),x76613)))) % 183.90/184.44 [7708]~P1(f333(f61(x77081),x77083))+E(f333(f333(f22(a875),f333(f37(x77081),x77082)),f333(f37(x77081),x77083)),f333(f37(x77081),f333(f333(f22(f882(x77081,a870)),x77082),x77083)))+~P1(f333(f333(f247(f882(x77081,a870)),x77083),x77082)) % 183.90/184.44 [7767]~P1(f333(f333(f247(a875),x77672),x77673))+~P1(f333(f333(f247(a875),x77671),f333(f333(f22(a875),x77673),x77672)))+P1(f333(f333(f247(a875),f333(f333(f79(a875),x77671),x77672)),x77673)) % 183.90/184.44 [7821]P1(f333(f61(x78211),x78212))+~P1(f333(f61(x78211),x78213))+~P1(f333(f61(x78211),f333(f333(f22(f882(x78211,a870)),x78212),x78213))) % 183.90/184.44 [7827]~P1(f333(f61(x78271),x78272))+E(f333(f37(x78271),f333(f333(f22(f882(x78271,a870)),x78272),f333(f333(f311(x78271),x78273),f196(f882(x78271,a870))))),f333(f333(f22(a875),f333(f37(x78271),x78272)),f77(a875)))+~P1(f333(f333(f335(x78271),x78273),x78272)) % 183.90/184.44 [7903]P54(x79031,x79032)+~P54(x79031,x79033)+~P1(f333(f333(f247(f882(x79031,f882(x79031,a870))),x79032),x79033)) % 183.90/184.44 [7944]~P1(f333(f333(f247(a875),x79443),x79442))+P1(f333(f333(f247(a875),x79441),f333(f333(f22(a875),x79442),x79443)))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),x79441),x79443)),x79442)) % 183.90/184.44 [7962]P37(x79621,x79622)+~P37(x79621,x79623)+~P1(f333(f333(f247(f882(f881(x79621,x79621),a870)),x79622),x79623)) % 183.90/184.44 [7963]P52(x79631,x79632)+~P52(x79631,x79633)+~P1(f333(f333(f247(f882(f881(x79631,x79631),a870)),x79632),x79633)) % 183.90/184.44 [8209]~P120(x82091)+~P1(f333(f333(f248(x82091),f77(x82091)),x82092))+P1(f333(f333(f248(x82091),f333(f333(f258(x82091),x82092),x82093)),f333(f333(f80(x82091),x82092),f333(f333(f258(x82091),x82092),x82093)))) % 183.90/184.44 [8298]~P1(f333(x82981,f2(a1)))+~P1(f333(x82981,f333(f333(f22(a1),f333(f103(a1),x82982)),f333(f103(a1),x82983))))+P1(f333(x82981,f333(f103(a1),f333(f333(f22(a875),x82982),x82983)))) % 183.90/184.44 [8311]~P1(f333(f333(f247(a875),x83113),x83112))+P1(f333(x83111,f333(f333(f22(a1),f333(f103(a1),x83112)),f333(f103(a1),x83113))))+~P1(f333(x83111,f333(f103(a1),f333(f333(f22(a875),x83112),x83113)))) % 183.90/184.44 [8329]P1(f333(f333(f248(a875),x83291),x83292))+~P1(f333(x83293,f333(f333(f22(a1),f333(f103(a1),x83291)),f333(f103(a1),x83292))))+P1(f333(x83293,f333(f103(a1),f333(f333(f22(a875),x83291),x83292)))) % 183.90/184.44 [8383]~P122(x83832)+E(x83831,f2(x83832))+P1(f333(f333(f248(x83832),f2(x83832)),f333(f333(f79(x83832),f333(f333(f80(x83832),x83833),x83833)),f333(f333(f80(x83832),x83831),x83831)))) % 183.90/184.44 [8384]~P122(x83842)+E(x83841,f2(x83842))+P1(f333(f333(f248(x83842),f2(x83842)),f333(f333(f79(x83842),f333(f333(f80(x83842),x83841),x83841)),f333(f333(f80(x83842),x83843),x83843)))) % 183.90/184.44 [8493]~P1(f333(f333(f248(a875),f2(a875)),x84931))+~P1(f333(f333(f248(a1),x84932),x84933))+P1(f333(f333(f248(a1),f333(f333(f80(a1),f333(f103(a1),x84931)),x84932)),f333(f333(f80(a1),f333(f103(a1),x84931)),x84933))) % 183.90/184.44 [8549]E(f333(f333(f104(f882(x85491,a870)),x85492),f39(f882(x85491,a870),x85493)),f196(f882(x85491,a870)))+P1(f333(f333(f335(f882(x85491,a870)),x85492),x85493))+P1(f333(f333(f335(f882(x85491,a870)),f823(x85493,x85492,x85491)),f333(f333(f311(f882(x85491,a870)),x85492),x85493))) % 183.90/184.44 [8550]E(f333(f333(f104(f882(x85501,a870)),x85502),f39(f882(x85501,a870),x85503)),f196(f882(x85501,a870)))+P1(f333(f333(f335(f882(x85501,a870)),x85502),x85503))+P1(f333(f333(f335(f882(x85501,a870)),f822(x85503,x85502,x85501)),f333(f333(f311(f882(x85501,a870)),x85502),x85503))) % 183.90/184.44 [8577]E(x85771,x85772)+~E(f333(f197(f876(x85773)),x85771),f333(f197(f876(x85773)),x85772))+P1(f333(f333(f335(f881(x85773,x85773)),f683(x85773,x85771,x85772)),f333(f174(f881(x85773,x85773)),f333(f333(f184(x85773,x85773),x85772),x85771)))) % 183.90/184.44 [8808]E(f309(x88081,x88082),f309(x88081,x88083))+~P1(f333(f333(f247(f882(f881(x88081,x88081),a870)),x88083),f309(x88081,x88082)))+~P1(f333(f333(f247(f882(f881(x88081,x88081),a870)),x88082),x88083)) % 183.90/184.44 [8868]~P39(x88681,f256(f882(x88681,a870)),x88683)+P1(f333(f333(f247(f882(f881(f876(x88681),f876(x88681)),a870)),f158(x88681,x88682)),f159(x88681,x88683)))+~P1(f333(f333(f247(f882(f881(x88681,x88681),a870)),x88682),x88683)) % 183.90/184.44 [9076]P37(x90761,x90762)+~P1(f333(f333(f335(x90761),x90763),f630(x90762,x90761)))+P1(f333(f333(f335(f881(x90761,x90761)),f333(f333(f268(x90761,x90761),f656(x90762,x90761,x90763)),x90763)),x90762)) % 183.90/184.44 [9110]~P1(f333(f61(x91101),x91102))+P1(f333(f61(f882(x91101,a870)),f333(f333(f60(x91101),x91102),x91103)))+~P1(f333(f333(f247(f882(f881(x91101,x91101),a870)),x91103),f333(f333(f270(x91101,x91101),x91102),f333(f16(f882(x91101,a870),x91101),x91102)))) % 183.90/184.44 [9145]P39(x91451,x91452,x91453)+P1(f333(f333(f335(x91451),f582(x91453,x91452,x91451)),x91452))+~P1(f333(f333(f247(f882(f881(x91451,x91451),a870)),x91453),f333(f333(f270(x91451,x91451),x91452),f333(f16(f882(x91451,a870),x91451),x91452)))) % 183.90/184.44 [9146]P39(x91461,x91462,x91463)+P1(f333(f333(f335(x91461),f590(x91462,x91463,x91461)),x91462))+~P1(f333(f333(f247(f882(f881(x91461,x91461),a870)),x91463),f333(f333(f270(x91461,x91461),x91462),f333(f16(f882(x91461,a870),x91461),x91462)))) % 183.90/184.44 [9181]~P61(x91811)+~P1(f333(f333(f248(x91811),x91812),x91813))+P1(f333(f333(f248(x91811),f333(f333(f291(x91811),f333(f333(f79(x91811),x91812),x91813)),f333(f333(f79(x91811),f77(x91811)),f77(x91811)))),x91813)) % 183.90/184.44 [9210]~P60(x92101)+P1(f333(f333(f247(x92101),x92102),x92103))+~P1(f333(f333(f247(x92101),f333(f333(f80(x92101),f455(x92103,x92102,x92101)),x92102)),x92103)) % 183.90/184.44 [9346]E(f333(f197(f876(f876(x93461))),f333(f137(f876(x93461),f333(f333(f8(a875,a870,f876(x93461)),f333(f248(a875),x93462)),f197(f876(x93461)))),f182(x93461,x93463))),f333(f197(f876(x93461)),f333(f333(f166(f876(x93461)),x93463),x93462)))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x93461),a875),f197(f876(x93461))),x93463)))+~P1(f333(f333(f248(a875),x93462),f333(f197(f876(f876(x93461))),x93463))) % 183.90/184.44 [9454]~P37(x94541,x94542)+P26(x94541,f333(f333(f268(f882(f881(x94541,x94541),a870),f882(f881(x94541,x94541),a870)),x94542),x94543))+~P1(f333(f333(f247(f882(f881(x94541,x94541),a870)),f333(f333(f290(x94541,x94541,x94541),x94542),x94543)),x94542)) % 183.90/184.44 [9461]E(f333(f333(f155(f876(x94611),x94611),f333(f333(f7(f876(x94611),a875,x94611),f166(x94611)),x94612)),f333(f137(f876(x94611),f333(f333(f8(a875,a870,f876(x94611)),f333(f248(a875),x94612)),f197(f876(x94611)))),f182(x94611,x94613))),f333(f333(f166(f876(x94611)),x94613),x94612))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x94611),a875),f197(f876(x94611))),x94613)))+~P1(f333(f333(f248(a875),x94612),f333(f197(f876(f876(x94611))),x94613))) % 183.90/184.44 [9595]P39(x95951,x95952,x95953)+~P1(f333(f333(f335(f881(x95951,x95951)),f333(f333(f268(x95951,x95951),f582(x95953,x95952,x95951)),f582(x95953,x95952,x95951))),x95953))+~P1(f333(f333(f247(f882(f881(x95951,x95951),a870)),x95953),f333(f333(f270(x95951,x95951),x95952),f333(f16(f882(x95951,a870),x95951),x95952)))) % 183.90/184.44 [9596]P39(x95961,x95962,x95963)+~P1(f333(f333(f335(f881(x95961,x95961)),f333(f333(f268(x95961,x95961),f590(x95962,x95963,x95961)),f590(x95962,x95963,x95961))),x95963))+~P1(f333(f333(f247(f882(f881(x95961,x95961),a870)),x95963),f333(f333(f270(x95961,x95961),x95962),f333(f16(f882(x95961,a870),x95961),x95962)))) % 183.90/184.44 [9770]~P138(x97701)+~P119(x97701)+E(f333(f333(f291(x97701),f333(f105(x97701),f333(f333(f72(f881(a1,a1),a1,x97702,f267(a1,a1)),f224(x97702)),x97703))),f333(f105(x97701),f333(f333(f72(f881(a1,a1),a1,x97702,f271(a1,a1)),f224(x97702)),x97703))),f237(x97702,x97701,x97703)) % 183.90/184.44 [9971]~E(x99713,f2(a875))+~E(f333(f197(f876(x99711)),f333(f333(f166(f876(x99711)),x99712),f746(x99713,x99711,x99712))),x99713)+E(f333(f333(f155(a875,f876(x99711)),f333(f333(f7(a875,f876(a875),f876(x99711)),f333(f333(f8(f882(a875,x99711),f882(f876(a875),f876(x99711)),a875),f155(a875,x99711)),f333(f7(a875,a875,x99711),f333(f333(f8(f876(x99711),f882(a875,x99711),a875),f166(x99711)),f333(f166(f876(x99711)),x99712))))),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(f876(x99711))),x99712))))),f140(a875,f333(f303(a875,f2(a875)),x99713))),f182(x99711,x99712)) % 183.90/184.44 [9972]E(x99721,f116(f876(x99722)))+~E(f333(f197(f876(x99722)),f333(f333(f166(f876(x99722)),x99721),f746(x99723,x99722,x99721))),x99723)+E(f333(f333(f155(a875,f876(x99722)),f333(f333(f7(a875,f876(a875),f876(x99722)),f333(f333(f8(f882(a875,x99722),f882(f876(a875),f876(x99722)),a875),f155(a875,x99722)),f333(f7(a875,a875,x99722),f333(f333(f8(f876(x99722),f882(a875,x99722),a875),f166(x99722)),f333(f166(f876(x99722)),x99721))))),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(f876(x99722))),x99721))))),f140(a875,f333(f303(a875,f2(a875)),x99723))),f182(x99722,x99721)) % 183.90/184.44 [9973]~E(x99733,f2(a875))+E(f333(f333(f155(a875,f876(x99731)),f333(f333(f7(a875,f876(a875),f876(x99731)),f333(f333(f8(f882(a875,x99731),f882(f876(a875),f876(x99731)),a875),f155(a875,x99731)),f333(f7(a875,a875,x99731),f333(f333(f8(f876(x99731),f882(a875,x99731),a875),f166(x99731)),f333(f166(f876(x99731)),x99732))))),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(f876(x99731))),x99732))))),f140(a875,f333(f303(a875,f2(a875)),x99733))),f182(x99731,x99732))+P1(f333(f333(f248(a875),f746(x99733,x99731,x99732)),f333(f197(f876(f876(x99731))),x99732))) % 183.90/184.44 [9974]E(x99741,f116(f876(x99742)))+E(f333(f333(f155(a875,f876(x99742)),f333(f333(f7(a875,f876(a875),f876(x99742)),f333(f333(f8(f882(a875,x99742),f882(f876(a875),f876(x99742)),a875),f155(a875,x99742)),f333(f7(a875,a875,x99742),f333(f333(f8(f876(x99742),f882(a875,x99742),a875),f166(x99742)),f333(f166(f876(x99742)),x99741))))),f140(a875,f333(f303(a875,f2(a875)),f333(f197(f876(f876(x99742))),x99741))))),f140(a875,f333(f303(a875,f2(a875)),x99743))),f182(x99742,x99741))+P1(f333(f333(f248(a875),f746(x99743,x99742,x99741)),f333(f197(f876(f876(x99742))),x99741))) % 183.90/184.44 [7705]E(f333(f333(f79(a875),f333(f106(a875),x77051)),f333(f333(f79(a875),f333(f106(a875),x77052)),x77053)),f333(f333(f79(a875),f333(f106(a875),f333(f333(f79(a1),x77051),x77052))),x77053))+P1(f333(a201,f333(f106(a1),x77051)))+P1(f333(a201,f333(f106(a1),x77052))) % 183.90/184.44 [8484]~P1(f333(f61(x84841),x84842))+~P1(f333(f333(f335(x84841),x84843),x84842))+E(f333(a115,f333(f37(x84841),f333(f333(f22(f882(x84841,a870)),x84842),f333(f333(f311(x84841),x84843),f196(f882(x84841,a870)))))),f333(f37(x84841),x84842)) % 183.90/184.44 [8503]~P1(f333(f61(x85031),x85032))+~P1(f333(f333(f335(x85031),x85033),x85032))+E(f333(f333(f79(a875),f77(a875)),f333(f37(x85031),f333(f333(f22(f882(x85031,a870)),x85032),f333(f333(f311(x85031),x85033),f196(f882(x85031,a870)))))),f333(f37(x85031),x85032)) % 183.90/184.44 [8586]~P106(x85861)+~P1(f333(f61(x85861),x85863))+E(f333(f333(f149(x85861,x85861,f5(x85861)),x85862),f140(x85861,f333(f333(f22(f882(x85861,a870)),x85863),f333(f333(f311(x85861),x85862),f196(f882(x85861,a870)))))),f140(x85861,f333(f333(f311(x85861),x85862),x85863))) % 183.90/184.44 [8737]~P1(f333(f61(x87371),x87373))+~P1(f333(f61(x87371),x87372))+E(f333(f333(f79(a875),f333(f37(x87371),f333(f333(f113(f882(x87371,a870)),x87372),x87373))),f333(f37(x87371),f333(f333(f104(f882(x87371,a870)),x87372),x87373))),f333(f333(f79(a875),f333(f37(x87371),x87372)),f333(f37(x87371),x87373))) % 183.90/184.44 [9919]~P25(x99191,f882(f882(x99191,a870),a870),f333(f333(f7(x99191,f882(f881(x99191,x99191),a870),f882(f882(x99191,a870),a870)),f333(f333(f8(f882(x99191,a870),f882(f882(f881(x99191,x99191),a870),f882(f882(x99191,a870),a870)),x99191),f60(x99191)),f333(f333(f7(x99191,f882(x99191,a870),f882(x99191,a870)),f311(x99191)),f196(f882(x99191,a870))))),x99193),x99192)+~P1(f333(f61(x99191),x99192))+E(f333(f37(f882(x99191,a870)),f333(f333(f60(x99191),x99192),x99193)),f333(f37(x99191),x99192)) % 183.90/184.44 [7979]~P90(x79791)+P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x79793)))+E(f333(f333(f258(x79791),x79792),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x79793),x79793)),a100))),f77(x79791)) % 183.90/184.44 [9437]~P90(x94371)+~P1(f333(f333(f247(a1),f2(a1)),f333(f106(a1),x94373)))+E(f333(f333(f258(x94371),x94372),f333(f106(a875),f333(f333(f22(a1),f333(f333(f79(a1),x94373),x94373)),a100))),f333(f333(f85(x94371,x94371),f333(f333(f258(x94371),x94372),f333(f106(a875),x94373))),f333(f333(f18(x94371,x94371,x94371),f333(f333(f8(x94371,f882(x94371,x94371),x94371),f80(x94371)),f333(f80(x94371),x94372))),f5(x94371)))) % 183.90/184.44 [9829]~P1(f333(f138(x98291),x98293))+~P1(f333(f333(f335(x98291),x98292),f333(f174(x98291),x98293)))+E(f333(f333(f139(x98291),f333(f197(f876(x98291)),f179(x98291,f333(f333(f8(a870,a870,x98291),a328),f333(f333(f7(x98291,x98291,a870),a330),x98292)),f333(f170(x98291),x98293)))),f333(f170(x98291),x98293)),f333(f333(f152(x98291),x98292),f333(f170(x98291),f179(x98291,f333(f333(f8(a870,a870,x98291),a328),f333(f333(f7(x98291,x98291,a870),a330),x98292)),x98293)))) % 183.90/184.44 [9900]P1(f333(f333(f247(f882(f881(x99001,x99001),a870)),f309(x99001,x99002)),x99003))+~P1(f333(f333(f247(f882(f881(x99001,x99001),a870)),f309(x99001,f196(f882(f881(x99001,x99001),a870)))),x99003))+~P1(f333(f333(f247(f882(f881(x99001,x99001),a870)),f333(f333(f290(x99001,x99001,x99001),f333(f333(f104(f882(f881(x99001,x99001),a870)),f309(x99001,x99002)),x99003)),x99002)),x99003)) % 183.90/184.44 [9741]~P1(f333(f61(x97411),f333(f253(x97411),x97413)))+~P1(f333(f61(x97411),f333(f253(x97411),x97412)))+P1(f333(f61(x97411),f333(f253(x97411),f333(f333(f18(x97411,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97411),a332),x97412)),x97413)))) % 183.90/184.44 [10034]P1(f333(f333(f247(f882(f881(x100341,x100341),a870)),f333(f333(f290(x100341,x100341,x100341),x100342),f309(x100341,x100342))),x100343))+~P1(f333(f333(f247(f882(f881(x100341,x100341),a870)),x100342),x100343))+~P1(f333(f333(f247(f882(f881(x100341,x100341),a870)),f333(f333(f290(x100341,x100341,x100341),f333(f333(f104(f882(f881(x100341,x100341),a870)),f333(f333(f290(x100341,x100341,x100341),x100342),f309(x100341,x100342))),x100343)),x100342)),x100343)) % 183.90/184.44 [9987]~P114(x99872)+E(x99871,f2(x99872))+~E(f333(f333(f79(x99872),f333(f333(f258(x99872),x99873),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x99872),x99871),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f2(x99872)) % 183.90/184.44 [9988]~P114(x99882)+E(x99881,f2(x99882))+~E(f333(f333(f79(x99882),f333(f333(f258(x99882),x99881),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x99882),x99883),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f2(x99882)) % 183.90/184.44 [9993]~P1(f333(f138(x99931),x99933))+~P1(f333(f333(f335(x99931),x99932),f333(f174(x99931),x99933)))+E(f333(f170(x99931),f333(f173(x99931),f333(f333(f139(x99931),f333(f197(f876(x99931)),f179(x99931,f333(f333(f8(a870,a870,x99931),a328),f333(f333(f7(x99931,x99931,a870),a330),x99932)),x99933))),x99933))),f179(x99931,f333(f333(f8(a870,a870,x99931),a328),f333(f333(f7(x99931,x99931,a870),a330),x99932)),f333(f170(x99931),x99933))) % 183.90/184.44 [10079]~P114(x100792)+E(x100791,f2(x100792))+P1(f333(f333(f248(x100792),f2(x100792)),f333(f333(f79(x100792),f333(f333(f258(x100792),x100793),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x100792),x100791),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))) % 183.90/184.44 [10080]~P114(x100802)+E(x100801,f2(x100802))+P1(f333(f333(f248(x100802),f2(x100802)),f333(f333(f79(x100802),f333(f333(f258(x100802),x100801),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x100802),x100803),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))) % 183.90/184.44 [10122]~P114(x101221)+P1(f333(f333(f247(x101221),f2(x101221)),x101222))+~P1(f333(f333(f247(x101221),f2(x101221)),f333(f333(f258(x101221),x101222),f333(a115,f333(f333(f80(a875),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),x101223))))) % 183.90/184.44 [5486]~P24(x54861,x54864,x54863)+P24(x54861,x54862,x54863)+~P24(x54861,x54862,x54864) % 183.90/184.44 [4957]~E(x49572,f89(x49573,x49571))+P1(f333(x49571,x49572))+~P1(f333(x49571,x49574)) % 183.90/184.44 [6691]~P37(x66912,x66914)+~P37(x66911,x66913)+P37(f881(x66911,x66912),f326(x66911,x66912,x66913,x66914)) % 183.90/184.44 [5136]~P6(x51364,x51361)+~E(f333(x51361,x51362),f333(x51361,x51363))+P1(f333(f333(x51361,x51362),x51363)) % 183.90/184.44 [5301]~P6(x53014,x53011)+E(f333(x53011,x53012),f333(x53011,x53013))+~P1(f333(f333(x53011,x53012),x53013)) % 183.90/184.44 [5393]~P18(x53933,x53934,x53931)+E(f333(x53931,x53932),f333(f63(x53933,x53934),x53932))+~P1(f333(f61(x53933),x53932)) % 183.90/184.44 [5394]~P8(x53943,x53944,x53941)+E(f333(x53941,x53942),f333(f63(x53943,x53944),x53942))+~P1(f333(f61(x53943),x53942)) % 183.90/184.44 [5519]~P6(x55194,x55191)+~P1(f333(f333(x55191,x55193),x55192))+P1(f333(f333(x55191,x55192),x55193)) % 183.90/184.44 [5589]E(x55891,x55892)+~E(f333(f267(x55893,x55894),x55891),f333(f267(x55893,x55894),x55892))+~E(f333(f271(x55893,x55894),x55891),f333(f271(x55893,x55894),x55892)) % 183.90/184.44 [5614]E(x56141,x56142)+~P1(f333(f47(x56143,x56144),x56142))+~P1(f333(f47(x56143,x56144),x56141)) % 183.90/184.44 [5804]~P66(x58042)+E(f238(x58041,x58042,x58043,x58044),f2(x58042))+P1(f333(f61(x58041),x58044)) % 183.90/184.44 [5939]~P1(f333(f321(x59391,x59392),x59394))+P1(f333(f321(x59391,x59392),x59393))+~P1(f333(f333(x59392,x59393),x59394)) % 183.90/184.44 [7816]E(x78161,f2(a875))+~P1(f333(x78162,x78163))+P1(f333(x78162,f810(x78162,x78163,x78161,x78164))) % 183.90/184.44 [7898]~P106(x78982)+~P1(f333(f138(x78981),x78984))+P1(f333(f138(x78981),f151(x78981,x78982,x78983,x78984))) % 183.90/184.44 [8127]~P1(f333(f61(x81272),x81274))+~P1(f333(f61(x81271),x81273))+P1(f333(f61(f880(x81271,x81272)),f320(x81271,x81272,x81273,x81274))) % 183.90/184.44 [8128]~P1(f333(f138(x81282),x81284))+~P1(f333(f138(x81281),x81283))+P1(f333(f138(f881(x81281,x81282)),f59(x81281,x81282,x81283,x81284))) % 183.90/184.44 [8132]P1(f333(f333(f335(f876(x81321)),f333(f333(f135(x81321),x81322),x81323)),f162(x81321,x81324)))+~P1(f333(f333(f335(f876(x81321)),x81323),f162(x81321,x81324)))+~P1(f333(f333(f335(f876(x81321)),x81322),f162(x81321,x81324))) % 183.90/184.44 [8417]E(x84171,f2(a875))+P1(f333(x84172,x84173))+~P1(f333(x84172,f811(x84172,x84173,x84171,x84174))) % 183.90/184.44 [8464]~P106(x84643)+~P1(f333(f138(x84641),f151(x84641,x84643,x84644,x84642)))+P1(f333(f138(x84641),x84642)) % 183.90/184.44 [8728]~P1(f333(f333(f335(f881(x87281,x87281)),f333(f333(f268(x87281,x87281),x87282),x87284)),f309(x87281,x87283)))+P1(f333(f333(f335(x87281),x87282),f322(x87281,x87283)))+~P1(f333(f333(f335(x87281),x87284),f322(x87281,x87283))) % 183.90/184.44 [5120]~P66(x51202)+E(f333(f333(f6(x51201,x51202),x51203),x51204),f2(x51202))+P1(f333(f61(x51201),x51204)) % 183.90/184.44 [5123]~P73(x51232)+E(f333(f333(f9(x51231,x51232),x51233),x51234),f77(x51232))+P1(f333(f61(x51231),x51234)) % 183.90/184.44 [5264]~P69(x52643)+E(x52641,x52642)+~E(f333(f333(f79(x52643),x52644),x52641),f333(f333(f79(x52643),x52644),x52642)) % 183.90/184.44 [5265]~P70(x52653)+E(x52651,x52652)+~E(f333(f333(f79(x52653),x52654),x52651),f333(f333(f79(x52653),x52654),x52652)) % 183.90/184.44 [5267]~P69(x52673)+E(x52671,x52672)+~E(f333(f333(f79(x52673),x52671),x52674),f333(f333(f79(x52673),x52672),x52674)) % 183.90/184.44 [5389]~P4(x53893)+E(x53891,f196(f882(x53892,a870)))+E(f333(f333(f41(x53892,x53893),x53891),f333(f16(x53893,x53892),x53894)),x53894) % 183.90/184.44 [5390]~P4(x53903)+E(x53901,f196(f882(x53902,a870)))+E(f333(f333(f42(x53902,x53903),x53901),f333(f16(x53903,x53902),x53904)),x53904) % 183.90/184.44 [5602]~P108(x56023)+E(x56021,x56022)+~E(f304(x56023,x56024,x56021),f333(f333(f311(x56023),x56022),f196(f882(x56023,a870)))) % 183.90/184.44 [5603]~P108(x56033)+E(x56031,x56032)+~E(f304(x56033,x56031,x56032),f333(f333(f311(x56033),x56034),f196(f882(x56033,a870)))) % 183.90/184.44 [5663]~P35(x56633,x56631,x56634)+P35(x56633,x56631,f333(f333(f152(x56633),x56632),x56634))+P1(f333(x56631,x56632)) % 183.90/184.44 [5764]~P31(x57641,x57642,x57644)+~P1(f333(x57642,x57643))+P31(x57641,x57642,f333(f333(f152(x57641),x57643),x57644)) % 183.90/184.44 [5895]P1(f333(x58951,x58952))+~P1(f333(f261(x58953,x58951),x58954))+~P1(f333(f333(f335(x58953),x58952),x58954)) % 183.90/184.44 [5904]~P31(x59041,x59042,x59044)+~P31(x59041,x59042,x59043)+P31(x59041,x59042,f333(f333(f135(x59041),x59043),x59044)) % 183.90/184.44 [5914]P33(x59141,x59142,x59143)+~P33(x59141,x59142,f333(f333(f152(x59141),x59144),x59143))+P1(f333(x59142,x59144)) % 183.90/184.44 [5915]P35(x59151,x59152,x59153)+~P35(x59151,x59152,f333(f333(f152(x59151),x59154),x59153))+P1(f333(x59152,x59154)) % 183.90/184.44 [5928]E(x59281,x59282)+~P1(f333(f333(f202(x59283),x59284),x59282))+~P1(f333(f333(f202(x59283),x59284),x59281)) % 183.90/184.44 [5994]P33(x59941,x59942,x59943)+P33(x59941,x59942,x59944)+~P33(x59941,x59942,f333(f333(f135(x59941),x59944),x59943)) % 183.90/184.44 [6013]~P66(x60131)+E(f333(f333(f6(a875,x60131),x60132),f333(f303(a875,x60133),f333(a115,x60134))),f2(x60131))+~P1(f333(f333(f248(a875),x60134),x60133)) % 183.90/184.44 [6018]~P56(x60181)+~E(f44(x60181,x60182,x60183),f44(x60181,x60184,x60183))+E(f44(x60181,f333(f78(x60181),x60182),x60183),f44(x60181,f333(f78(x60181),x60184),x60183)) % 183.90/184.44 [6086]P1(f333(x60861,x60862))+~E(f333(f137(x60863,x60861),x60864),x60864)+~P1(f333(f333(f335(x60863),x60862),f333(f174(x60863),x60864))) % 183.90/184.44 [6105]~E(f333(f333(f79(a875),x61053),x61052),f333(f333(f79(a875),x61051),x61054))+~P1(f333(f333(f248(a875),x61053),x61054))+P1(f333(f333(f248(a875),x61051),x61052)) % 183.90/184.44 [6109]P33(x61091,x61092,x61093)+~P1(f333(x61092,x61094))+~P1(f333(f333(f335(x61091),x61094),f333(f174(x61091),x61093))) % 183.90/184.44 [6145]~P31(x61453,x61451,x61454)+P1(f333(x61451,x61452))+~P1(f333(f333(f335(x61453),x61452),f333(f174(x61453),x61454))) % 183.90/184.44 [6147]~E(f333(f137(x61471,x61472),x61473),f116(x61471))+~P1(f333(x61472,x61474))+~P1(f333(f333(f335(x61471),x61474),f333(f174(x61471),x61473))) % 183.90/184.44 [6148]~E(f179(x61483,x61481,x61484),x61484)+P1(f333(x61481,x61482))+~P1(f333(f333(f335(x61483),x61482),f333(f174(x61483),x61484))) % 183.90/184.44 [6177]~E(x61774,f196(f882(x61772,a870)))+~E(x61773,f196(f882(x61771,a870)))+E(f320(x61771,x61772,x61773,x61774),f196(f882(f880(x61771,x61772),a870))) % 183.90/184.44 [6322]P1(f333(x63221,x63222))+~P1(f333(f161(x63223,x63221),x63224))+~P1(f333(f333(f335(x63223),x63222),f333(f174(x63223),x63224))) % 183.90/184.44 [6589]~P66(x65891)+E(f333(f333(f6(a875,x65891),x65892),f304(a875,x65893,f333(a115,x65894))),f2(x65891))+~P1(f333(f333(f248(a875),f333(a115,x65894)),x65893)) % 183.90/184.44 [6730]~P106(x67301)+E(f333(f333(f22(f882(x67301,a870)),f333(f303(x67301,x67302),x67303)),f333(f303(x67301,x67302),x67304)),f333(f303(x67301,x67304),x67303))+~P1(f333(f333(f247(x67301),x67302),x67304)) % 183.90/184.44 [6802]~E(x68023,x68024)+E(x68021,f2(a875))+P1(f333(f333(f335(x68022),x68023),f333(f174(x68022),f171(x68022,x68021,x68024)))) % 183.90/184.44 [7084]~P1(f333(f333(f335(f876(x70841)),x70844),f162(x70841,x70843)))+P1(f333(f333(f335(x70841),x70842),x70843))+~P1(f333(f333(f335(x70841),x70842),f333(f174(x70841),x70844))) % 183.90/184.44 [7091]~P37(x70911,x70912)+P1(f333(f333(f335(x70911),f631(x70912,x70911,x70913)),x70913))+~P1(f333(f333(f335(x70911),x70914),x70913)) % 183.90/184.44 [7147]~P66(x71471)+E(f333(f333(f333(f65(x71471,x71472,f79(x71471)),x71473),f2(x71471)),x71474),f333(f333(f6(x71472,x71471),x71473),x71474))+~P1(f333(f61(x71472),x71474)) % 183.90/184.44 [7149]~P73(x71491)+E(f333(f333(f333(f65(x71491,x71492,f80(x71491)),x71493),f77(x71491)),x71494),f333(f333(f9(x71492,x71491),x71493),x71494))+~P1(f333(f61(x71492),x71494)) % 183.90/184.44 [7177]P25(x71771,x71772,x71773,x71774)+~E(f333(f37(x71772),f333(f312(x71771,x71772,x71773),x71774)),f333(f37(x71771),x71774))+~P1(f333(f61(x71771),x71774)) % 183.90/184.44 [7363]~P66(x73631)+E(f333(f333(f79(x73631),f333(x73632,x73633)),f333(f333(f6(a875,x73631),x73632),f306(a875,x73633,x73634))),f333(f333(f6(a875,x73631),x73632),f304(a875,x73633,x73634)))+~P1(f333(f333(f247(a875),x73633),x73634)) % 183.90/184.44 [7373]~P66(x73731)+~P25(x73732,x73731,x73733,x73734)+E(f333(f333(f6(x73731,x73731),f33(x73731)),f333(f312(x73732,x73731,x73733),x73734)),f333(f333(f6(x73732,x73731),x73733),x73734)) % 183.90/184.44 [7374]~P73(x73741)+~P25(x73742,x73741,x73743,x73744)+E(f333(f333(f9(x73741,x73741),f33(x73741)),f333(f312(x73742,x73741,x73743),x73744)),f333(f333(f9(x73742,x73741),x73743),x73744)) % 183.90/184.44 [7427]E(f333(f37(f880(x74271,x74272)),f320(x74271,x74272,x74273,x74274)),f333(f333(f79(a875),f333(f37(x74271),x74273)),f333(f37(x74272),x74274)))+~P1(f333(f61(x74272),x74274))+~P1(f333(f61(x74271),x74273)) % 183.90/184.44 [7514]E(x75141,x75142)+P1(f333(f333(f335(x75143),x75141),f333(f174(x75143),f172(x75143,x75142,x75144))))+~P1(f333(f333(f335(x75143),x75141),f333(f174(x75143),x75144))) % 183.90/184.44 [7742]~P66(x77421)+E(f333(f333(f79(x77421),f333(f333(f6(a875,x77421),x77422),f333(f303(a875,x77423),x77424))),f333(x77422,x77424)),f333(f333(f6(a875,x77421),x77422),f333(f303(a875,x77423),f333(a115,x77424))))+P1(f333(f333(f248(a875),x77424),x77423)) % 183.90/184.44 [7798]~P25(x77981,x77982,x77983,f256(f882(x77981,a870)))+~P1(f333(f61(x77982),x77984))+P1(f333(f61(x77981),f333(f313(x77981,x77982,x77983),x77984))) % 183.90/184.44 [7911]P1(f333(f333(f335(f876(x79111)),f333(f333(f152(x79111),x79112),x79113)),f162(x79111,x79114)))+~P1(f333(f333(f335(f876(x79111)),x79113),f162(x79111,x79114)))+~P1(f333(f333(f335(x79111),x79112),x79114)) % 183.90/184.44 [8003]~E(f333(f312(x80033,x80031,x80034),f256(f882(x80033,a870))),f256(f882(x80031,a870)))+P1(f333(f61(x80031),x80032))+~P1(f333(f61(x80033),f333(f313(x80033,x80031,x80034),x80032))) % 183.90/184.44 [8099]~P25(x80991,x80993,x80994,x80992)+P1(f333(f61(x80991),x80992))+~P1(f333(f61(x80993),f333(f312(x80991,x80993,x80994),x80992))) % 183.90/184.44 [8120]~E(x81202,x81203)+P1(f333(f333(f335(f881(x81201,x81201)),f333(f333(f268(x81201,x81201),x81202),x81203)),f265(x81201,x81204)))+~P1(f333(f333(f335(x81201),x81202),x81204)) % 183.90/184.44 [8159]~P66(x81591)+E(f333(f333(f79(x81591),f333(f333(f6(a875,x81591),x81592),f304(a875,x81593,x81594))),f333(x81592,f333(a115,x81594))),f333(f333(f6(a875,x81591),x81592),f304(a875,x81593,f333(a115,x81594))))+P1(f333(f333(f248(a875),f333(a115,x81594)),x81593)) % 183.90/184.44 [8223]P1(f333(x82231,x82232))+~P1(f333(x82231,f333(f333(f166(x82233),x82234),f681(x82231,x82234,x82233))))+~P1(f333(f333(f335(x82233),x82232),f333(f174(x82233),x82234))) % 183.90/184.44 [8362]~P1(f333(f333(f335(x83621),x83622),f322(x83621,x83624)))+P1(f333(f333(f335(f876(x83621)),f333(f333(f152(x83621),x83622),x83623)),f322(f876(x83621),f158(x83621,x83624))))+~P1(f333(f333(f335(f876(x83621)),x83623),f322(f876(x83621),f158(x83621,x83624)))) % 183.90/184.44 [8375]~P25(x83752,x83753,x83754,f827(x83754,x83753,x83752,x83751))+P25(x83752,x83753,x83754,f40(f882(x83752,a870),x83751))+E(x83751,f196(f882(f882(x83752,a870),a870))) % 183.90/184.44 [8647]E(x86471,x86472)+~P1(f333(f333(f335(f881(x86473,x86473)),f333(f333(f268(x86473,x86473),x86471),x86472)),f309(x86473,x86474)))+P1(f333(f333(f335(x86473),x86471),f333(f266(x86473,x86473),x86474))) % 183.90/184.44 [8912]E(x89121,f2(a875))+P1(f333(x89122,x89123))+P1(f333(f333(f335(x89124),f811(x89122,x89123,x89121,x89124)),f333(f174(x89124),f171(x89124,x89121,x89123)))) % 183.90/184.44 [8922]E(x89221,f2(a875))+~P1(f333(x89223,x89224))+P1(f333(f333(f335(x89222),f810(x89223,x89224,x89221,x89222)),f333(f174(x89222),f171(x89222,x89221,x89224)))) % 183.90/184.44 [8930]P25(x89302,x89303,x89304,f40(f882(x89302,a870),x89301))+E(x89301,f196(f882(f882(x89302,a870),a870)))+P1(f333(f333(f335(f882(x89302,a870)),f827(x89304,x89303,x89302,x89301)),x89301)) % 183.90/184.44 [9067]P1(f333(f61(x90671),x90672))+~P1(f333(f61(x90674),f333(f312(x90671,x90674,x90673),x90672)))+P1(f333(f333(f335(x90671),f496(x90673,x90674,x90672,x90671)),x90672)) % 183.90/184.44 [9159]~P4(x91592)+E(f333(f333(f64(x91591,x91592,f333(f333(f8(x91592,f882(x91592,x91592),x91591),f113(x91592)),x91593)),f196(x91592)),x91594),f333(f333(f41(x91591,x91592),x91594),x91593))+~P1(f333(f61(x91591),x91594)) % 183.90/184.44 [9160]~P4(x91602)+E(f333(f333(f64(x91601,x91602,f333(f333(f8(x91602,f882(x91602,x91602),x91601),f104(x91602)),x91603)),f256(x91602)),x91604),f333(f333(f42(x91601,x91602),x91604),x91603))+~P1(f333(f61(x91601),x91604)) % 183.90/184.44 [9243]P1(f333(x92431,x92432))+~P1(f333(x92431,f333(f333(f166(x92433),x92434),f732(x92432,x92431,x92434,x92433))))+~P1(f333(f333(f335(x92433),x92432),f333(f174(x92433),x92434))) % 183.90/184.44 [9263]E(x92631,x92632)+~P1(f333(f333(f335(f881(x92633,x92633)),f333(f333(f268(x92633,x92633),x92631),x92632)),f309(x92633,x92634)))+P1(f333(f333(f335(f881(x92633,x92633)),f333(f333(f268(x92633,x92633),x92631),x92632)),f333(f333(f290(x92633,x92633,x92633),x92634),f309(x92633,x92634)))) % 183.90/184.44 [9312]~E(f333(f197(f876(x93121)),x93122),f333(f197(f876(x93121)),x93123))+~P1(f333(f333(f335(f881(f876(x93121),f876(x93121))),f333(f333(f268(f876(x93121),f876(x93121)),x93122),x93123)),f148(x93121,x93124)))+P1(f333(f333(f335(f881(f876(x93121),f876(x93121))),f333(f333(f268(f876(x93121),f876(x93121)),x93122),x93123)),f146(x93121,x93124))) % 183.90/184.44 [9542]P31(x95421,f333(f333(f18(x95421,a870,a870),f333(f333(f8(a870,f882(a870,a870),x95421),a332),f333(f333(f8(a870,a870,x95421),a328),x95422))),f333(a330,x95423)),x95424)+~P1(f333(x95422,x95423))+~P35(x95421,x95422,f333(f333(f152(x95421),x95423),x95424)) % 183.90/184.44 [9703]~P31(x97031,f333(f333(f18(x97031,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97031),a332),f333(f333(f8(a870,a870,x97031),a328),x97032))),f333(a330,x97033)),x97034)+~P1(f333(x97032,x97033))+P35(x97031,x97032,f333(f333(f152(x97031),x97033),x97034)) % 183.90/184.44 [9707]~P35(x97071,x97072,x97074)+~P31(x97071,f333(f333(f18(x97071,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97071),a332),f333(f333(f8(a870,a870,x97071),a328),x97072))),f333(a330,x97073)),x97074)+P35(x97071,x97072,f333(f333(f152(x97071),x97073),x97074)) % 183.90/184.44 [9744]~P65(x97441)+E(f333(f333(f6(a875,x97441),f333(f333(f18(a875,x97441,x97441),f333(f333(f8(x97441,f882(x97441,x97441),a875),f22(x97441)),x97442)),f333(f333(f8(a875,x97441,a875),x97442),f333(f333(f7(a875,a875,a875),f79(a875)),f77(a875))))),f304(a875,x97443,x97444)),f2(x97441))+P1(f333(f333(f247(a875),x97443),x97444)) % 183.90/184.44 [9986]~P37(x99862,x99864)+~P25(x99862,x99861,x99863,f256(f882(x99862,a870)))+P37(x99861,f333(f312(f881(x99862,x99862),f881(x99861,x99861),f273(x99862,x99861,x99862,x99861,x99863,x99863)),x99864)) % 183.90/184.44 [10148]~E(f333(f197(f876(x101481)),x101483),f333(f197(f876(x101481)),x101482))+P1(f333(f333(f335(f881(f876(x101481),f876(x101481))),f333(f333(f268(f876(x101481),f876(x101481)),x101482),x101483)),f159(x101481,x101484)))+~P1(f333(f333(f272(x101481,x101481,a870),f333(f333(f7(x101481,f882(f881(x101481,x101481),a870),f882(x101481,a870)),f333(f333(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)),f333(f333(f8(f882(x101481,f881(x101481,x101481)),f882(x101481,f882(f882(f881(x101481,x101481),a870),a870)),x101481),f333(f8(f881(x101481,x101481),f882(f882(f881(x101481,x101481),a870),a870),x101481),f335(f881(x101481,x101481)))),f268(x101481,x101481)))),x101484)),f684(x101484,x101483,x101482,x101481))) % 183.90/184.44 [5978]~E(x59784,x59782)+P1(f333(x59781,x59782))+P1(f333(f333(f202(f31(x59781,x59783)),x59782),x59784)) % 183.90/184.44 [6070]~P55(x60701)+~E(x60702,f2(x60701))+E(f333(f333(f38(x60701),f333(f333(f80(x60701),x60702),x60703)),f333(f333(f80(x60701),x60702),x60704)),f2(x60701)) % 183.90/184.44 [6108]E(x61081,f116(x61082))+E(x61083,f333(f333(f22(a875),f333(f197(f876(x61082)),x61081)),f77(a875)))+E(f145(x61082,f333(f333(f160(x61082,x61081),x61083),x61084)),f145(x61082,x61081)) % 183.90/184.44 [6136]E(x61361,x61362)+P1(f333(x61363,x61362))+~P1(f333(f333(f333(f311(x61364),x61361),x61363),x61362)) % 183.90/184.44 [6152]~P66(x61521)+~P1(f333(f138(x61522),x61524))+E(f333(f167(x61521),f333(f333(f155(x61522,x61521),x61523),x61524)),f333(f333(f6(x61522,x61521),x61523),f333(f174(x61522),x61524))) % 183.90/184.44 [6170]~P73(x61702)+~P1(f333(f61(x61701),x61704))+E(f333(f333(f9(x61701,x61702),f333(f16(x61702,x61701),x61703)),x61704),f333(f333(f258(x61702),x61703),f333(f37(x61701),x61704))) % 183.90/184.44 [6225]~P55(x62252)+E(x62251,f2(x62252))+E(f333(f333(f38(x62252),f333(f333(f80(x62252),x62253),x62251)),f333(f333(f80(x62252),x62254),x62251)),f333(f333(f38(x62252),x62253),x62254)) % 183.90/184.44 [6227]~P58(x62272)+E(x62271,f2(x62272))+E(f333(f333(f291(x62272),f333(f333(f80(x62272),x62273),x62271)),f333(f333(f80(x62272),x62274),x62271)),f333(f333(f291(x62272),x62273),x62274)) % 183.90/184.44 [6228]~P58(x62282)+E(x62281,f2(x62282))+E(f333(f333(f291(x62282),f333(f333(f80(x62282),x62281),x62283)),f333(f333(f80(x62282),x62281),x62284)),f333(f333(f291(x62282),x62283),x62284)) % 183.90/184.44 [6229]~P55(x62292)+E(x62291,f2(x62292))+E(f333(f333(f38(x62292),f333(f333(f80(x62292),x62291),x62293)),f333(f333(f80(x62292),x62291),x62294)),f333(f333(f38(x62292),x62293),x62294)) % 183.90/184.44 [6292]P1(f333(x62921,x62922))+~E(x62923,f333(f333(f79(a875),x62924),x62922))+~P1(f333(x62921,f333(f333(f22(a875),x62923),x62924))) % 183.90/184.44 [6373]P28(x63731,x63732,x63733)+P27(x63731,f600(x63733,x63732,x63731),x63734)+~P1(f333(f333(f335(f874(x63731)),x63734),x63732)) % 183.90/184.44 [6375]~P1(f333(x63752,x63753))+~P1(f333(f161(x63751,x63752),x63754))+P1(f333(f161(x63751,x63752),f333(f333(f152(x63751),x63753),x63754))) % 183.90/184.44 [6415]E(x64151,f116(x64152))+~E(x64153,f333(f333(f22(a875),f333(f197(f876(x64152)),x64151)),f77(a875)))+E(f145(x64152,f333(f333(f160(x64152,x64151),x64153),x64154)),x64154) % 183.90/184.44 [6438]~P98(x64381)+~P1(f333(f333(f248(x64381),x64382),x64384))+P1(f333(f333(f248(x64381),x64382),f333(f333(f113(x64381),x64383),x64384))) % 183.90/184.44 [6439]~P98(x64391)+~P1(f333(f333(f248(x64391),x64392),x64393))+P1(f333(f333(f248(x64391),x64392),f333(f333(f113(x64391),x64393),x64394))) % 183.90/184.44 [6441]~P106(x64411)+~P1(f333(f333(f248(x64411),x64412),x64414))+P1(f333(f333(f248(x64411),x64412),f333(f333(f246(x64411),x64413),x64414))) % 183.90/184.44 [6443]~P106(x64431)+~P1(f333(f333(f248(x64431),x64432),x64433))+P1(f333(f333(f248(x64431),x64432),f333(f333(f246(x64431),x64433),x64434))) % 183.90/184.44 [6444]~P98(x64441)+~P1(f333(f333(f247(x64441),x64442),x64444))+P1(f333(f333(f247(x64441),x64442),f333(f333(f113(x64441),x64443),x64444))) % 183.90/184.44 [6445]~P98(x64451)+~P1(f333(f333(f247(x64451),x64452),x64453))+P1(f333(f333(f247(x64451),x64452),f333(f333(f113(x64451),x64453),x64454))) % 183.90/184.44 [6447]~P106(x64471)+~P1(f333(f333(f247(x64471),x64472),x64474))+P1(f333(f333(f247(x64471),x64472),f333(f333(f246(x64471),x64473),x64474))) % 183.90/184.44 [6449]~P106(x64491)+~P1(f333(f333(f247(x64491),x64492),x64493))+P1(f333(f333(f247(x64491),x64492),f333(f333(f246(x64491),x64493),x64494))) % 183.90/184.44 [6534]~E(f333(f333(f166(x65341),x65342),x65343),x65344)+E(f333(f333(f160(x65341,x65342),x65343),x65344),x65342)+~P1(f333(f333(f248(a875),x65343),f333(f197(f876(x65341)),x65342))) % 183.90/184.44 [6551]E(x65511,x65512)+P1(f333(x65513,x65511))+~P1(f333(f333(f202(f31(x65513,x65514)),x65511),x65512)) % 183.90/184.44 [6575]P1(f333(x65751,x65752))+~P1(f333(x65753,x65752))+~P1(f333(f333(f247(f882(x65754,a870)),x65753),x65751)) % 183.90/184.44 [6607]~E(f333(f333(f160(x66071,x66072),x66073),x66074),x66072)+E(f333(f333(f166(x66071),x66072),x66073),x66074)+~P1(f333(f333(f248(a875),x66073),f333(f197(f876(x66071)),x66072))) % 183.90/184.44 [6622]~P1(f333(f161(x66221,x66222),x66224))+~P1(f333(f161(x66221,x66222),x66223))+P1(f333(f161(x66221,x66222),f333(f333(f135(x66221),x66223),x66224))) % 183.90/184.44 [6718]P27(x67181,x67182,x67183)+~P27(x67181,f333(a115,x67182),f601(x67182,x67184,x67181))+~P1(f333(f333(f335(f874(x67181)),x67183),x67184)) % 183.90/184.44 [6727]E(x67271,f196(f882(x67272,a870)))+E(x67273,f196(f882(x67274,a870)))+~E(f333(f333(f270(x67274,x67272),x67273),f333(f16(f882(x67272,a870),x67274),x67271)),f196(f882(f881(x67274,x67272),a870))) % 183.90/184.44 [6746]E(x67461,x67462)+P1(f333(f333(f335(x67463),x67461),x67464))+~P1(f333(f333(f335(x67463),x67461),f333(f333(f311(x67463),x67462),x67464))) % 183.90/184.44 [6762]~P106(x67621)+P1(f333(f333(f248(x67621),x67622),x67623))+~P1(f333(f333(f248(x67621),x67622),f333(f333(f245(x67621),x67624),x67623))) % 183.90/184.44 [6763]~P106(x67631)+P1(f333(f333(f248(x67631),x67632),x67633))+~P1(f333(f333(f248(x67631),x67632),f333(f333(f245(x67631),x67633),x67634))) % 183.90/184.44 [6765]~P99(x67651)+P1(f333(f333(f247(x67651),x67652),x67653))+~P1(f333(f333(f247(x67651),x67652),f333(f333(f104(x67651),x67654),x67653))) % 183.90/184.44 [6767]~P99(x67671)+P1(f333(f333(f247(x67671),x67672),x67673))+~P1(f333(f333(f247(x67671),x67672),f333(f333(f104(x67671),x67673),x67674))) % 183.90/184.44 [6769]~P106(x67691)+P1(f333(f333(f247(x67691),x67692),x67693))+~P1(f333(f333(f247(x67691),x67692),f333(f333(f245(x67691),x67694),x67693))) % 183.90/184.44 [6771]~P106(x67711)+P1(f333(f333(f247(x67711),x67712),x67713))+~P1(f333(f333(f247(x67711),x67712),f333(f333(f245(x67711),x67713),x67714))) % 183.90/184.44 [6793]~E(f333(f333(f166(x67931),x67933),x67934),x67932)+P1(f333(f333(f335(x67931),x67932),f333(f174(x67931),x67933)))+~P1(f333(f333(f248(a875),x67934),f333(f197(f876(x67931)),x67933))) % 183.90/184.44 [6805]~P106(x68051)+~P14(x68051,f333(f333(f152(x68051),x68052),f333(f333(f152(x68051),x68053),x68054)))+P1(f333(f333(f247(x68051),x68052),x68053)) % 183.90/184.44 [6947]~P31(x69472,x69471,x69473)+P1(f333(x69471,f333(f333(f166(x69472),x69473),x69474)))+~P1(f333(f333(f248(a875),x69474),f333(f197(f876(x69472)),x69473))) % 183.90/184.44 [6966]E(x69661,f2(a1))+E(f333(f333(f38(a1),x69662),x69661),x69663)+~P1(f333(f48(x69662,x69661),f333(f333(f268(a1,a1),x69663),x69664))) % 183.90/184.44 [6987]E(f44(a1,x69872,x69871),x69873)+E(x69871,f2(a1))+~P1(f333(f48(x69872,x69871),f333(f333(f268(a1,a1),x69874),x69873))) % 183.90/184.44 [7105]P1(f333(f333(f335(x71051),x71052),x71053))+~P1(f333(f333(f335(x71051),x71052),x71054))+~P1(f333(f333(f248(f882(x71051,a870)),x71054),x71053)) % 183.90/184.44 [7109]P1(f333(f333(f335(x71091),x71092),x71093))+~P1(f333(f333(f335(x71091),x71092),x71094))+~P1(f333(f333(f247(f882(x71091,a870)),x71094),x71093)) % 183.90/184.44 [7217]P33(x72171,x72172,x72173)+~P1(f333(x72172,f333(f333(f166(x72171),x72173),x72174)))+~P1(f333(f333(f248(a875),x72174),f333(f197(f876(x72171)),x72173))) % 183.90/184.44 [7328]~P107(x73282)+~P1(f333(f333(f248(f882(x73281,x73282)),x73283),x73284))+P1(f333(f333(f247(f882(x73281,x73282)),x73283),x73284)) % 183.90/184.44 [7415]~P24(x74151,x74152,x74154)+P24(x74151,x74152,f333(f333(f311(f874(x74151)),x74153),x74154))+~P24(x74151,x74152,f333(f333(f311(f874(x74151)),x74153),f196(f882(f874(x74151),a870)))) % 183.90/184.44 [7460]~P1(f333(f333(f335(x74601),x74602),x74604))+P1(f333(f333(f335(x74601),x74602),f39(f882(x74601,a870),x74603)))+~P1(f333(f333(f335(f882(x74601,a870)),x74604),x74603)) % 183.90/184.44 [7472]P27(x74721,x74722,x74723)+P1(f333(f333(f335(f874(x74721)),f601(x74722,x74724,x74721)),x74724))+~P1(f333(f333(f335(f874(x74721)),x74723),x74724)) % 183.90/184.44 [7492]~P79(x74921)+~P1(f333(f333(f248(x74921),x74923),x74924))+P1(f333(f333(f248(x74921),f333(f333(f79(x74921),x74922),x74923)),f333(f333(f79(x74921),x74922),x74924))) % 183.90/184.44 [7493]~P80(x74931)+~P1(f333(f333(f248(x74931),x74933),x74934))+P1(f333(f333(f248(x74931),f333(f333(f79(x74931),x74932),x74933)),f333(f333(f79(x74931),x74932),x74934))) % 183.90/184.44 [7494]~P79(x74941)+~P1(f333(f333(f248(x74941),x74942),x74944))+P1(f333(f333(f248(x74941),f333(f333(f79(x74941),x74942),x74943)),f333(f333(f79(x74941),x74944),x74943))) % 183.90/184.44 [7495]~P80(x74951)+~P1(f333(f333(f248(x74951),x74952),x74954))+P1(f333(f333(f248(x74951),f333(f333(f79(x74951),x74952),x74953)),f333(f333(f79(x74951),x74954),x74953))) % 183.90/184.44 [7496]~P80(x74961)+~P1(f333(f333(f247(x74961),x74963),x74964))+P1(f333(f333(f247(x74961),f333(f333(f79(x74961),x74962),x74963)),f333(f333(f79(x74961),x74962),x74964))) % 183.90/184.44 [7497]~P81(x74971)+~P1(f333(f333(f247(x74971),x74973),x74974))+P1(f333(f333(f247(x74971),f333(f333(f79(x74971),x74972),x74973)),f333(f333(f79(x74971),x74972),x74974))) % 183.90/184.44 [7498]~P80(x74981)+~P1(f333(f333(f247(x74981),x74982),x74984))+P1(f333(f333(f247(x74981),f333(f333(f79(x74981),x74982),x74983)),f333(f333(f79(x74981),x74984),x74983))) % 183.90/184.44 [7499]~P81(x74991)+~P1(f333(f333(f247(x74991),x74992),x74994))+P1(f333(f333(f247(x74991),f333(f333(f79(x74991),x74992),x74993)),f333(f333(f79(x74991),x74994),x74993))) % 183.90/184.44 [7508]~P103(x75081)+~P91(x75081)+E(f333(f333(f22(x75081),f333(f333(f80(x75081),x75082),f333(f106(x75081),x75083))),f333(f333(f80(x75081),x75084),f333(f106(x75081),x75083))),f333(f333(f80(x75081),f333(f333(f22(x75081),x75082),x75084)),f333(f106(x75081),x75083))) % 183.90/184.44 [7509]~P135(x75091)+~P91(x75091)+E(f333(f333(f79(x75091),f333(f333(f80(x75091),x75092),f333(f106(x75091),x75093))),f333(f333(f80(x75091),x75094),f333(f106(x75091),x75093))),f333(f333(f80(x75091),f333(f333(f79(x75091),x75092),x75094)),f333(f106(x75091),x75093))) % 183.90/184.44 [7545]~P66(x75451)+E(f333(f333(f79(x75451),f333(x75452,x75453)),f333(f333(f6(a875,x75451),x75452),f304(a875,f333(a115,x75453),x75454))),f333(f333(f6(a875,x75451),x75452),f304(a875,x75453,x75454)))+~P1(f333(f333(f247(a875),x75453),x75454)) % 183.90/184.44 [7556]~P25(x75562,x75561,x75563,f333(f174(x75562),x75564))+~P1(f333(f138(x75562),x75564))+P1(f333(f138(x75561),f333(f333(f155(x75562,x75561),x75563),x75564))) % 183.90/184.44 [7605]~P1(f333(f333(f248(a875),x76052),x76054))+~P1(f333(f333(f248(a875),x76051),x76053))+P1(f333(f333(f248(a875),f333(f333(f79(a875),x76051),x76052)),f333(f333(f79(a875),x76053),x76054))) % 183.90/184.44 [7606]~P1(f333(f333(f248(a1),x76061),x76063))+~P1(f333(f333(f247(a1),x76062),x76064))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x76061),x76062)),f333(f333(f79(a1),x76063),x76064))) % 183.90/184.44 [7607]~P1(f333(f333(f247(a875),x76072),x76074))+~P1(f333(f333(f247(a875),x76071),x76073))+P1(f333(f333(f247(a875),f333(f333(f79(a875),x76071),x76072)),f333(f333(f79(a875),x76073),x76074))) % 183.90/184.44 [7608]~P1(f333(f333(f247(a875),x76082),x76084))+~P1(f333(f333(f247(a875),x76081),x76083))+P1(f333(f333(f247(a875),f333(f333(f80(a875),x76081),x76082)),f333(f333(f80(a875),x76083),x76084))) % 183.90/184.44 [7656]P1(f333(f333(f335(x76561),x76562),x76563))+~P1(f333(f333(f335(x76561),x76562),f40(f882(x76561,a870),x76564)))+~P1(f333(f333(f335(f882(x76561,a870)),x76563),x76564)) % 183.90/184.44 [7672]~P1(f333(x76721,f679(x76721,x76723,x76722)))+P1(f333(x76721,f333(f333(f166(x76722),x76723),x76724)))+~P1(f333(f333(f248(a875),x76724),f333(f197(f876(x76722)),x76723))) % 183.90/184.44 [7678]P1(f333(x76781,x76782))+~P1(f333(f333(f335(x76784),x76782),f333(f174(x76784),x76783)))+P1(f333(f333(f248(a875),f681(x76781,x76783,x76784)),f333(f197(f876(x76784)),x76783))) % 183.90/184.44 [7698]~P1(f333(f333(f202(x76982),x76983),x76984))+~P1(f333(f333(f202(f31(x76981,x76982)),x76984),x76983))+P1(f333(f333(f202(f31(x76981,x76982)),x76983),x76983)) % 183.90/184.44 [7727]~P107(x77271)+~P1(f333(f333(f247(f882(x77272,x77271)),x77274),x77273))+~P1(f333(f333(f248(f882(x77272,x77271)),x77273),x77274)) % 183.90/184.44 [7775]~P1(f333(x77754,x77752))+~P1(f333(f333(f335(x77751),x77752),x77753))+P1(f333(f333(f335(x77751),x77752),f333(f333(f104(f882(x77751,a870)),x77753),f333(f253(x77751),x77754)))) % 183.90/184.44 [7920]~P1(f333(f333(f335(x79201),x79203),x79204))+~P1(f333(f333(f248(f882(x79201,a870)),x79202),x79204))+P1(f333(f333(f248(f882(x79201,a870)),x79202),f333(f333(f311(x79201),x79203),x79204))) % 183.90/184.44 [7922]E(f333(f333(f104(f882(x79221,a870)),x79222),x79223),f196(f882(x79221,a870)))+~E(f333(f333(f104(f882(x79221,a870)),f39(f882(x79221,a870),x79224)),x79223),f196(f882(x79221,a870)))+~P1(f333(f333(f335(f882(x79221,a870)),x79222),x79224)) % 183.90/184.44 [7999]P1(f333(f333(f335(x79991),x79992),x79993))+~P1(f333(f333(f247(f882(x79991,a870)),x79993),f333(f333(f311(x79991),x79992),x79994)))+P1(f333(f333(f247(f882(x79991,a870)),x79993),x79994)) % 183.90/184.44 [8021]P1(f333(f333(f335(x80212),f679(x80211,x80213,x80212)),f333(f174(x80212),x80213)))+P1(f333(x80211,f333(f333(f166(x80212),x80213),x80214)))+~P1(f333(f333(f248(a875),x80214),f333(f197(f876(x80212)),x80213))) % 183.90/184.44 [8029]~P1(f333(f333(f248(f882(x80291,a870)),x80292),x80294))+P1(f333(f333(f248(f882(x80291,a870)),x80292),x80293))+~P1(f333(f333(f248(f882(x80291,a870)),x80294),x80293)) % 183.90/184.44 [8030]~P1(f333(f333(f247(f882(x80301,a870)),x80302),x80304))+P1(f333(f333(f248(f882(x80301,a870)),x80302),x80303))+~P1(f333(f333(f248(f882(x80301,a870)),x80304),x80303)) % 183.90/184.44 [8031]~P1(f333(f333(f247(f882(x80311,a870)),x80314),x80313))+~P1(f333(f333(f248(f882(x80311,a870)),x80312),x80314))+P1(f333(f333(f248(f882(x80311,a870)),x80312),x80313)) % 183.90/184.44 [8032]~P1(f333(f333(f247(f882(x80321,a870)),x80322),x80324))+P1(f333(f333(f247(f882(x80321,a870)),x80322),x80323))+~P1(f333(f333(f247(f882(x80321,a870)),x80324),x80323)) % 183.90/184.44 [8072]~P1(f333(f333(f335(x80721),x80724),x80723))+~P1(f333(f333(f248(f882(x80721,a870)),x80722),f333(f333(f311(x80721),x80724),x80723)))+P1(f333(f333(f248(f882(x80721,a870)),x80722),x80723)) % 183.90/184.44 [8084]~P80(x80841)+P1(f333(f333(f248(x80841),x80842),x80843))+~P1(f333(f333(f248(x80841),f333(f333(f79(x80841),x80844),x80842)),f333(f333(f79(x80841),x80844),x80843))) % 183.90/184.44 [8086]~P80(x80861)+P1(f333(f333(f248(x80861),x80862),x80863))+~P1(f333(f333(f248(x80861),f333(f333(f79(x80861),x80862),x80864)),f333(f333(f79(x80861),x80863),x80864))) % 183.90/184.44 [8088]~P80(x80881)+P1(f333(f333(f247(x80881),x80882),x80883))+~P1(f333(f333(f247(x80881),f333(f333(f79(x80881),x80884),x80882)),f333(f333(f79(x80881),x80884),x80883))) % 183.90/184.44 [8090]~P80(x80901)+P1(f333(f333(f247(x80901),x80902),x80903))+~P1(f333(f333(f247(x80901),f333(f333(f79(x80901),x80902),x80904)),f333(f333(f79(x80901),x80903),x80904))) % 183.90/184.44 [8139]P1(f333(x81391,x81392))+~E(f333(f333(f139(x81393),f333(f197(f876(x81393)),f179(x81393,x81391,x81394))),x81394),f116(x81393))+~P1(f333(f333(f335(x81393),x81392),f333(f174(x81393),x81394))) % 183.90/184.44 [8265]P1(f333(x82651,x82652))+~P1(f333(f333(f335(x82653),x82652),f333(f174(x82653),x82654)))+P1(f333(f333(f248(a875),f333(f197(f876(x82653)),f333(f137(x82653,x82651),x82654))),f333(f197(f876(x82653)),x82654))) % 183.90/184.44 [8392]E(x83921,x83922)+P1(f333(f333(f202(x83923),x83921),f866(x83922,x83921,x83923,x83924)))+~P1(f333(f333(f202(f31(x83924,x83923)),x83921),x83922)) % 183.90/184.44 [8423]~P1(f333(x84234,x84232))+P1(f333(f333(f202(x84231),x84232),f866(x84233,x84232,x84231,x84234)))+~P1(f333(f333(f202(f31(x84234,x84231)),x84232),x84233)) % 183.90/184.44 [8739]~P1(f333(x87391,f780(x87391,x87393,x87392,x87394)))+P1(f333(x87391,f333(f333(f166(x87392),x87393),x87394)))+~P1(f333(f333(f248(a875),x87394),f333(f197(f876(x87392)),x87393))) % 183.90/184.44 [8762]~P25(x87624,x87623,x87621,f256(f882(x87624,a870)))+E(f333(x87621,f828(x87622,x87621,x87623,x87624)),x87622)+~P1(f333(f333(f335(x87623),x87622),f333(f312(x87624,x87623,x87621),f256(f882(x87624,a870))))) % 183.90/184.44 [8828]E(f179(x88281,x88282,x88283),f333(f333(f177(x88281),x88284),x88283))+P1(f333(f333(f248(a875),f757(x88282,x88283,x88281,x88284)),x88284))+P1(f333(f333(f248(a875),x88284),f333(f197(f876(x88281)),x88283))) % 183.90/184.44 [8831]E(f179(x88311,x88312,x88313),f333(f333(f177(x88311),x88314),x88313))+P1(f333(f333(f248(a875),f757(x88312,x88313,x88311,x88314)),x88314))+P1(f333(x88312,f333(f333(f166(x88311),x88313),x88314))) % 183.90/184.44 [8860]P1(f333(x88601,x88602))+~P1(f333(f333(f335(x88604),x88602),f333(f174(x88604),x88603)))+P1(f333(f333(f248(a875),f732(x88602,x88601,x88603,x88604)),f333(f197(f876(x88604)),x88603))) % 183.90/184.44 [8863]E(f179(x88631,x88632,x88633),f333(f333(f177(x88631),x88634),x88633))+P1(f333(f333(f248(a875),x88634),f333(f197(f876(x88631)),x88633)))+P1(f333(f333(f248(a875),f757(x88632,x88633,x88631,x88634)),f333(f197(f876(x88631)),x88633))) % 183.90/184.44 [8870]E(f179(x88701,x88702,x88703),f333(f333(f177(x88701),x88704),x88703))+P1(f333(x88702,f333(f333(f166(x88701),x88703),x88704)))+P1(f333(f333(f248(a875),f757(x88702,x88703,x88701,x88704)),f333(f197(f876(x88701)),x88703))) % 183.90/184.44 [8897]~P120(x88974)+P1(f333(f333(f335(x88971),f662(x88972,x88973,x88971,x88974)),x88973))+P1(f333(f333(f248(x88974),f2(x88974)),f333(f333(f9(x88971,x88974),x88972),x88973))) % 183.90/184.44 [8898]~P120(x88984)+P1(f333(f333(f335(x88981),f666(x88982,x88983,x88981,x88984)),x88983))+P1(f333(f333(f247(x88984),f2(x88984)),f333(f333(f9(x88981,x88984),x88982),x88983))) % 183.90/184.44 [8932]~P1(f333(f61(x89321),x89324))+P1(f333(f333(f335(x89321),f577(x89322,x89323,x89324,x89321)),x89324))+P1(f333(f61(f881(x89321,x89323)),f333(f333(f270(x89321,x89323),x89324),x89322))) % 183.90/184.44 [8966]P1(f333(f333(f335(x89662),f780(x89661,x89663,x89662,x89664)),f333(f174(x89662),x89663)))+P1(f333(x89661,f333(f333(f166(x89662),x89663),x89664)))+~P1(f333(f333(f248(a875),x89664),f333(f197(f876(x89662)),x89663))) % 183.90/184.44 [8981]E(x89811,x89812)+P1(f333(f333(f202(f31(x89813,x89814)),f866(x89811,x89812,x89814,x89813)),x89811))+~P1(f333(f333(f202(f31(x89813,x89814)),x89812),x89811)) % 183.90/184.44 [9001]~P1(f333(x90011,x90014))+P1(f333(f333(f202(f31(x90011,x90012)),f866(x90013,x90014,x90012,x90011)),x90013))+~P1(f333(f333(f202(f31(x90011,x90012)),x90014),x90013)) % 183.90/184.44 [9096]P1(f333(f333(f247(a875),x90964),f333(f197(f876(x90962)),f179(x90962,x90963,x90961))))+P1(f333(f333(f248(a875),f759(x90961,x90962,x90963,x90964)),x90964))+~P1(f333(f333(f247(a875),x90964),f333(f197(f876(x90962)),x90961))) % 183.90/184.44 [9200]~E(f333(f333(f180(x92001,x92002),x92003),f769(x92004,x92003,x92002,x92001)),f333(f333(f180(x92001,x92002),x92004),f769(x92004,x92003,x92002,x92001)))+E(f333(f180(x92001,x92002),x92003),f333(f180(x92001,x92002),x92004))+~E(f333(f174(x92001),f333(f333(f155(f881(x92001,x92002),x92001),f267(x92001,x92002)),x92003)),f333(f174(x92001),f333(f333(f155(f881(x92001,x92002),x92001),f267(x92001,x92002)),x92004))) % 183.90/184.44 [9246]E(f179(x92461,x92462,x92463),f333(f333(f177(x92461),x92464),x92463))+~P1(f333(x92462,f333(f333(f166(x92461),x92463),f757(x92462,x92463,x92461,x92464))))+P1(f333(f333(f248(a875),x92464),f333(f197(f876(x92461)),x92463))) % 183.90/184.44 [9250]E(f179(x92501,x92502,x92503),f333(f333(f177(x92501),x92504),x92503))+~P1(f333(x92502,f333(f333(f166(x92501),x92503),f757(x92502,x92503,x92501,x92504))))+P1(f333(x92502,f333(f333(f166(x92501),x92503),x92504))) % 183.90/184.44 [9257]~P1(f333(f61(x92571),x92573))+~P1(f333(f61(x92572),f333(x92574,f577(x92574,x92572,x92573,x92571))))+P1(f333(f61(f881(x92571,x92572)),f333(f333(f270(x92571,x92572),x92573),x92574))) % 183.90/184.44 [9265]~P120(x92651)+~P1(f333(f333(f248(x92651),f2(x92651)),f333(x92653,f662(x92653,x92654,x92652,x92651))))+P1(f333(f333(f248(x92651),f2(x92651)),f333(f333(f9(x92652,x92651),x92653),x92654))) % 183.90/184.44 [9266]~P120(x92661)+~P1(f333(f333(f247(x92661),f2(x92661)),f333(x92663,f666(x92663,x92664,x92662,x92661))))+P1(f333(f333(f247(x92661),f2(x92661)),f333(f333(f9(x92662,x92661),x92663),x92664))) % 183.90/184.44 [9272]~E(f333(f197(f876(x92724)),x92722),f333(f197(f876(x92724)),x92723))+P1(f333(f333(f335(f881(f876(x92724),f876(x92724))),f333(f333(f268(f876(x92724),f876(x92724)),x92723),x92722)),f159(x92724,x92721)))+P1(f333(f333(f248(a875),f671(x92721,x92722,x92723,x92724)),f333(f197(f876(x92724)),x92723))) % 183.90/184.44 [9326]~P1(f333(x93263,f333(f333(f166(x93262),x93264),f759(x93264,x93262,x93263,x93261))))+P1(f333(f333(f247(a875),x93261),f333(f197(f876(x93262)),f179(x93262,x93263,x93264))))+~P1(f333(f333(f247(a875),x93261),f333(f197(f876(x93262)),x93264))) % 183.90/184.44 [9403]E(f333(f333(f177(x94031),f680(x94032,x94033,x94034,x94031)),x94033),f333(f333(f177(x94031),f680(x94032,x94033,x94034,x94031)),x94034))+~P1(f333(f333(f335(f881(f876(x94031),f876(x94031))),f333(f333(f268(f876(x94031),f876(x94031)),x94034),x94033)),f148(x94031,x94032)))+P1(f333(f333(f248(a875),f333(f197(f876(x94031)),x94034)),f333(f197(f876(x94031)),x94033))) % 183.90/184.44 [9457]~P1(f333(f333(f248(a875),f2(a875)),x94573))+~P1(f333(f333(f248(a875),x94574),x94571))+P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),x94571),f44(a875,x94572,x94573))),x94574)),f333(f333(f80(a875),x94571),x94573))) % 183.90/184.44 [9648]~P107(x96482)+~P1(f333(f333(f247(x96482),f333(x96483,f861(x96484,x96483,x96481,x96482))),f333(x96484,f861(x96484,x96483,x96481,x96482))))+P1(f333(f333(f247(f882(x96481,x96482)),x96483),x96484)) % 183.90/184.44 [9751]~P65(x97511)+E(f333(f333(f6(a875,x97511),f333(f333(f18(a875,x97511,x97511),f333(f333(f8(x97511,f882(x97511,x97511),a875),f22(x97511)),x97512)),f333(f333(f8(a875,x97511,a875),x97512),f333(f333(f7(a875,a875,a875),f79(a875)),f77(a875))))),f304(a875,x97513,x97514)),f333(f333(f22(x97511),f333(x97512,x97513)),f333(x97512,f333(f333(f79(a875),x97514),f77(a875)))))+~P1(f333(f333(f247(a875),x97513),x97514)) % 183.90/184.44 [6797]E(f333(f333(f135(x67971),x67972),x67973),x67974)+~E(x67973,f333(f333(f139(x67971),f333(f197(f876(x67971)),x67972)),x67974))+~E(f333(f333(f177(x67971),f333(f197(f876(x67971)),x67972)),x67974),x67972) % 183.90/184.44 [6853]~P59(x68532)+E(x68531,f2(x68532))+E(f333(f333(f291(x68532),f333(f333(f258(x68532),x68533),x68534)),f333(f333(f258(x68532),x68531),x68534)),f333(f333(f258(x68532),f333(f333(f291(x68532),x68533),x68531)),x68534)) % 183.90/184.44 [6989]~E(f333(f197(f876(x69891)),x69893),f333(f197(f876(x69892)),x69894))+~P1(f333(f138(x69891),x69893))+E(f186(x69891,x69892,f333(f180(x69891,x69892),f333(f333(f184(x69891,x69892),x69893),x69894))),f333(f174(x69891),x69893)) % 183.90/184.44 [7008]~P99(x70081)+~P1(f333(f333(f248(x70081),x70083),x70084))+P1(f333(f333(f248(x70081),f333(f333(f104(x70081),x70082),x70083)),x70084)) % 183.90/184.44 [7009]~P99(x70091)+~P1(f333(f333(f248(x70091),x70092),x70094))+P1(f333(f333(f248(x70091),f333(f333(f104(x70091),x70092),x70093)),x70094)) % 183.90/184.44 [7011]~P106(x70111)+~P1(f333(f333(f248(x70111),x70113),x70114))+P1(f333(f333(f248(x70111),f333(f333(f245(x70111),x70112),x70113)),x70114)) % 183.90/184.44 [7013]~P106(x70131)+~P1(f333(f333(f248(x70131),x70132),x70134))+P1(f333(f333(f248(x70131),f333(f333(f245(x70131),x70132),x70133)),x70134)) % 183.90/184.44 [7014]~P99(x70141)+~P1(f333(f333(f247(x70141),x70143),x70144))+P1(f333(f333(f247(x70141),f333(f333(f104(x70141),x70142),x70143)),x70144)) % 183.90/184.44 [7015]~P99(x70151)+~P1(f333(f333(f247(x70151),x70152),x70154))+P1(f333(f333(f247(x70151),f333(f333(f104(x70151),x70152),x70153)),x70154)) % 183.90/184.44 [7017]~P106(x70171)+~P1(f333(f333(f247(x70171),x70173),x70174))+P1(f333(f333(f247(x70171),f333(f333(f245(x70171),x70172),x70173)),x70174)) % 183.90/184.44 [7019]~P106(x70191)+~P1(f333(f333(f247(x70191),x70192),x70194))+P1(f333(f333(f247(x70191),f333(f333(f245(x70191),x70192),x70193)),x70194)) % 183.90/184.44 [7039]~P1(f333(x70393,x70394))+~P1(f333(x70392,x70394))+P1(f333(f333(f333(f104(f882(x70391,a870)),x70392),x70393),x70394)) % 183.90/184.44 [7163]P24(x71631,x71632,x71633)+~P24(x71631,x71634,x71633)+~P1(f333(f333(f247(f882(f874(x71631),a870)),x71634),x71632)) % 183.90/184.44 [7164]P24(x71641,x71642,x71643)+~P24(x71641,x71642,x71644)+~P1(f333(f333(f247(f882(f874(x71641),a870)),x71643),x71644)) % 183.90/184.44 [7535]~P66(x75351)+E(f333(f333(f79(x75351),f333(x75352,x75353)),f333(f333(f6(a875,x75351),x75352),f333(f303(a875,f333(a115,x75353)),x75354))),f333(f333(f6(a875,x75351),x75352),f333(f303(a875,x75353),x75354)))+~P1(f333(f333(f248(a875),x75353),x75354)) % 183.90/184.44 [7563]~P106(x75631)+P1(f333(f333(f248(x75631),x75632),x75633))+~P1(f333(f333(f248(x75631),f333(f333(f246(x75631),x75634),x75632)),x75633)) % 183.90/184.44 [7564]~P106(x75641)+P1(f333(f333(f248(x75641),x75642),x75643))+~P1(f333(f333(f248(x75641),f333(f333(f246(x75641),x75642),x75644)),x75643)) % 183.90/184.44 [7566]~P98(x75661)+P1(f333(f333(f247(x75661),x75662),x75663))+~P1(f333(f333(f247(x75661),f333(f333(f113(x75661),x75664),x75662)),x75663)) % 183.90/184.44 [7568]~P98(x75681)+P1(f333(f333(f247(x75681),x75682),x75683))+~P1(f333(f333(f247(x75681),f333(f333(f113(x75681),x75682),x75684)),x75683)) % 183.90/184.44 [7570]~P106(x75701)+P1(f333(f333(f247(x75701),x75702),x75703))+~P1(f333(f333(f247(x75701),f333(f333(f246(x75701),x75704),x75702)),x75703)) % 183.90/184.44 [7572]~P106(x75721)+P1(f333(f333(f247(x75721),x75722),x75723))+~P1(f333(f333(f247(x75721),f333(f333(f246(x75721),x75722),x75724)),x75723)) % 183.90/184.44 [7648]~P1(f333(f333(f335(x76481),x76482),x76484))+P1(f333(f333(f335(x76481),x76482),x76483))+P1(f333(f333(f335(x76481),x76482),f333(f333(f22(f882(x76481,a870)),x76484),x76483))) % 183.90/184.44 [7734]P1(f333(x77341,x77342))+P1(f333(x77343,x77342))+~P1(f333(f333(f333(f113(f882(x77344,a870)),x77343),x77341),x77342)) % 183.90/184.44 [7745]~P1(f333(f333(f335(x77451),x77452),x77454))+~P1(f333(f333(f335(x77451),x77452),x77453))+P1(f333(f333(f335(x77451),x77452),f333(f333(f104(f882(x77451,a870)),x77453),x77454))) % 183.90/184.44 [7799]~P98(x77991)+~P1(f333(f61(x77991),x77994))+E(f333(f333(f64(x77991,x77991,f113(x77991)),x77992),f333(f333(f311(x77991),x77993),x77994)),f333(f333(f113(x77991),x77993),f333(f333(f64(x77991,x77991,f113(x77991)),x77992),x77994))) % 183.90/184.44 [7800]~P99(x78001)+~P1(f333(f61(x78001),x78004))+E(f333(f333(f64(x78001,x78001,f104(x78001)),x78002),f333(f333(f311(x78001),x78003),x78004)),f333(f333(f104(x78001),x78003),f333(f333(f64(x78001,x78001,f104(x78001)),x78002),x78004))) % 183.90/184.44 [7801]~P106(x78011)+~P1(f333(f61(x78011),x78014))+E(f333(f333(f64(x78011,x78011,f245(x78011)),x78012),f333(f333(f311(x78011),x78013),x78014)),f333(f333(f245(x78011),x78013),f333(f333(f64(x78011,x78011,f245(x78011)),x78012),x78014))) % 183.90/184.44 [7802]~P106(x78021)+~P1(f333(f61(x78021),x78024))+E(f333(f333(f64(x78021,x78021,f246(x78021)),x78022),f333(f333(f311(x78021),x78023),x78024)),f333(f333(f246(x78021),x78023),f333(f333(f64(x78021,x78021,f246(x78021)),x78022),x78024))) % 183.90/184.44 [7803]~P103(x78031)+~P91(x78031)+E(f333(f333(f22(x78031),f333(f333(f80(x78031),f333(f106(x78031),x78032)),x78033)),f333(f333(f80(x78031),f333(f106(x78031),x78032)),x78034)),f333(f333(f80(x78031),f333(f106(x78031),x78032)),f333(f333(f22(x78031),x78033),x78034))) % 183.90/184.44 [7804]~P135(x78041)+~P91(x78041)+E(f333(f333(f79(x78041),f333(f333(f80(x78041),f333(f106(x78041),x78042)),x78043)),f333(f333(f80(x78041),f333(f106(x78041),x78042)),x78044)),f333(f333(f80(x78041),f333(f106(x78041),x78042)),f333(f333(f79(x78041),x78043),x78044))) % 183.90/184.44 [7918]E(x79181,x79182)+P1(f333(f333(f335(x79183),x79181),f333(f174(x79183),x79184)))+~P1(f333(f333(f335(x79183),x79181),f333(f174(x79183),f333(f333(f152(x79183),x79182),x79184)))) % 183.90/184.44 [7943]~P57(x79431)+~E(f333(f197(f876(x79432)),x79433),f333(f197(f876(x79431)),f55(x79431)))+E(f333(f333(f180(x79431,x79432),f333(f333(f184(x79431,x79432),f55(x79431)),x79433)),x79434),f333(f240(x79432),f731(x79434,x79433,x79432,x79431))) % 183.90/184.44 [8097]P49(x80971,x80972,x80973)+~P49(x80971,x80972,x80974)+~P1(f333(f333(f247(f882(f881(x80971,x80972),a870)),x80973),x80974)) % 183.90/184.44 [8142]P1(f333(f333(f335(x81421),x81422),x81423))+P1(f333(f333(f335(x81421),x81422),x81424))+~P1(f333(f333(f335(x81421),x81422),f333(f333(f113(f882(x81421,a870)),x81424),x81423))) % 183.90/184.44 [8153]~P39(x81531,x81534,x81533)+~P1(f333(f333(f335(x81531),x81532),x81534))+P1(f333(f333(f335(f881(x81531,x81531)),f333(f333(f268(x81531,x81531),x81532),x81532)),x81533)) % 183.90/184.44 [8168]~P1(f333(f61(x81682),x81684))+~P1(f333(f61(x81681),x81683))+P1(f333(f61(f881(x81681,x81682)),f333(f333(f270(x81681,x81682),x81683),f333(f16(f882(x81682,a870),x81681),x81684)))) % 183.90/184.44 [8169]~P1(f333(f333(f335(x81691),x81692),x81694))+~P1(f333(f333(f247(f882(x81691,a870)),x81693),x81694))+P1(f333(f333(f247(f882(x81691,a870)),f333(f333(f311(x81691),x81692),x81693)),x81694)) % 183.90/184.44 [8177]~P73(x81772)+~P141(x81772)+E(f333(f333(f9(x81771,x81772),f333(f333(f8(a875,x81772,x81771),f103(x81772)),x81773)),x81774),f333(f103(x81772),f333(f333(f9(x81771,a875),x81773),x81774))) % 183.90/184.44 [8178]~P73(x81782)+~P138(x81782)+E(f333(f333(f9(x81781,x81782),f333(f333(f8(a1,x81782,x81781),f105(x81782)),x81783)),x81784),f333(f105(x81782),f333(f333(f9(x81781,a1),x81783),x81784))) % 183.90/184.44 [8204]E(f333(f333(f22(f882(x82041,a870)),x82042),f333(f333(f22(f882(x82041,a870)),x82043),x82044)),x82044)+~P1(f333(f333(f247(f882(x82041,a870)),x82042),x82043))+~P1(f333(f333(f247(f882(x82041,a870)),x82044),x82042)) % 183.90/184.44 [8299]~P1(f333(f61(x82991),x82994))+E(f333(f333(f22(a875),f333(f333(f6(x82991,a875),x82992),x82993)),f333(f333(f6(x82991,a875),x82992),x82994)),f333(f333(f6(x82991,a875),x82992),f333(f333(f22(f882(x82991,a870)),x82993),x82994)))+~P1(f333(f333(f247(f882(x82991,a870)),x82994),x82993)) % 183.90/184.44 [8457]~P7(x84571,x84574,x84573)+~P1(f333(f333(f335(x84571),x84572),x84574))+P1(f333(f333(f335(x84571),x84572),f333(f287(x84571,x84571,x84573),f333(f333(f311(x84571),x84572),f196(f882(x84571,a870)))))) % 183.90/184.44 [8519]~P1(f333(f333(f247(f882(x85191,a870)),x85192),x85193))+~P1(f333(f333(f247(f882(x85191,a870)),x85192),x85194))+P1(f333(f333(f247(f882(x85191,a870)),x85192),f333(f333(f104(f882(x85191,a870)),x85193),x85194))) % 183.90/184.44 [8615]E(x86151,f196(f882(x86152,a870)))+P1(f333(f61(x86153),x86154))+~P1(f333(f61(f881(x86153,x86152)),f333(f333(f270(x86153,x86152),x86154),f333(f16(f882(x86152,a870),x86153),x86151)))) % 183.90/184.44 [8616]E(x86161,f196(f882(x86162,a870)))+P1(f333(f61(x86163),x86164))+~P1(f333(f61(f881(x86162,x86163)),f333(f333(f270(x86162,x86163),x86161),f333(f16(f882(x86163,a870),x86162),x86164)))) % 183.90/184.44 [8682]P1(f333(f333(f335(x86821),x86822),f322(x86821,x86823)))+~P1(f333(f333(f335(x86821),x86824),f322(x86821,x86823)))+~P1(f333(f333(f335(f881(x86821,x86821)),f333(f333(f268(x86821,x86821),x86822),x86824)),x86823)) % 183.90/184.44 [8734]~P37(x87341,x87344)+P1(f333(f333(f335(f881(x87341,x87341)),f333(f333(f268(x87341,x87341),x87343),x87342)),f309(x87341,x87344)))+P37(x87341,f333(f333(f311(f881(x87341,x87341)),f333(f333(f268(x87341,x87341),x87342),x87343)),x87344)) % 183.90/184.44 [8735]~P52(x87351,x87354)+P1(f333(f333(f335(f881(x87351,x87351)),f333(f333(f268(x87351,x87351),x87353),x87352)),f309(x87351,x87354)))+P52(x87351,f333(f333(f311(f881(x87351,x87351)),f333(f333(f268(x87351,x87351),x87352),x87353)),x87354)) % 183.90/184.44 [8813]~E(x88132,x88133)+~P1(f333(f333(f335(x88131),x88132),f333(f174(x88131),x88134)))+P1(f333(f333(f335(f881(x88131,x88131)),f333(f333(f268(x88131,x88131),x88132),x88133)),f333(f174(f881(x88131,x88131)),f333(f333(f184(x88131,x88131),x88134),x88134)))) % 183.90/184.44 [8895]~E(x88953,x88954)+P1(f333(f333(f272(x88951,x88951,a870),a330),x88952))+~P1(f333(f333(f335(f881(x88951,x88951)),x88952),f333(f174(f881(x88951,x88951)),f333(f333(f184(x88951,x88951),x88953),x88954)))) % 183.90/184.44 [8923]~P1(f333(x89234,x89232))+P1(f333(f333(f333(f333(a204,x89231),x89232),x89233),f478(x89233,x89232,x89231,x89234)))+~P1(f333(f333(f333(f333(a204,f31(x89234,x89231)),x89232),x89233),x89232)) % 183.90/184.44 [8950]P1(f333(f333(f335(f881(f876(x89501),f876(x89501))),f333(f333(f268(f876(x89501),f876(x89501)),x89502),x89503)),f148(x89501,x89504)))+~E(f333(f333(f177(x89501),f333(f197(f876(x89501)),x89502)),x89503),x89502)+~P1(f333(f333(f248(a875),f333(f197(f876(x89501)),x89502)),f333(f197(f876(x89501)),x89503))) % 183.90/184.44 [9048]~P1(f333(f61(x90481),x90484))+P1(f333(f333(f335(x90481),f803(x90482,x90483,x90484,x90481)),x90484))+P1(f333(f61(x90483),f333(f333(f41(x90481,f882(x90483,a870)),x90484),x90482))) % 183.90/184.44 [9049]~P1(f333(f61(x90491),x90494))+P1(f333(f333(f335(x90491),f842(x90492,x90493,x90494,x90491)),x90494))+P1(f333(f61(x90493),f333(f333(f41(x90491,f882(x90493,a870)),x90494),x90492))) % 183.90/184.44 [9130]P1(f333(f333(f335(f881(x91301,x91301)),x91302),f333(f333(f290(x91301,x91301,x91301),x91303),f309(x91301,x91303))))+~P1(f333(f333(f248(a875),f2(a875)),x91304))+~P1(f333(f333(f335(f881(x91301,x91301)),x91302),f333(f333(f191(f881(x91301,x91301),a870),x91304),x91303))) % 183.90/184.44 [9138]~P37(x91381,x91382)+~P1(f333(f333(f335(f881(x91381,x91381)),f333(f333(f268(x91381,x91381),x91384),x91383)),x91382))+~P1(f333(f333(f335(f881(x91381,x91381)),f333(f333(f268(x91381,x91381),x91383),x91384)),x91382)) % 183.90/184.44 [9264]~P1(f333(f61(x92641),x92644))+E(f333(f333(f6(x92641,a875),f333(f333(f8(f882(x92642,a870),a875,x92641),f37(x92642)),x92643)),x92644),f333(f37(f881(x92641,x92642)),f333(f333(f270(x92641,x92642),x92644),x92643)))+P1(f333(f333(f335(x92641),f578(x92643,x92642,x92644,x92641)),x92644)) % 183.90/184.44 [9268]~P1(f333(f138(x92681),x92682))+P1(f333(f138(x92681),f333(f333(f160(x92681,x92682),x92683),x92684)))+P1(f333(f333(f335(x92681),x92684),f333(f333(f22(f882(x92681,a870)),f333(f174(x92681),x92682)),f333(f333(f311(x92681),f333(f333(f166(x92681),x92682),x92683)),f196(f882(x92681,a870)))))) % 183.90/184.44 [9284]~P1(f333(f61(x92842),x92843))+~P1(f333(f61(x92841),f333(x92844,f803(x92844,x92841,x92843,x92842))))+P1(f333(f61(x92841),f333(f333(f41(x92842,f882(x92841,a870)),x92843),x92844))) % 183.90/184.44 [9285]~P1(f333(f61(x92852),x92853))+~P1(f333(f61(x92851),f333(x92854,f842(x92854,x92851,x92853,x92852))))+P1(f333(f61(x92851),f333(f333(f41(x92852,f882(x92851,a870)),x92853),x92854))) % 183.90/184.44 [9364]~P1(f333(f333(f335(f881(x93641,x93641)),x93642),f333(f333(f290(x93641,x93641,x93641),x93644),f309(x93641,x93644))))+P1(f333(f333(f335(f881(x93641,x93641)),x93642),f333(f333(f290(x93641,x93641,x93641),x93643),f309(x93641,x93643))))+~P1(f333(f333(f247(f882(f881(x93641,x93641),a870)),x93644),x93643)) % 183.90/184.44 [9371]E(f333(f333(f177(x93711),f680(x93714,x93713,x93712,x93711)),x93713),f333(f333(f177(x93711),f680(x93714,x93713,x93712,x93711)),x93712))+~P1(f333(f333(f335(f881(f876(x93711),f876(x93711))),f333(f333(f268(f876(x93711),f876(x93711)),x93712),x93713)),f148(x93711,x93714)))+E(f333(f333(f177(x93711),f333(f197(f876(x93711)),x93712)),x93713),x93712) % 183.90/184.44 [9388]~P1(f333(f61(x93881),x93884))+E(f333(f333(f6(x93881,a875),f333(f333(f8(f882(x93882,a870),a875,x93881),f37(x93882)),x93883)),x93884),f333(f37(f881(x93881,x93882)),f333(f333(f270(x93881,x93882),x93884),x93883)))+~P1(f333(f61(x93882),f333(x93883,f578(x93883,x93882,x93884,x93881)))) % 183.90/184.44 [9392]~E(f333(f197(f876(x93921)),x93923),f333(f197(f876(x93921)),x93922))+P1(f333(f333(f335(f881(f876(x93921),f876(x93921))),f333(f333(f268(f876(x93921),f876(x93921)),x93922),x93923)),f159(x93921,x93924)))+P1(f333(f333(f335(f881(x93921,x93921)),f684(x93924,x93923,x93922,x93921)),f333(f174(f881(x93921,x93921)),f333(f333(f184(x93921,x93921),x93922),x93923)))) % 183.90/184.44 [9469]~P1(f333(f333(f335(f881(f876(x94691),f876(x94691))),f333(f333(f268(f876(x94691),f876(x94691)),x94692),x94693)),f148(x94691,x94694)))+E(f333(f333(f177(x94691),f333(f197(f876(x94691)),x94692)),x94693),x94692)+P1(f333(f333(f248(a875),f680(x94694,x94693,x94692,x94691)),f333(f333(f245(a875),f333(f197(f876(x94691)),x94692)),f333(f197(f876(x94691)),x94693)))) % 183.90/184.44 [9470]E(f333(f180(x94701,x94702),x94703),f333(f180(x94701,x94702),x94704))+~E(f333(f174(x94701),f333(f333(f155(f881(x94701,x94702),x94701),f267(x94701,x94702)),x94703)),f333(f174(x94701),f333(f333(f155(f881(x94701,x94702),x94701),f267(x94701,x94702)),x94704)))+P1(f333(f333(f335(x94701),f769(x94703,x94704,x94702,x94701)),f333(f174(x94701),f333(f333(f155(f881(x94701,x94702),x94701),f267(x94701,x94702)),x94704)))) % 183.90/184.44 [9486]~P1(f333(x94861,x94864))+P1(f333(f333(f333(f333(a204,f31(x94861,x94862)),f478(x94863,x94864,x94862,x94861)),x94863),x94864))+~P1(f333(f333(f333(f333(a204,f31(x94861,x94862)),x94864),x94863),x94864)) % 183.90/184.44 [9491]~P1(f333(f333(f335(f881(f876(x94911),f876(x94911))),f333(f333(f268(f876(x94911),f876(x94911)),x94912),x94913)),f148(x94911,x94914)))+P1(f333(f333(f248(a875),f333(f197(f876(x94911)),x94912)),f333(f197(f876(x94911)),x94913)))+P1(f333(f333(f248(a875),f680(x94914,x94913,x94912,x94911)),f333(f333(f245(a875),f333(f197(f876(x94911)),x94912)),f333(f197(f876(x94911)),x94913)))) % 183.90/184.44 [9788]~P1(f333(f333(f333(x97881,f734(x97881,x97884,x97883,x97882)),f735(x97881,x97884,x97883,x97882)),f736(x97881,x97884,x97883,x97882)))+P1(f333(f333(f333(x97881,x97882),x97883),x97884))+~P1(f333(f321(f881(f882(a1,f879(f876(a329))),f881(a1,a1)),a319),f333(f333(f268(f882(a1,f879(f876(a329))),f881(a1,a1)),x97882),f333(f333(f268(a1,a1),x97883),x97884)))) % 183.90/184.44 [9867]P1(f333(f333(f333(x98671,x98672),x98673),x98674))+P1(f333(f321(f881(f882(a1,f879(f876(a329))),f881(a1,a1)),a319),f333(f333(f268(f882(a1,f879(f876(a329))),f881(a1,a1)),f734(x98671,x98674,x98673,x98672)),f333(f333(f268(a1,a1),f735(x98671,x98674,x98673,x98672)),f736(x98671,x98674,x98673,x98672)))))+~P1(f333(f321(f881(f882(a1,f879(f876(a329))),f881(a1,a1)),a319),f333(f333(f268(f882(a1,f879(f876(a329))),f881(a1,a1)),x98672),f333(f333(f268(a1,a1),x98673),x98674)))) % 183.90/184.44 [9906]~P1(f333(f333(f335(f881(f876(x99061),f876(x99061))),f333(f333(f268(f876(x99061),f876(x99061)),x99062),x99063)),f148(x99061,x99064)))+E(f333(f333(f177(x99061),f333(f197(f876(x99061)),x99062)),x99063),x99062)+P1(f333(f333(f335(f881(x99061,x99061)),f333(f333(f268(x99061,x99061),f333(f333(f166(x99061),x99062),f680(x99064,x99063,x99062,x99061))),f333(f333(f166(x99061),x99063),f680(x99064,x99063,x99062,x99061)))),x99064)) % 183.90/184.44 [9907]~P1(f333(f333(f335(f881(f876(x99071),f876(x99071))),f333(f333(f268(f876(x99071),f876(x99071)),x99072),x99073)),f148(x99071,x99074)))+P1(f333(f333(f248(a875),f333(f197(f876(x99071)),x99072)),f333(f197(f876(x99071)),x99073)))+P1(f333(f333(f335(f881(x99071,x99071)),f333(f333(f268(x99071,x99071),f333(f333(f166(x99071),x99072),f680(x99074,x99073,x99072,x99071))),f333(f333(f166(x99071),x99073),f680(x99074,x99073,x99072,x99071)))),x99074)) % 183.90/184.44 [9964]~E(f333(f197(f876(x99641)),x99642),f333(f197(f876(x99641)),x99643))+P1(f333(f333(f335(f881(f876(x99641),f876(x99641))),f333(f333(f268(f876(x99641),f876(x99641)),x99642),x99643)),f159(x99641,x99644)))+~P1(f333(f333(f335(f881(x99641,x99641)),f333(f333(f268(x99641,x99641),f333(f333(f166(x99641),x99642),f671(x99644,x99643,x99642,x99641))),f333(f333(f166(x99641),x99643),f671(x99644,x99643,x99642,x99641)))),x99644)) % 183.90/184.44 [10100]~P66(x101001)+~P1(f333(f61(x101002),x101004))+E(f333(f167(x101001),f333(f333(f155(x101002,x101001),x101003),f89(f876(x101002),f333(f333(f18(f876(x101002),a870,a870),f333(f333(f8(a870,f882(a870,a870),f876(x101002)),a331),f333(f333(f7(f876(x101002),f882(x101002,a870),a870),f333(f333(f8(f882(x101002,a870),f882(f882(x101002,a870),a870),f876(x101002)),a330),f174(x101002))),x101004))),f138(x101002))))),f238(x101002,x101001,x101003,x101004)) % 183.90/184.44 [7375]~P58(x73752)+E(x73751,f2(x73752))+E(f333(f333(f291(x73752),f333(f333(f79(x73752),x73753),f333(f333(f80(x73752),x73754),x73751))),x73751),f333(f333(f79(x73752),x73754),f333(f333(f291(x73752),x73753),x73751))) % 183.90/184.44 [7376]~P55(x73762)+E(x73761,f2(x73762))+E(f333(f333(f38(x73762),f333(f333(f79(x73762),x73763),f333(f333(f80(x73762),x73764),x73761))),x73761),f333(f333(f79(x73762),x73764),f333(f333(f38(x73762),x73763),x73761))) % 183.90/184.44 [7377]~P55(x73772)+E(x73771,f2(x73772))+E(f333(f333(f38(x73772),f333(f333(f79(x73772),x73773),f333(f333(f80(x73772),x73771),x73774))),x73771),f333(f333(f79(x73772),x73774),f333(f333(f38(x73772),x73773),x73771))) % 183.90/184.44 [7611]~P59(x76112)+E(x76111,f2(x76112))+E(f333(f333(f291(x76112),f333(f333(f22(x76112),x76113),f333(f333(f80(x76112),x76111),x76114))),x76111),f333(f333(f22(x76112),f333(f333(f291(x76112),x76113),x76111)),x76114)) % 183.90/184.44 [7612]~P58(x76122)+E(x76121,f2(x76122))+E(f333(f333(f291(x76122),f333(f333(f79(x76122),x76123),f333(f333(f80(x76122),x76124),x76121))),x76121),f333(f333(f79(x76122),f333(f333(f291(x76122),x76123),x76121)),x76124)) % 183.90/184.44 [7613]~P59(x76132)+E(x76131,f2(x76132))+E(f333(f333(f291(x76132),f333(f333(f79(x76132),x76133),f333(f333(f80(x76132),x76131),x76134))),x76131),f333(f333(f79(x76132),f333(f333(f291(x76132),x76133),x76131)),x76134)) % 183.90/184.44 [8327]~P1(f333(f161(x83271,x83273),x83274))+~P1(f333(f161(x83271,x83272),x83274))+P1(f333(f161(x83271,f333(f333(f104(f882(x83271,a870)),x83272),x83273)),x83274)) % 183.90/184.44 [8696]~E(f333(f333(f290(x86961,x86961,x86961),x86962),x86964),f196(f882(f881(x86961,x86961),a870)))+~E(f333(f333(f290(x86961,x86961,x86961),x86962),x86963),f196(f882(f881(x86961,x86961),a870)))+E(f333(f333(f290(x86961,x86961,x86961),x86962),f333(f333(f113(f882(f881(x86961,x86961),a870)),x86963),x86964)),f196(f882(f881(x86961,x86961),a870))) % 183.90/184.44 [8814]~P1(f333(f333(f247(f882(x88141,a870)),x88143),x88144))+~P1(f333(f333(f247(f882(x88141,a870)),x88142),x88144))+P1(f333(f333(f247(f882(x88141,a870)),f333(f333(f113(f882(x88141,a870)),x88142),x88143)),x88144)) % 183.90/184.44 [9194]~P1(f333(f61(x91941),x91944))+~P1(f333(f61(x91941),x91943))+E(f333(f333(f22(a875),f333(f333(f79(a875),f333(f333(f6(x91941,a875),x91942),x91943)),f333(f333(f6(x91941,a875),x91942),x91944))),f333(f333(f6(x91941,a875),x91942),f333(f333(f104(f882(x91941,a870)),x91943),x91944))),f333(f333(f6(x91941,a875),x91942),f333(f333(f113(f882(x91941,a870)),x91943),x91944))) % 183.90/184.44 [9281]~P1(f333(f333(f335(x92811),x92813),x92812))+~P1(f333(f333(f247(f882(x92811,a870)),x92812),f333(f333(f311(x92811),x92813),x92814)))+P1(f333(f333(f247(f882(x92811,a870)),f333(f333(f22(f882(x92811,a870)),x92812),f333(f333(f311(x92811),x92813),f196(f882(x92811,a870))))),x92814)) % 183.90/184.44 [9441]~P1(f333(f333(f335(x94411),x94413),x94412))+P1(f333(f333(f247(f882(x94411,a870)),x94412),f333(f333(f311(x94411),x94413),x94414)))+~P1(f333(f333(f247(f882(x94411,a870)),f333(f333(f22(f882(x94411,a870)),x94412),f333(f333(f311(x94411),x94413),f196(f882(x94411,a870))))),x94414)) % 183.90/184.44 [9531]~P1(f333(f333(f248(a875),x95312),x95314))+~P1(f333(f333(f247(a875),x95311),x95313))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x95311),x95312)),f333(f333(f268(a875,a875),x95313),x95314))),a34)) % 183.90/184.44 [9532]~P1(f333(f333(f247(a875),x95322),x95324))+~P1(f333(f333(f247(a875),x95321),x95323))+P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),f333(f333(f268(a875,a875),x95321),x95322)),f333(f333(f268(a875,a875),x95323),x95324))),a69)) % 183.90/184.44 [9827]~P1(f333(f333(f335(f876(x98271)),x98274),f162(x98271,x98273)))+~P1(f333(f333(f335(f876(x98271)),x98274),f162(x98271,x98272)))+P1(f333(f161(x98271,f333(f333(f104(f882(x98271,a870)),f333(f333(f7(x98271,f882(x98271,a870),a870),f335(x98271)),x98272)),f333(f333(f7(x98271,f882(x98271,a870),a870),f335(x98271)),x98273))),x98274)) % 183.90/184.44 [9929]~P25(x99291,f882(f882(x99291,a870),a870),f333(f333(f7(x99291,f882(f881(x99291,x99291),a870),f882(f882(x99291,a870),a870)),f333(f333(f8(f882(x99291,a870),f882(f882(f881(x99291,x99291),a870),f882(f882(x99291,a870),a870)),x99291),f60(x99291)),f333(f333(f7(x99291,f882(x99291,a870),f882(x99291,a870)),f311(x99291)),f196(f882(x99291,a870))))),x99293),x99292)+~P1(f333(f333(f335(x99291),x99294),x99292))+E(f333(f333(f22(f882(f882(x99291,a870),a870)),f333(f333(f60(x99291),x99292),x99293)),f333(f333(f60(x99291),f333(f333(f311(x99291),x99294),f196(f882(x99291,a870)))),x99293)),f333(f333(f60(x99291),f333(f333(f22(f882(x99291,a870)),x99292),f333(f333(f311(x99291),x99294),f196(f882(x99291,a870))))),x99293)) % 183.90/184.44 [10064]~P39(x100641,x100642,x100644)+~P1(f333(f333(f335(f881(x100641,x100641)),x100643),x100644))+P1(f333(f333(f272(x100641,x100641,a870),f333(f333(f7(x100641,f882(x100641,a870),f882(x100641,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x100641,a870),f882(x100641,a870)),x100641),f8(a870,a870,x100641)),f333(f333(f8(a870,f882(a870,a870),x100641),a331),f333(f333(f7(x100641,f882(x100641,a870),a870),f335(x100641)),x100642)))),f333(f333(f7(x100641,f882(x100641,a870),a870),f335(x100641)),x100642))),x100643)) % 183.90/184.44 [10076]P1(f333(f61(x100761),x100762))+~P1(f333(f61(x100763),f333(f312(x100761,x100763,x100764),x100762)))+~P1(f333(f61(x100761),f333(f253(x100761),f333(f333(f18(x100761,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100761),a331),f333(f333(f7(x100761,f882(x100761,a870),a870),f335(x100761)),x100762))),f333(f333(f7(x100761,x100763,a870),f333(f333(f8(x100763,f882(x100763,a870),x100761),a330),x100764)),f333(x100764,f496(x100764,x100763,x100762,x100761))))))) % 183.90/184.44 [8079]~P59(x80792)+E(x80791,f2(x80792))+E(f333(f333(f291(x80792),f333(f333(f22(x80792),f333(f333(f80(x80792),x80791),x80793)),x80794)),x80791),f333(f333(f22(x80792),x80793),f333(f333(f291(x80792),x80794),x80791))) % 183.90/184.44 [8080]~P59(x80802)+E(x80801,f2(x80802))+E(f333(f333(f291(x80802),f333(f333(f79(x80802),f333(f333(f80(x80802),x80801),x80803)),x80804)),x80801),f333(f333(f79(x80802),x80803),f333(f333(f291(x80802),x80804),x80801))) % 183.90/184.44 [8980]~E(f333(f333(f290(x89801,x89801,x89801),x89803),x89804),f196(f882(f881(x89801,x89801),a870)))+~E(f333(f333(f290(x89801,x89801,x89801),x89802),x89804),f196(f882(f881(x89801,x89801),a870)))+E(f333(f333(f290(x89801,x89801,x89801),f333(f333(f113(f882(f881(x89801,x89801),a870)),x89802),x89803)),x89804),f196(f882(f881(x89801,x89801),a870))) % 183.90/184.44 [10006]~P142(x100061)+~P142(x100062)+E(f333(f333(f318(x100061),f333(f333(f7(x100061,a102,f879(f876(a329))),f333(f333(f8(f882(x100062,f879(f876(a329))),f882(a102,f879(f876(a329))),x100061),f318(x100062)),f333(f333(f8(f882(x100062,f881(x100061,x100062)),f882(x100062,f879(f876(a329))),x100061),f333(f8(f881(x100061,x100062),f879(f876(a329)),x100062),x100063)),f268(x100061,x100062)))),x100064)),x100064),f333(f333(f318(f881(x100061,x100062)),x100063),x100064)) % 183.90/184.44 [9736]~P1(f333(f161(x97361,x97363),x97364))+~P1(f333(f161(x97361,x97362),x97364))+P1(f333(f161(x97361,f333(f333(f18(x97361,a870,a870),f333(f333(f8(a870,f882(a870,a870),x97361),a331),x97362)),x97363)),x97364)) % 183.90/184.44 [9998]P1(f333(x99981,f493(x99982,x99983,x99981,x99984)))+~P1(f333(f61(x99984),f333(f253(x99984),x99981)))+P1(f333(f61(x99983),f333(f253(x99983),f333(f333(f8(f882(x99984,a870),a870,x99983),f86(x99984)),f333(f333(f8(f882(x99984,a870),f882(x99984,a870),x99983),f333(f18(x99984,a870,a870),f333(f333(f8(a870,f882(a870,a870),x99984),a331),x99981))),x99982))))) % 183.90/184.44 [10019]~P1(f333(f61(x100192),f333(f253(x100192),x100193)))+~P1(f333(f61(x100191),f333(f253(x100191),f333(f333(f7(x100191,x100192,a870),x100194),f493(x100194,x100191,x100193,x100192)))))+P1(f333(f61(x100191),f333(f253(x100191),f333(f333(f8(f882(x100192,a870),a870,x100191),f86(x100192)),f333(f333(f8(f882(x100192,a870),f882(x100192,a870),x100191),f333(f18(x100192,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100192),a331),x100193))),x100194))))) % 183.90/184.44 [5032]~E(x50322,x50324)+E(f171(x50321,x50322,x50323),f171(x50321,x50324,x50325))+~E(x50322,f2(a875)) % 183.90/184.44 [5284]E(x52841,x52842)+~E(f171(x52844,x52843,x52841),f171(x52844,x52845,x52842))+E(x52843,f2(a875)) % 183.90/184.44 [6515]E(x65151,x65152)+~E(f333(x65153,x65151),f333(x65153,x65152))+~P25(x65154,x65155,x65153,f256(f882(x65154,a870))) % 183.90/184.44 [6675]~E(f333(x66753,x66755),f209(x66752))+~E(f333(x66754,x66755),f209(x66752))+E(f333(f187(x66751,x66752,x66753,x66754),x66755),f209(x66752)) % 183.90/184.44 [7410]E(x74101,x74102)+~P25(x74103,x74104,x74105,f256(f882(x74103,a870)))+~E(f333(f312(x74103,x74104,x74105),x74101),f333(f312(x74103,x74104,x74105),x74102)) % 183.90/184.44 [7665]P25(x76652,x76653,f348(x76654,x76653,x76652,x76651),x76651)+~E(f333(f312(x76653,x76652,x76655),x76654),x76651)+E(x76651,f196(f882(x76652,a870))) % 183.90/184.44 [8215]~P1(f333(f333(x82153,x82152),x82155))+~P1(f333(f333(x82153,x82154),x82152))+P1(f333(f333(f335(x82151),x82152),f300(x82151,x82153,x82154,x82155))) % 183.90/184.44 [8216]~P1(f333(f333(x82163,x82162),x82165))+~P1(f333(f333(x82163,x82164),x82162))+P1(f333(f333(f335(x82161),x82162),f297(x82161,x82163,x82164,x82165))) % 183.90/184.44 [8771]~P25(x87711,x87713,x87715,f256(f882(x87711,a870)))+~P25(x87713,x87712,x87714,f256(f882(x87713,a870)))+P25(x87711,x87712,f333(f72(x87713,x87712,x87711,x87714),x87715),f256(f882(x87711,a870))) % 183.90/184.44 [9340]P1(f333(f333(f335(f881(x93401,x93401)),f333(f333(f268(x93401,x93401),x93402),x93403)),f309(x93401,x93404)))+~P1(f333(f333(f335(f881(x93401,x93401)),f333(f333(f268(x93401,x93401),x93402),x93405)),f309(x93401,x93404)))+~P1(f333(f333(f335(f881(x93401,x93401)),f333(f333(f268(x93401,x93401),x93405),x93403)),f309(x93401,x93404))) % 183.90/184.44 [9378]~P106(x93782)+~P1(f333(f138(x93781),x93785))+P1(f333(f138(x93781),f150(x93781,x93782,x93783,x93784,x93785))) % 183.90/184.44 [5355]~E(x53552,f116(x53551))+E(f333(f333(f135(x53551),x53552),x53553),f333(f333(f152(x53551),x53554),x53555))+~E(x53553,f333(f333(f152(x53551),x53554),x53555)) % 183.90/184.44 [5356]~E(x53562,f116(x53561))+E(f333(f333(f135(x53561),x53562),x53563),f333(f333(f152(x53561),x53564),x53565))+~E(f333(f333(f152(x53561),x53564),x53565),x53563) % 183.90/184.44 [6472]~E(f333(f197(f876(x64721)),x64725),f333(f197(f876(x64722)),x64724))+E(f333(f333(f155(f881(x64721,x64722),x64722),f271(x64721,x64722)),x64723),x64724)+~E(f333(f333(f184(x64721,x64722),x64725),x64724),x64723) % 183.90/184.44 [6473]~E(f333(f197(f876(x64731)),x64734),f333(f197(f876(x64732)),x64735))+E(f333(f333(f155(f881(x64731,x64732),x64731),f267(x64731,x64732)),x64733),x64734)+~E(f333(f333(f184(x64731,x64732),x64734),x64735),x64733) % 183.90/184.44 [6948]~P106(x69481)+~P14(x69481,f333(f333(f155(x69482,x69481),x69483),x69485))+P14(x69481,f333(f333(f155(x69482,x69481),x69483),f333(f137(x69482,x69484),x69485))) % 183.90/184.44 [6995]~P1(f333(x69953,x69955))+~P1(f333(f333(x69952,x69954),x69955))+P1(f333(f333(f94(x69951,x69952,x69953),x69954),x69955)) % 183.90/184.44 [7092]~P106(x70921)+P14(x70921,f333(f333(f155(x70922,x70921),x70923),f172(x70922,x70924,x70925)))+~P14(x70921,f333(f333(f155(x70922,x70921),x70923),x70925)) % 183.90/184.44 [7115]~P49(x71153,x71152,x71155)+~P49(x71151,x71153,x71154)+P49(x71151,x71152,f333(f333(f290(x71151,x71153,x71152),x71154),x71155)) % 183.90/184.44 [7207]E(x72071,x72072)+~P25(x72073,x72074,x72075,f256(f882(x72073,a870)))+~E(f333(f333(f155(x72073,x72074),x72075),x72071),f333(f333(f155(x72073,x72074),x72075),x72072)) % 183.90/184.44 [7361]~P1(f333(f333(f248(a875),x73611),f333(x73613,x73615)))+P1(f333(f333(f248(a875),x73611),f156(x73612,x73613,x73614)))+~P1(f333(f333(f335(x73612),x73615),f333(f174(x73612),x73614))) % 183.90/184.44 [7362]~P1(f333(f333(f247(a875),x73621),f333(x73623,x73625)))+P1(f333(f333(f247(a875),x73621),f156(x73622,x73623,x73624)))+~P1(f333(f333(f335(x73622),x73625),f333(f174(x73622),x73624))) % 183.90/184.44 [7768]P1(f333(x77681,x77682))+~P1(f333(x77681,x77683))+~P1(f333(f333(f335(x77684),x77682),f333(f174(x77684),f171(x77684,x77685,x77683)))) % 183.90/184.44 [7769]P1(f333(x77691,x77692))+~P1(f333(x77691,x77693))+~P1(f333(f333(f335(x77694),x77693),f333(f174(x77694),f171(x77694,x77695,x77692)))) % 183.90/184.44 [7774]~P108(x77741)+P1(f333(f333(f247(f882(x77741,a870)),f304(x77741,x77742,x77743)),f304(x77741,x77744,x77745)))+P1(f333(f333(f247(x77741),x77742),x77743)) % 183.90/184.44 [7797]~P4(x77971)+P1(f333(f333(f247(x77971),f333(f333(f42(x77972,x77971),x77973),x77974)),f333(x77974,x77975)))+~P1(f333(f333(f335(x77972),x77975),x77973)) % 183.90/184.44 [7864]~P25(x78641,x78642,x78644,x78643)+E(f333(f76(x78641,x78642,x78643,x78644),f333(x78644,x78645)),x78645)+~P1(f333(f333(f335(x78641),x78645),x78643)) % 183.90/184.44 [8067]~P1(f333(x80671,x80675))+P1(f333(x80671,f418(x80671,x80672,x80673,x80674)))+~P1(f333(f333(f335(x80674),x80675),x80673)) % 183.90/184.44 [8068]~P1(f333(x80681,x80685))+P1(f333(x80681,f418(x80681,x80682,x80683,x80684)))+~P1(f333(f333(f335(x80684),x80685),x80682)) % 183.90/184.44 [8166]P1(f333(f61(x81661),x81662))+~P1(f333(f61(x81663),x81664))+~P1(f333(f333(f247(f882(x81661,a870)),x81662),f333(f312(x81663,x81661,x81665),x81664))) % 183.90/184.44 [8331]E(x83311,x83312)+~P25(x83313,x83314,x83315,f333(f333(f113(f882(x83313,a870)),f333(f174(x83313),x83311)),f333(f174(x83313),x83312)))+~E(f333(f333(f155(x83313,x83314),x83315),x83311),f333(f333(f155(x83313,x83314),x83315),x83312)) % 183.90/184.44 [8385]~P108(x83851)+~P1(f333(f333(f248(f882(x83851,a870)),f304(x83851,x83854,x83855)),f304(x83851,x83852,x83853)))+P1(f333(f333(f247(x83851),x83852),x83853)) % 183.90/184.44 [8455]~P25(x84551,x84554,x84555,f256(f882(x84551,a870)))+~P1(f333(f333(f335(x84554),f333(x84555,x84552)),f333(f312(x84551,x84554,x84555),x84553)))+P1(f333(f333(f335(x84551),x84552),x84553)) % 183.90/184.44 [8532]P1(f333(x85321,x85322))+~P1(f333(x85321,f378(x85321,x85323,x85324,x85325)))+~P1(f333(f333(f335(x85325),x85322),x85324)) % 183.90/184.44 [8533]P1(f333(x85331,x85332))+~P1(f333(x85331,f378(x85331,x85333,x85334,x85335)))+~P1(f333(f333(f335(x85335),x85332),x85333)) % 183.90/184.44 [8811]~P25(x88112,x88113,x88111,x88114)+E(f333(x88111,f333(f76(x88112,x88113,x88114,x88111),x88115)),x88115)+~P1(f333(f333(f335(x88113),x88115),f333(f312(x88112,x88113,x88111),x88114))) % 183.90/184.44 [8917]E(x89171,f116(x89172))+E(f333(f333(f152(x89172),x89173),f697(x89174,x89173,x89175,x89171,x89172)),x89171)+~E(f333(f333(f135(x89172),x89171),x89175),f333(f333(f152(x89172),x89173),x89174)) % 183.90/184.44 [8918]E(x89181,f116(x89182))+E(f333(f333(f152(x89182),x89183),f698(x89184,x89181,x89185,x89183,x89182)),x89181)+~E(f333(f333(f135(x89182),x89181),x89184),f333(f333(f152(x89182),x89183),x89185)) % 183.90/184.44 [8936]E(f333(f333(f152(x89362),x89363),f697(x89364,x89363,x89361,x89365,x89362)),x89365)+~E(f333(f333(f135(x89362),x89365),x89361),f333(f333(f152(x89362),x89363),x89364))+E(x89361,f333(f333(f152(x89362),x89363),x89364)) % 183.90/184.44 [8937]E(f333(f333(f152(x89371),x89372),f698(x89374,x89375,x89373,x89372,x89371)),x89375)+~E(f333(f333(f135(x89371),x89375),x89374),f333(f333(f152(x89371),x89372),x89373))+E(f333(f333(f152(x89371),x89372),x89373),x89374) % 183.90/184.44 [9018]~E(f333(f312(x90183,x90182,x90184),f256(f882(x90183,a870))),f256(f882(x90182,a870)))+~E(f333(f312(x90181,x90183,x90185),f256(f882(x90181,a870))),f256(f882(x90183,a870)))+E(f333(f312(x90181,x90182,f333(f72(x90183,x90182,x90181,x90184),x90185)),f256(f882(x90181,a870))),f256(f882(x90182,a870))) % 183.90/184.44 [9385]E(x93851,f116(x93852))+~E(f333(f333(f135(x93852),x93851),x93853),f333(f333(f152(x93852),x93855),x93854))+E(f333(f333(f135(x93852),f698(x93853,x93851,x93854,x93855,x93852)),x93853),x93854) % 183.90/184.44 [9386]E(x93861,f116(x93862))+~E(f333(f333(f135(x93862),x93861),x93865),f333(f333(f152(x93862),x93864),x93863))+E(f333(f333(f135(x93862),f697(x93863,x93864,x93865,x93861,x93862)),x93865),x93863) % 183.90/184.44 [9393]E(f333(f333(f135(x93932),f697(x93934,x93933,x93931,x93935,x93932)),x93931),x93934)+~E(f333(f333(f135(x93932),x93935),x93931),f333(f333(f152(x93932),x93933),x93934))+E(x93931,f333(f333(f152(x93932),x93933),x93934)) % 183.90/184.44 [9394]~E(f333(f333(f135(x93941),x93945),x93944),f333(f333(f152(x93941),x93942),x93943))+E(f333(f333(f135(x93941),f698(x93944,x93945,x93943,x93942,x93941)),x93944),x93943)+E(f333(f333(f152(x93941),x93942),x93943),x93944) % 183.90/184.44 [9395]E(f333(f333(f135(x93951),x93955),f700(x93953,x93952,x93954,x93955,x93951)),x93952)+E(f333(f333(f135(x93951),x93952),f699(x93953,x93952,x93954,x93955,x93951)),x93955)+~E(f333(f333(f135(x93951),x93955),x93954),f333(f333(f135(x93951),x93952),x93953)) % 183.90/184.44 [9427]~P106(x94271)+P14(x94271,f333(f333(f155(x94272,x94271),x94273),f150(x94272,x94271,x94273,x94274,x94275)))+~P14(x94271,f333(f333(f155(x94272,x94271),x94273),x94275)) % 183.90/184.44 [9438]~P53(x94385,x94381,x94384,x94383)+P1(f333(f333(x94381,x94382),f558(x94383,x94384,x94381,x94385,x94382)))+~P1(f333(f333(f335(x94385),x94382),x94384)) % 183.90/184.44 [9543]~P1(f333(f333(f335(f881(x95431,x95431)),f333(f333(f268(x95431,x95431),x95435),x95433)),f309(x95431,x95434)))+P1(f333(f333(f335(f881(x95431,x95431)),f333(f333(f268(x95431,x95431),x95432),x95433)),f333(f333(f290(x95431,x95431,x95431),x95434),f309(x95431,x95434))))+~P1(f333(f333(f335(f881(x95431,x95431)),f333(f333(f268(x95431,x95431),x95432),x95435)),f333(f333(f290(x95431,x95431,x95431),x95434),f309(x95431,x95434)))) % 183.90/184.44 [9544]~P1(f333(f333(f335(f881(x95441,x95441)),f333(f333(f268(x95441,x95441),x95442),x95445)),f309(x95441,x95444)))+P1(f333(f333(f335(f881(x95441,x95441)),f333(f333(f268(x95441,x95441),x95442),x95443)),f333(f333(f290(x95441,x95441,x95441),x95444),f309(x95441,x95444))))+~P1(f333(f333(f335(f881(x95441,x95441)),f333(f333(f268(x95441,x95441),x95445),x95443)),f333(f333(f290(x95441,x95441,x95441),x95444),f309(x95441,x95444)))) % 183.90/184.44 [9547]P1(f333(f333(f335(f881(f876(x95471),f876(x95471))),f333(f333(f268(f876(x95471),f876(x95471)),x95472),x95473)),f159(x95471,f309(x95471,x95474))))+~P1(f333(f333(f335(f881(f876(x95471),f876(x95471))),f333(f333(f268(f876(x95471),f876(x95471)),x95472),x95475)),f159(x95471,f309(x95471,x95474))))+~P1(f333(f333(f335(f881(f876(x95471),f876(x95471))),f333(f333(f268(f876(x95471),f876(x95471)),x95475),x95473)),f159(x95471,f309(x95471,x95474)))) % 183.90/184.44 [9551]E(f333(f333(f135(x95511),x95512),f699(x95513,x95512,x95514,x95515,x95511)),x95515)+E(f333(f333(f135(x95511),f700(x95513,x95512,x95514,x95515,x95511)),x95513),x95514)+~E(f333(f333(f135(x95511),x95512),x95513),f333(f333(f135(x95511),x95515),x95514)) % 183.90/184.44 [9552]E(f333(f333(f135(x95521),x95522),f700(x95523,x95524,x95525,x95522,x95521)),x95524)+E(f333(f333(f135(x95521),f699(x95523,x95524,x95525,x95522,x95521)),x95525),x95523)+~E(f333(f333(f135(x95521),x95522),x95525),f333(f333(f135(x95521),x95524),x95523)) % 183.90/184.44 [9606]P1(f333(f333(f335(f881(x96061,x96061)),f333(f333(f268(x96061,x96061),x96062),x96063)),f333(f333(f290(x96061,x96061,x96061),x96064),f309(x96061,x96064))))+~P1(f333(f333(f335(f881(x96061,x96061)),f333(f333(f268(x96061,x96061),x96062),x96065)),f333(f333(f290(x96061,x96061,x96061),x96064),f309(x96061,x96064))))+~P1(f333(f333(f335(f881(x96061,x96061)),f333(f333(f268(x96061,x96061),x96065),x96063)),f333(f333(f290(x96061,x96061,x96061),x96064),f309(x96061,x96064)))) % 183.90/184.44 [9633]P34(x96331,x96332,x96333,x96334,x96335)+~E(f333(f197(f876(x96331)),x96334),f333(f197(f876(x96332)),x96335))+~P1(f333(f333(f272(x96331,x96332,a870),x96333),f733(x96335,x96334,x96333,x96332,x96331))) % 183.90/184.44 [9634]P34(x96341,x96342,x96343,x96344,x96345)+~E(f333(f197(f876(x96341)),x96344),f333(f197(f876(x96342)),x96345))+~P1(f333(f333(f272(x96341,x96342,a870),x96343),f737(x96343,x96345,x96344,x96342,x96341))) % 183.90/184.44 [9639]E(f333(f333(f135(x96391),f699(x96392,x96393,x96394,x96395,x96391)),x96394),x96392)+~E(f333(f333(f135(x96391),x96393),x96392),f333(f333(f135(x96391),x96395),x96394))+E(f333(f333(f135(x96391),f700(x96392,x96393,x96394,x96395,x96391)),x96392),x96394) % 183.90/184.44 [9654]~P106(x96542)+E(f333(f333(f149(x96541,x96542,x96543),x96544),x96545),f333(f333(f152(x96541),x96544),x96545))+P1(f333(f333(f335(x96541),f785(x96544,x96543,x96545,x96541,x96542)),f333(f174(x96541),x96545))) % 183.90/184.44 [9659]~P53(x96591,x96594,x96593,x96592)+~P1(f333(f333(f335(x96591),x96595),x96593))+P1(f333(f333(f335(x96591),f558(x96592,x96593,x96594,x96591,x96595)),x96592)) % 183.90/184.44 [9779]~P1(f333(f333(f335(f881(f882(x97791,a870),f882(x97791,a870))),f333(f333(f268(f882(x97791,a870),f882(x97791,a870)),x97794),x97793)),f325(x97791,x97792)))+~P1(f333(f333(f335(x97791),x97795),x97794))+P1(f333(f333(f335(x97791),f622(x97792,x97793,x97794,x97791,x97795)),x97793)) % 183.90/184.44 [9791]~P106(x97912)+E(f333(f333(f149(x97911,x97912,x97913),x97914),x97915),f333(f333(f152(x97911),x97914),x97915))+~P1(f333(f333(f247(x97912),f333(x97913,x97914)),f333(x97913,f785(x97914,x97913,x97915,x97911,x97912)))) % 183.90/184.44 [9981]P34(x99811,x99812,x99813,x99814,x99815)+~E(f333(f197(f876(x99811)),x99814),f333(f197(f876(x99812)),x99815))+~P1(f333(f333(x99813,f333(f333(f166(x99811),x99814),f738(x99815,x99814,x99813,x99812,x99811))),f333(f333(f166(x99812),x99815),f738(x99815,x99814,x99813,x99812,x99811)))) % 183.90/184.44 [9982]P34(x99821,x99822,x99823,x99824,x99825)+~E(f333(f197(f876(x99821)),x99824),f333(f197(f876(x99822)),x99825))+~P1(f333(f333(x99823,f333(f333(f166(x99821),x99824),f774(x99823,x99825,x99822,x99824,x99821))),f333(f333(f166(x99822),x99825),f774(x99823,x99825,x99822,x99824,x99821)))) % 183.90/184.44 [6543]~P17(x65432,x65435,x65431)+~P1(f333(f61(x65432),x65434))+E(f333(x65431,f333(f333(f311(x65432),x65433),x65434)),f333(f333(f64(x65432,x65432,x65435),x65433),x65434)) % 183.90/184.44 [6544]~E(x65443,x65444)+~E(x65442,x65445)+E(f333(f333(f311(x65441),x65442),f333(f333(f311(x65441),x65443),f196(f882(x65441,a870)))),f333(f333(f311(x65441),x65444),f333(f333(f311(x65441),x65445),f196(f882(x65441,a870))))) % 183.90/184.44 [6555]P1(f333(x65552,x65555))+E(f179(x65551,x65552,f333(f333(f135(x65551),x65553),x65554)),f179(x65551,x65552,x65553))+~P1(f333(f333(f335(x65551),x65555),f333(f174(x65551),x65553))) % 183.90/184.44 [6592]E(f333(x65921,x65922),f196(f882(x65923,a870)))+~E(f333(f333(f41(x65924,f882(x65923,a870)),x65925),x65921),f196(f882(x65923,a870)))+~P1(f333(f333(f335(x65924),x65922),x65925)) % 183.90/184.44 [6593]E(f333(x65931,x65932),f256(f882(x65933,a870)))+~E(f333(f333(f42(x65934,f882(x65933,a870)),x65935),x65931),f256(f882(x65933,a870)))+~P1(f333(f333(f335(x65934),x65932),x65935)) % 183.90/184.44 [6897]~P1(f333(f333(f202(x68971),x68973),x68975))+~P1(f333(f333(f202(x68972),x68975),x68974))+P1(f333(f333(f202(f32(x68971,x68972)),x68973),x68974)) % 183.90/184.44 [7102]~E(x71022,x71024)+~P139(x71021)+E(f333(f333(f79(x71021),f333(f333(f80(x71021),x71022),x71023)),f333(f333(f80(x71021),x71024),x71025)),f333(f333(f79(x71021),f333(f333(f80(x71021),x71022),x71025)),f333(f333(f80(x71021),x71024),x71023))) % 183.90/184.44 [7162]~P4(x71621)+~P1(f333(f333(f335(x71624),x71623),x71625))+P1(f333(f333(f247(x71621),f333(x71622,x71623)),f333(f333(f41(x71624,x71621),x71625),x71622))) % 183.90/184.44 [7212]~P107(x72121)+P1(f333(f333(f247(x72121),f333(x72122,x72123)),f333(x72124,x72123)))+~P1(f333(f333(f247(f882(x72125,x72121)),x72122),x72124)) % 183.90/184.44 [7329]E(x73291,x73292)+E(x73293,x73291)+~E(f333(f333(f311(x73294),x73291),f333(f333(f311(x73294),x73295),f196(f882(x73294,a870)))),f333(f333(f311(x73294),x73292),f333(f333(f311(x73294),x73293),f196(f882(x73294,a870))))) % 183.90/184.44 [7330]E(x73301,x73302)+E(x73303,x73301)+~E(f333(f333(f311(x73304),x73303),f333(f333(f311(x73304),x73302),f196(f882(x73304,a870)))),f333(f333(f311(x73304),x73305),f333(f333(f311(x73304),x73301),f196(f882(x73304,a870))))) % 183.90/184.44 [7331]E(x73311,x73312)+E(x73311,x73313)+~E(f333(f333(f311(x73314),x73313),f333(f333(f311(x73314),x73312),f196(f882(x73314,a870)))),f333(f333(f311(x73314),x73315),f333(f333(f311(x73314),x73311),f196(f882(x73314,a870))))) % 183.90/184.44 [7332]E(x73321,x73322)+E(x73321,x73323)+~E(f333(f333(f311(x73324),x73321),f333(f333(f311(x73324),x73325),f196(f882(x73324,a870)))),f333(f333(f311(x73324),x73322),f333(f333(f311(x73324),x73323),f196(f882(x73324,a870))))) % 183.90/184.44 [7874]P25(x78741,x78742,x78743,x78744)+~P25(x78741,x78742,x78743,x78745)+~P1(f333(f333(f247(f882(x78741,a870)),x78744),x78745)) % 183.90/184.44 [7881]~P1(f333(f333(f247(a875),x78815),x78813))+~P1(f333(f333(f333(f333(a204,x78811),x78812),x78815),x78814))+P1(f333(f333(f333(f333(a204,x78811),x78812),x78813),x78814)) % 183.90/184.44 [7978]P1(f333(x79781,x79782))+~P1(f333(f333(f202(x79784),x79782),x79785))+P1(f333(f333(f202(f29(x79781,x79783,x79784)),x79782),x79785)) % 183.90/184.44 [8006]~P1(f333(x80061,x80064))+~P1(f333(f333(f202(x80062),x80064),x80065))+P1(f333(f333(f202(f29(x80061,x80062,x80063)),x80064),x80065)) % 183.90/184.44 [8057]E(x80571,x80572)+~E(f333(f312(x80573,x80574,x80575),x80571),f333(f312(x80573,x80574,x80575),x80572))+~P25(x80573,x80574,x80575,f333(f333(f113(f882(x80573,a870)),x80571),x80572)) % 183.90/184.44 [8131]P1(f333(x81312,x81314))+E(f333(f333(f139(x81311),f333(f197(f876(x81311)),f179(x81311,x81312,x81313))),x81313),f333(f333(f152(x81311),x81314),x81315))+~E(f333(f333(f135(x81311),f179(x81311,x81312,x81313)),f333(f333(f152(x81311),x81314),x81315)),x81313) % 183.90/184.44 [8163]~P25(x81631,x81632,x81633,x81635)+~P25(x81631,x81632,x81633,x81634)+P25(x81631,x81632,x81633,f333(f333(f104(f882(x81631,a870)),x81634),x81635)) % 183.90/184.44 [8272]~P66(x82721)+E(f333(f333(f79(x82721),f333(x82722,x82723)),f333(f167(x82721),f333(f333(f155(x82724,x82721),x82722),f172(x82724,x82723,x82725)))),f333(f167(x82721),f333(f333(f155(x82724,x82721),x82722),x82725)))+~P1(f333(f333(f335(x82724),x82723),f333(f174(x82724),x82725))) % 183.90/184.44 [8361]~P106(x83611)+~P14(x83611,f333(f333(f155(x83612,x83611),x83613),x83615))+P14(x83611,f333(f333(f155(x83612,x83611),x83613),f333(f333(f149(x83612,x83611,x83613),x83614),x83615))) % 183.90/184.44 [8440]P1(f333(x84401,x84402))+P1(f333(f333(f202(x84403),x84402),x84404))+~P1(f333(f333(f202(f29(x84401,x84405,x84403)),x84402),x84404)) % 183.90/184.44 [8451]~P4(x84511)+P1(f333(f333(f247(x84511),f333(f333(f41(x84512,x84511),x84513),x84514)),f333(f333(f41(x84512,x84511),x84515),x84514)))+~P1(f333(f333(f247(f882(x84512,a870)),x84513),x84515)) % 183.90/184.44 [8452]~P4(x84521)+P1(f333(f333(f247(x84521),f333(f333(f42(x84522,x84521),x84523),x84524)),f333(f333(f42(x84522,x84521),x84525),x84524)))+~P1(f333(f333(f247(f882(x84522,a870)),x84525),x84523)) % 183.90/184.44 [8463]~P1(f333(x84634,x84632))+P1(f333(f333(f202(x84631),x84632),x84633))+~P1(f333(f333(f202(f29(x84634,x84631,x84635)),x84632),x84633)) % 183.90/184.44 [8486]~P106(x84863)+P1(f333(f138(x84861),x84862))+~P1(f333(f138(x84861),f333(f333(f149(x84861,x84863,x84864),x84865),x84862))) % 183.90/184.44 [8496]P1(f333(f333(f202(x84961),x84962),x84963))+P1(f333(f333(f202(x84964),x84962),x84963))+~P1(f333(f333(f202(f29(x84965,x84961,x84964)),x84962),x84963)) % 183.90/184.44 [8626]~P106(x86261)+~P1(f333(f333(f335(x86262),x86263),f333(f174(x86262),x86264)))+~P1(f333(f138(x86262),f333(f333(f149(x86262,x86261,x86265),x86263),x86264))) % 183.90/184.44 [8706]~P106(x87061)+P14(x87061,f333(f333(f155(x87062,x87061),x87063),x87064))+~P14(x87061,f333(f333(f155(x87062,x87061),x87063),f333(f333(f149(x87062,x87061,x87063),x87065),x87064))) % 183.90/184.44 [8798]~P106(x87982)+E(f333(f333(f149(x87981,x87982,x87983),x87984),x87985),f150(x87981,x87982,x87983,x87984,x87985))+P1(f333(f333(f335(x87982),f333(x87983,x87984)),f333(f312(x87981,x87982,x87983),f333(f174(x87981),x87985)))) % 183.90/184.44 [8873]~P106(x88732)+E(f150(x88731,x88732,x88733,x88734,x88735),x88735)+~P1(f333(f333(f335(x88732),f333(x88733,x88734)),f333(f312(x88731,x88732,x88733),f333(f174(x88731),x88735)))) % 183.90/184.44 [8889]~P25(x88892,x88891,x88893,x88895)+P1(f333(f333(f248(f882(x88891,a870)),f333(f312(x88892,x88891,x88893),x88894)),f333(f312(x88892,x88891,x88893),x88895)))+~P1(f333(f333(f248(f882(x88892,a870)),x88894),x88895)) % 183.90/184.44 [9060]~P25(x90601,x90602,x90603,f256(f882(x90601,a870)))+~P1(f333(f333(f247(f882(x90602,a870)),x90604),f333(f312(x90601,x90602,x90603),x90605)))+P1(f333(f333(f247(f882(x90601,a870)),f333(f313(x90601,x90602,x90603),x90604)),x90605)) % 183.90/184.44 [9080]~E(f333(f312(x90803,x90801,x90804),f256(f882(x90803,a870))),f256(f882(x90801,a870)))+P1(f333(f333(f247(f882(x90801,a870)),x90802),f333(f312(x90803,x90801,x90804),x90805)))+~P1(f333(f333(f247(f882(x90803,a870)),f333(f313(x90803,x90801,x90804),x90802)),x90805)) % 183.90/184.44 [9104]~E(f333(f240(x91042),x91044),f333(f333(f180(x91041,x91042),x91045),x91043))+~P1(f333(f138(x91041),f333(f333(f155(f881(x91041,x91042),x91041),f267(x91041,x91042)),x91045)))+P1(f333(f333(f335(f881(x91041,x91042)),f333(f333(f268(x91041,x91042),x91043),x91044)),f333(f174(f881(x91041,x91042)),x91045))) % 183.90/184.44 [9186]~P25(x91861,x91864,x91865,f256(f882(x91861,a870)))+~P1(f333(f333(f247(f882(x91864,a870)),f333(f312(x91861,x91864,x91865),x91862)),f333(f312(x91861,x91864,x91865),x91863)))+P1(f333(f333(f247(f882(x91861,a870)),x91862),x91863)) % 183.90/184.44 [9251]E(f333(f240(x92511),x92512),f333(f333(f180(x92513,x92511),x92514),x92515))+~P1(f333(f138(x92513),f333(f333(f155(f881(x92513,x92511),x92513),f267(x92513,x92511)),x92514)))+~P1(f333(f333(f335(f881(x92513,x92511)),f333(f333(f268(x92513,x92511),x92515),x92512)),f333(f174(f881(x92513,x92511)),x92514))) % 183.90/184.44 [9253]E(f333(f333(f180(x92531,x92532),x92533),x92534),f333(f240(x92532),x92535))+~P1(f333(f138(x92531),f333(f333(f155(f881(x92531,x92532),x92531),f267(x92531,x92532)),x92533)))+~P1(f333(f333(f335(f881(x92531,x92532)),f333(f333(f268(x92531,x92532),x92534),x92535)),f333(f174(f881(x92531,x92532)),x92533))) % 183.90/184.44 [9308]~P78(x93081)+~E(f333(x93083,f754(x93083,x93084,x93085,x93082,x93081)),f2(x93081))+E(f333(f167(x93081),f333(f333(f155(x93082,x93081),x93083),f333(f137(x93082,x93084),x93085))),f333(f167(x93081),f333(f333(f155(x93082,x93081),x93083),x93085))) % 183.90/184.44 [9485]~P16(x94851,x94852,x94853)+~P1(f333(f61(x94851),x94855))+P1(f333(f66(x94851,x94852,x94853,x94854,x94855),f333(f333(f64(x94851,x94852,x94853),x94854),x94855))) % 183.90/184.44 [9564]P1(f333(x95641,f658(x95642,x95641,x95643,x95644,x95645)))+~P1(f333(f333(f247(f882(x95645,a870)),x95644),x95643))+P1(f333(f333(f247(f882(x95645,a870)),f333(f333(f104(f882(x95645,a870)),x95644),f333(f253(x95645),x95641))),f333(f333(f104(f882(x95645,a870)),x95643),f333(f253(x95645),x95642)))) % 183.90/184.44 [9578]~P78(x95781)+~P1(f333(x95784,f754(x95783,x95784,x95785,x95782,x95781)))+E(f333(f167(x95781),f333(f333(f155(x95782,x95781),x95783),f333(f137(x95782,x95784),x95785))),f333(f167(x95781),f333(f333(f155(x95782,x95781),x95783),x95785))) % 183.90/184.44 [9657]~P4(x96575)+P1(f333(f333(f335(x96571),f347(x96572,x96573,x96571,x96574,x96575)),x96573))+P1(f333(f333(f247(x96575),x96574),f333(f333(f42(x96571,x96575),x96573),x96572))) % 183.90/184.44 [9660]~P78(x96601)+E(f333(f167(x96601),f333(f333(f155(x96602,x96601),x96603),f333(f137(x96602,x96604),x96605))),f333(f167(x96601),f333(f333(f155(x96602,x96601),x96603),x96605)))+P1(f333(f333(f335(x96602),f754(x96603,x96604,x96605,x96602,x96601)),f333(f174(x96602),x96605))) % 183.90/184.44 [9670]~P1(f333(x96705,f658(x96705,x96703,x96704,x96702,x96701)))+~P1(f333(f333(f247(f882(x96701,a870)),x96702),x96704))+P1(f333(f333(f247(f882(x96701,a870)),f333(f333(f104(f882(x96701,a870)),x96702),f333(f253(x96701),x96703))),f333(f333(f104(f882(x96701,a870)),x96704),f333(f253(x96701),x96705)))) % 183.90/184.44 [9704]P34(x97041,x97042,x97043,x97044,x97045)+~E(f333(f197(f876(x97042)),x97045),f333(f197(f876(x97041)),x97044))+P1(f333(f333(f248(a875),f738(x97045,x97044,x97043,x97042,x97041)),f333(f197(f876(x97041)),x97044))) % 183.90/184.44 [9705]P34(x97051,x97052,x97053,x97054,x97055)+~E(f333(f197(f876(x97052)),x97055),f333(f197(f876(x97051)),x97054))+P1(f333(f333(f248(a875),f774(x97053,x97055,x97052,x97054,x97051)),f333(f197(f876(x97051)),x97054))) % 183.90/184.44 [9738]P1(f333(f333(f335(x97381),f658(x97382,x97383,x97384,x97385,x97381)),x97385))+~P1(f333(f333(f247(f882(x97381,a870)),x97385),x97384))+P1(f333(f333(f247(f882(x97381,a870)),f333(f333(f104(f882(x97381,a870)),x97385),f333(f253(x97381),x97383))),f333(f333(f104(f882(x97381,a870)),x97384),f333(f253(x97381),x97382)))) % 183.90/184.44 [9792]~P4(x97921)+~P1(f333(f333(f247(x97921),x97922),f333(x97925,f347(x97925,x97924,x97923,x97922,x97921))))+P1(f333(f333(f247(x97921),x97922),f333(f333(f42(x97923,x97921),x97924),x97925))) % 183.90/184.44 [9825]~P73(x98251)+~P1(f333(f61(x98252),x98255))+E(f333(f333(f333(f65(x98251,x98252,f80(x98251)),f333(f333(f18(x98252,x98251,x98251),f333(f333(f8(x98251,f882(x98251,x98251),x98252),f80(x98251)),x98253)),x98254)),f77(x98251)),x98255),f333(f333(f80(x98251),f333(f333(f333(f65(x98251,x98252,f80(x98251)),x98253),f77(x98251)),x98255)),f333(f333(f333(f65(x98251,x98252,f80(x98251)),x98254),f77(x98251)),x98255))) % 183.90/184.44 [9888]~P1(f333(f333(f335(f881(f882(x98881,a870),f882(x98881,a870))),f333(f333(f268(f882(x98881,a870),f882(x98881,a870)),x98885),x98884)),f325(x98881,x98883)))+~P1(f333(f333(f335(x98881),x98882),x98885))+P1(f333(f333(f335(f881(x98881,x98881)),f333(f333(f268(x98881,x98881),x98882),f622(x98883,x98884,x98885,x98881,x98882))),x98883)) % 183.90/184.44 [10016]~P1(f333(f333(f335(f881(f876(x100161),f876(x100161))),f333(f333(f268(f876(x100161),f876(x100161)),f333(f333(f135(x100161),x100165),x100162)),f333(f333(f135(x100161),x100165),x100163))),f148(x100161,x100164)))+P1(f333(f333(f335(f881(f876(x100161),f876(x100161))),f333(f333(f268(f876(x100161),f876(x100161)),x100162),x100163)),f148(x100161,x100164)))+P1(f333(f333(f335(f881(x100161,x100161)),f333(f333(f268(x100161,x100161),f705(x100164,x100163,x100162,x100165,x100161)),f705(x100164,x100163,x100162,x100165,x100161))),x100164)) % 183.90/184.44 [7142]~E(f333(f197(f876(x71421)),x71423),f333(f197(f876(x71422)),x71424))+E(f333(f333(f180(x71421,x71422),f333(f333(f184(x71421,x71422),x71423),x71424)),x71425),f209(x71422))+P1(f333(f333(f335(x71421),x71425),f333(f174(x71421),x71423))) % 183.90/184.44 [7215]~E(x72153,x72155)+E(f333(f333(f166(x72151),f333(f333(f160(x72151,x72152),x72153),x72154)),x72155),x72154)+~P1(f333(f333(f248(a875),x72153),f333(f197(f876(x72151)),x72152))) % 183.90/184.44 [7324]~E(f333(f333(f135(x73241),x73242),x73244),f333(f333(f135(x73241),x73243),x73245))+E(f333(f333(f177(x73241),f333(f197(f876(x73241)),x73242)),x73243),x73242)+P1(f333(f333(f247(a875),f333(f197(f876(x73241)),x73243)),f333(f197(f876(x73241)),x73242))) % 183.90/184.44 [7341]~E(x73415,x73412)+P1(f333(x73411,x73412))+P1(f333(f333(f333(f333(a204,f31(x73411,x73413)),x73412),x73414),x73415)) % 183.90/184.44 [7835]~E(f333(f333(f135(x78351),x78352),x78354),f333(f333(f135(x78351),x78353),x78355))+E(f333(f333(f177(x78351),f333(f197(f876(x78351)),x78352)),x78353),x78352)+~P1(f333(f333(f247(a875),f333(f197(f876(x78351)),x78352)),f333(f197(f876(x78351)),x78353))) % 183.90/184.44 [7859]~P1(f333(f61(x78591),f333(x78594,x78595)))+~P1(f333(f333(f335(x78592),x78595),x78593))+P1(f333(f61(x78591),f333(f333(f42(x78592,f882(x78591,a870)),x78593),x78594))) % 183.90/184.44 [7912]~E(f333(f197(f876(x79121)),x79122),f333(f197(f876(x79123)),x79124))+~E(f333(f333(f180(x79121,x79123),f333(f333(f184(x79121,x79123),x79122),x79124)),x79125),f209(x79123))+~P1(f333(f333(f335(x79121),x79125),f333(f174(x79121),x79122))) % 183.90/184.44 [8042]~P39(x80421,x80423,x80425)+~P39(x80421,x80422,x80424)+P39(x80421,f333(f333(f113(f882(x80421,a870)),x80422),x80423),f333(f333(f113(f882(f881(x80421,x80421),a870)),x80424),x80425)) % 183.90/184.44 [8043]~P39(x80431,x80433,x80435)+~P39(x80431,x80432,x80434)+P39(x80431,f333(f333(f104(f882(x80431,a870)),x80432),x80433),f333(f333(f104(f882(f881(x80431,x80431),a870)),x80434),x80435)) % 183.90/184.44 [8125]E(x81251,x81252)+P1(f333(x81253,x81251))+~P1(f333(f333(f333(f333(a204,f31(x81253,x81254)),x81251),x81255),x81252)) % 183.90/184.44 [8400]E(f333(f333(f268(x84001,x84002),f333(f333(f166(x84001),x84003),x84004)),f333(f333(f166(x84002),x84005),x84004)),f333(f333(f166(f881(x84001,x84002)),f333(f333(f184(x84001,x84002),x84003),x84005)),x84004))+~P1(f333(f333(f248(a875),x84004),f333(f197(f876(x84001)),x84003)))+~P1(f333(f333(f248(a875),x84004),f333(f197(f876(x84002)),x84005))) % 183.90/184.44 [8560]~P39(x85601,x85603,x85604)+P1(f333(f333(f335(x85601),x85602),x85603))+~P1(f333(f333(f335(f881(x85601,x85601)),f333(f333(f268(x85601,x85601),x85605),x85602)),x85604)) % 183.90/184.44 [8561]~P39(x85611,x85613,x85614)+P1(f333(f333(f335(x85611),x85612),x85613))+~P1(f333(f333(f335(f881(x85611,x85611)),f333(f333(f268(x85611,x85611),x85612),x85615)),x85614)) % 183.90/184.44 [8562]~P7(x85621,x85623,x85624)+P1(f333(f333(f335(x85621),x85622),x85623))+~P1(f333(f333(f335(f881(x85621,x85621)),f333(f333(f268(x85621,x85621),x85625),x85622)),x85624)) % 183.90/184.44 [8563]~P7(x85631,x85633,x85634)+P1(f333(f333(f335(x85631),x85632),x85633))+~P1(f333(f333(f335(f881(x85631,x85631)),f333(f333(f268(x85631,x85631),x85632),x85635)),x85634)) % 183.90/184.44 [8821]~P7(x88211,x88215,x88212)+E(f333(f287(x88211,x88211,x88212),f333(f333(f311(x88211),x88213),f196(f882(x88211,a870)))),f333(f287(x88211,x88211,x88212),f333(f333(f311(x88211),x88214),f196(f882(x88211,a870)))))+~P1(f333(f333(f335(f881(x88211,x88211)),f333(f333(f268(x88211,x88211),x88213),x88214)),x88212)) % 183.90/184.44 [8904]~P1(f333(f333(f333(f333(a204,x89042),x89043),x89044),x89045))+~P1(f333(f333(f333(f333(a204,f31(x89041,x89042)),x89045),x89044),x89043))+P1(f333(f333(f333(f333(a204,f31(x89041,x89042)),x89043),x89044),x89043)) % 183.90/184.44 [9015]P1(f333(x90151,x90152))+~P1(f333(f333(f335(x90153),x90152),x90155))+P1(f333(f333(f335(x90153),f378(x90151,x90154,x90155,x90153)),f333(f333(f113(f882(x90153,a870)),x90155),x90154))) % 183.90/184.44 [9016]P1(f333(x90161,x90162))+~P1(f333(f333(f335(x90163),x90162),x90164))+P1(f333(f333(f335(x90163),f378(x90161,x90164,x90165,x90163)),f333(f333(f113(f882(x90163,a870)),x90165),x90164))) % 183.90/184.44 [9024]~P1(f333(x90242,x90245))+~P1(f333(f333(f335(x90241),x90245),x90244))+P1(f333(f333(f335(x90241),f418(x90242,x90243,x90244,x90241)),f333(f333(f113(f882(x90241,a870)),x90244),x90243))) % 183.90/184.44 [9025]~P1(f333(x90252,x90255))+~P1(f333(f333(f335(x90251),x90255),x90253))+P1(f333(f333(f335(x90251),f418(x90252,x90253,x90254,x90251)),f333(f333(f113(f882(x90251,a870)),x90254),x90253))) % 183.90/184.44 [9040]~P1(f333(f333(f247(f882(x90401,a870)),x90403),x90405))+~P1(f333(f333(f247(f882(x90401,a870)),x90402),x90404))+P1(f333(f333(f247(f882(x90401,a870)),f333(f333(f113(f882(x90401,a870)),x90402),x90403)),f333(f333(f113(f882(x90401,a870)),x90404),x90405))) % 183.90/184.44 [9041]~P1(f333(f333(f247(f882(x90411,a870)),x90415),x90413))+~P1(f333(f333(f247(f882(x90411,a870)),x90412),x90414))+P1(f333(f333(f247(f882(x90411,a870)),f333(f333(f22(f882(x90411,a870)),x90412),x90413)),f333(f333(f22(f882(x90411,a870)),x90414),x90415))) % 183.90/184.44 [9042]~P1(f333(f333(f247(f882(x90421,a870)),x90423),x90425))+~P1(f333(f333(f247(f882(x90421,a870)),x90422),x90424))+P1(f333(f333(f247(f882(x90421,a870)),f333(f333(f104(f882(x90421,a870)),x90422),x90423)),f333(f333(f104(f882(x90421,a870)),x90424),x90425))) % 183.90/184.44 [9129]~E(f333(f197(f876(x91291)),x91293),f333(f197(f876(x91292)),x91294))+E(f333(f333(f180(x91291,x91292),f333(f333(f184(x91291,x91292),x91293),x91294)),x91295),f333(f240(x91292),f711(x91295,x91294,x91292,x91293,x91291)))+~P1(f333(f333(f335(x91291),x91295),f333(f174(x91291),x91293))) % 183.90/184.44 [9133]P1(f333(f333(f335(f881(x91331,x91331)),f333(f333(f268(x91331,x91331),x91332),x91333)),f327(x91331,x91334,x91335)))+~P1(f333(f333(f247(a875),f333(x91334,x91332)),f333(x91334,x91333)))+~P1(f333(f333(f335(f881(x91331,x91331)),f333(f333(f268(x91331,x91331),x91332),x91333)),x91335)) % 183.90/184.44 [9318]P1(f333(f333(f335(f881(x93181,x93181)),f333(f333(f268(x93181,x93181),x93182),x93183)),f309(x93181,x93184)))+~P1(f333(f333(f335(f881(x93181,x93181)),f333(f333(f268(x93181,x93181),x93182),x93185)),f309(x93181,x93184)))+~P1(f333(f333(f335(f881(x93181,x93181)),f333(f333(f268(x93181,x93181),x93185),x93183)),x93184)) % 183.90/184.44 [9319]P1(f333(f333(f335(f881(x93191,x93191)),f333(f333(f268(x93191,x93191),x93192),x93193)),f309(x93191,x93194)))+~P1(f333(f333(f335(f881(x93191,x93191)),f333(f333(f268(x93191,x93191),x93195),x93193)),f309(x93191,x93194)))+~P1(f333(f333(f335(f881(x93191,x93191)),f333(f333(f268(x93191,x93191),x93192),x93195)),x93194)) % 183.90/184.44 [9416]E(x94161,x94162)+E(f333(a115,f637(x94163,x94164,x94161,x94162,x94165)),x94164)+~P1(f333(f333(f335(f881(x94165,x94165)),f333(f333(f268(x94165,x94165),x94162),x94161)),f333(f333(f191(f881(x94165,x94165),a870),x94164),x94163))) % 183.90/184.44 [9417]E(x94171,x94172)+E(f333(a115,f639(x94173,x94174,x94171,x94172,x94175)),x94174)+~P1(f333(f333(f335(f881(x94175,x94175)),f333(f333(f268(x94175,x94175),x94172),x94171)),f333(f333(f191(f881(x94175,x94175),a870),x94174),x94173))) % 183.90/184.44 [9418]E(x94181,f2(a875))+E(f333(a115,f637(x94182,x94181,x94183,x94184,x94185)),x94181)+~P1(f333(f333(f335(f881(x94185,x94185)),f333(f333(f268(x94185,x94185),x94184),x94183)),f333(f333(f191(f881(x94185,x94185),a870),x94181),x94182))) % 183.90/184.44 [9419]E(x94191,f2(a875))+E(f333(a115,f639(x94192,x94191,x94193,x94194,x94195)),x94191)+~P1(f333(f333(f335(f881(x94195,x94195)),f333(f333(f268(x94195,x94195),x94194),x94193)),f333(f333(f191(f881(x94195,x94195),a870),x94191),x94192))) % 183.90/184.44 [9435]P1(f333(f333(f335(f881(x94351,x94351)),f333(f333(f268(x94351,x94351),x94352),x94353)),f333(f333(f290(x94351,x94351,x94351),x94354),f309(x94351,x94354))))+~P1(f333(f333(f335(f881(x94351,x94351)),f333(f333(f268(x94351,x94351),x94352),x94355)),x94354))+~P1(f333(f333(f335(f881(x94351,x94351)),f333(f333(f268(x94351,x94351),x94355),x94353)),x94354)) % 183.90/184.44 [9442]~P1(f333(f333(f335(f881(x94421,x94421)),f333(f333(f268(x94421,x94421),x94422),x94425)),f309(x94421,x94424)))+P1(f333(f333(f335(f881(x94421,x94421)),f333(f333(f268(x94421,x94421),x94422),x94423)),f333(f333(f290(x94421,x94421,x94421),x94424),f309(x94421,x94424))))+~P1(f333(f333(f335(f881(x94421,x94421)),f333(f333(f268(x94421,x94421),x94425),x94423)),x94424)) % 183.90/184.44 [9481]~P7(x94811,x94815,x94812)+~P1(f333(f333(f335(f881(x94811,x94811)),f333(f333(f268(x94811,x94811),x94813),x94814)),x94812))+P1(f333(f333(f247(f882(x94811,a870)),f333(f287(x94811,x94811,x94812),f333(f333(f311(x94811),x94813),f196(f882(x94811,a870))))),f333(f287(x94811,x94811,x94812),f333(f333(f311(x94811),x94814),f196(f882(x94811,a870)))))) % 183.90/184.44 [9503]E(x95031,x95032)+P1(f333(f333(f333(f333(a204,x95033),x95031),x95034),f481(x95032,x95034,x95031,x95033,x95035)))+~P1(f333(f333(f333(f333(a204,f31(x95035,x95033)),x95031),x95034),x95032)) % 183.90/184.44 [9507]~P1(f333(x95075,x95072))+P1(f333(f333(f333(f333(a204,x95071),x95072),x95073),f481(x95074,x95073,x95072,x95071,x95075)))+~P1(f333(f333(f333(f333(a204,f31(x95075,x95071)),x95072),x95073),x95074)) % 183.90/184.44 [9536]P1(f333(f333(f335(f881(x95361,x95361)),f333(f333(f268(x95361,x95361),x95362),x95363)),f333(f333(f290(x95361,x95361,x95361),x95364),f309(x95361,x95364))))+~P1(f333(f333(f335(f881(x95361,x95361)),f333(f333(f268(x95361,x95361),x95362),x95365)),f333(f333(f290(x95361,x95361,x95361),x95364),f309(x95361,x95364))))+~P1(f333(f333(f335(f881(x95361,x95361)),f333(f333(f268(x95361,x95361),x95365),x95363)),x95364)) % 183.90/184.44 [9537]P1(f333(f333(f335(f881(x95371,x95371)),f333(f333(f268(x95371,x95371),x95372),x95373)),f333(f333(f290(x95371,x95371,x95371),x95374),f309(x95371,x95374))))+~P1(f333(f333(f335(f881(x95371,x95371)),f333(f333(f268(x95371,x95371),x95375),x95373)),f333(f333(f290(x95371,x95371,x95371),x95374),f309(x95371,x95374))))+~P1(f333(f333(f335(f881(x95371,x95371)),f333(f333(f268(x95371,x95371),x95372),x95375)),x95374)) % 183.90/184.44 [9587]~P1(f333(f66(x95871,x95871,x95874,x95872,x95873),x95875))+P1(f333(f333(f335(x95871),x95872),x95873))+P1(f333(f62(x95871,x95874,f333(f333(f311(x95871),x95872),x95873)),x95875)) % 183.90/184.44 [9626]~E(f333(f312(x96263,x96262,x96265),x96264),x96261)+E(x96261,f196(f882(x96262,a870)))+P1(f333(f333(f247(f882(x96263,a870)),f333(f312(x96262,x96263,f348(x96264,x96263,x96262,x96261)),x96261)),x96264)) % 183.90/184.44 [9673]~P4(x96735)+P1(f333(f333(f335(x96731),f868(x96732,x96733,x96734,x96731,x96735)),x96734))+P1(f333(f333(f247(x96735),f333(f333(f41(x96731,x96735),x96734),x96733)),x96732)) % 183.90/184.44 [9724]P34(x97241,x97242,x97243,x97244,x97245)+~E(f333(f197(f876(x97241)),x97244),f333(f197(f876(x97242)),x97245))+P1(f333(f333(f335(f881(x97241,x97242)),f733(x97245,x97244,x97243,x97242,x97241)),f333(f174(f881(x97241,x97242)),f333(f333(f184(x97241,x97242),x97244),x97245)))) % 183.90/184.44 [9725]P34(x97251,x97252,x97253,x97254,x97255)+~E(f333(f197(f876(x97251)),x97254),f333(f197(f876(x97252)),x97255))+P1(f333(f333(f335(f881(x97251,x97252)),f737(x97253,x97255,x97254,x97252,x97251)),f333(f174(f881(x97251,x97252)),f333(f333(f184(x97251,x97252),x97254),x97255)))) % 183.90/184.44 [9855]E(x98551,x98552)+P1(f333(f333(f333(f333(a204,f31(x98553,x98554)),f481(x98551,x98555,x98552,x98554,x98553)),x98555),x98551))+~P1(f333(f333(f333(f333(a204,f31(x98553,x98554)),x98552),x98555),x98551)) % 183.90/184.44 [9857]~P1(f333(x98571,x98575))+P1(f333(f333(f333(f333(a204,f31(x98571,x98572)),f481(x98573,x98574,x98575,x98572,x98571)),x98574),x98573))+~P1(f333(f333(f333(f333(a204,f31(x98571,x98572)),x98575),x98574),x98573)) % 183.90/184.44 [9865]E(x98651,x98652)+P1(f333(f333(f335(f881(x98653,x98653)),f333(f333(f268(x98653,x98653),x98651),f638(x98654,x98655,x98652,x98651,x98653))),x98654))+~P1(f333(f333(f335(f881(x98653,x98653)),f333(f333(f268(x98653,x98653),x98651),x98652)),f333(f333(f191(f881(x98653,x98653),a870),x98655),x98654))) % 183.90/184.44 [9866]E(x98661,f2(a875))+P1(f333(f333(f335(f881(x98662,x98662)),f333(f333(f268(x98662,x98662),x98663),f638(x98664,x98661,x98665,x98663,x98662))),x98664))+~P1(f333(f333(f335(f881(x98662,x98662)),f333(f333(f268(x98662,x98662),x98663),x98665)),f333(f333(f191(f881(x98662,x98662),a870),x98661),x98664))) % 183.90/184.44 [9909]~P4(x99091)+~P1(f333(f333(f247(x99091),f333(x99094,f868(x99095,x99094,x99093,x99092,x99091))),x99095))+P1(f333(f333(f247(x99091),f333(f333(f41(x99092,x99091),x99093),x99094)),x99095)) % 183.90/184.44 [9951]E(x99511,x99512)+P1(f333(f333(f335(f881(x99513,x99513)),f333(f333(f268(x99513,x99513),f640(x99514,x99515,x99511,x99512,x99513)),x99511)),x99514))+~P1(f333(f333(f335(f881(x99513,x99513)),f333(f333(f268(x99513,x99513),x99512),x99511)),f333(f333(f191(f881(x99513,x99513),a870),x99515),x99514))) % 183.90/184.44 [9952]E(x99521,f2(a875))+P1(f333(f333(f335(f881(x99522,x99522)),f333(f333(f268(x99522,x99522),f640(x99523,x99521,x99524,x99525,x99522)),x99524)),x99523))+~P1(f333(f333(f335(f881(x99522,x99522)),f333(f333(f268(x99522,x99522),x99525),x99524)),f333(f333(f191(f881(x99522,x99522),a870),x99521),x99523))) % 183.90/184.44 [9956]E(x99561,x99562)+P1(f333(f333(f335(f881(x99563,x99563)),f333(f333(f268(x99563,x99563),x99561),f640(x99564,x99565,x99562,x99561,x99563))),f333(f333(f191(f881(x99563,x99563),a870),f639(x99564,x99565,x99562,x99561,x99563)),x99564)))+~P1(f333(f333(f335(f881(x99563,x99563)),f333(f333(f268(x99563,x99563),x99561),x99562)),f333(f333(f191(f881(x99563,x99563),a870),x99565),x99564))) % 183.90/184.44 [9957]E(x99571,f2(a875))+P1(f333(f333(f335(f881(x99572,x99572)),f333(f333(f268(x99572,x99572),x99573),f640(x99574,x99571,x99575,x99573,x99572))),f333(f333(f191(f881(x99572,x99572),a870),f639(x99574,x99571,x99575,x99573,x99572)),x99574)))+~P1(f333(f333(f335(f881(x99572,x99572)),f333(f333(f268(x99572,x99572),x99573),x99575)),f333(f333(f191(f881(x99572,x99572),a870),x99571),x99574))) % 183.90/184.44 [10007]E(x100071,x100072)+P1(f333(f333(f335(f881(x100073,x100073)),f333(f333(f268(x100073,x100073),f638(x100074,x100075,x100071,x100072,x100073)),x100071)),f333(f333(f191(f881(x100073,x100073),a870),f637(x100074,x100075,x100071,x100072,x100073)),x100074)))+~P1(f333(f333(f335(f881(x100073,x100073)),f333(f333(f268(x100073,x100073),x100072),x100071)),f333(f333(f191(f881(x100073,x100073),a870),x100075),x100074))) % 183.90/184.44 [10008]E(x100081,f2(a875))+P1(f333(f333(f335(f881(x100082,x100082)),f333(f333(f268(x100082,x100082),f638(x100083,x100081,x100084,x100085,x100082)),x100084)),f333(f333(f191(f881(x100082,x100082),a870),f637(x100083,x100081,x100084,x100085,x100082)),x100083)))+~P1(f333(f333(f335(f881(x100082,x100082)),f333(f333(f268(x100082,x100082),x100085),x100084)),f333(f333(f191(f881(x100082,x100082),a870),x100081),x100083))) % 183.90/184.44 [10042]~P66(x100422)+~P1(f333(f61(x100421),x100425))+E(f333(f333(f6(x100421,x100422),f333(f333(f7(x100421,x100422,x100422),f333(f333(f18(x100421,x100422,f882(x100422,x100422)),f333(f333(f8(a870,f882(x100422,f882(x100422,x100422)),x100421),f99(x100422)),f333(f333(f7(x100421,f882(x100421,a870),a870),f335(x100421)),x100423))),x100424)),f2(x100422))),x100425),f333(f333(f6(x100421,x100422),x100424),f333(f333(f104(f882(x100421,a870)),x100425),x100423))) % 183.90/184.44 [8623]~P66(x86231)+~P1(f333(f61(x86234),x86235))+E(f333(f333(f79(x86231),f333(x86232,x86233)),f333(f333(f6(x86234,x86231),x86232),f333(f333(f22(f882(x86234,a870)),x86235),f333(f333(f311(x86234),x86233),f196(f882(x86234,a870)))))),f333(f333(f6(x86234,x86231),x86232),f333(f333(f311(x86234),x86233),x86235))) % 183.90/184.44 [8624]~P73(x86241)+~P1(f333(f61(x86244),x86245))+E(f333(f333(f80(x86241),f333(x86242,x86243)),f333(f333(f9(x86244,x86241),x86242),f333(f333(f22(f882(x86244,a870)),x86245),f333(f333(f311(x86244),x86243),f196(f882(x86244,a870)))))),f333(f333(f9(x86244,x86241),x86242),f333(f333(f311(x86244),x86243),x86245))) % 183.90/184.44 [8945]~P106(x89452)+~P14(x89452,f333(f170(x89452),f333(f333(f155(x89451,x89452),x89454),x89455)))+E(f333(f137(x89451,f333(f333(f8(x89452,a870,x89451),f333(f248(x89452),x89453)),x89454)),x89455),f179(x89451,f333(f333(f8(x89452,a870,x89451),f333(f248(x89452),x89453)),x89454),x89455)) % 183.90/184.44 [8970]~P66(x89701)+E(f333(f333(f79(x89701),f333(f333(f6(a875,x89701),x89702),f304(a875,x89703,x89704))),f333(f333(f6(a875,x89701),x89702),f304(a875,f333(f333(f79(a875),x89704),f77(a875)),f333(f333(f79(a875),x89704),x89705)))),f333(f333(f6(a875,x89701),x89702),f304(a875,x89703,f333(f333(f79(a875),x89704),x89705))))+~P1(f333(f333(f247(a875),x89703),f333(f333(f79(a875),x89704),f77(a875)))) % 183.90/184.44 [8971]~P1(f333(f333(f335(x89711),x89714),x89715))+~P1(f333(f333(f247(f882(x89711,a870)),f333(f174(x89711),x89712)),x89715))+P1(f333(f333(f247(f882(x89711,a870)),f333(f174(x89711),f333(f333(f160(x89711,x89712),x89713),x89714))),x89715)) % 183.90/184.44 [9196]~P4(x91962)+~P1(f333(f61(x91961),x91965))+E(f333(f333(f64(x91961,x91962,f333(f333(f8(x91962,f882(x91962,x91962),x91961),f113(x91962)),x91963)),x91964),x91965),f333(f333(f113(x91962),x91964),f333(f333(f41(x91961,x91962),x91965),x91963))) % 183.90/184.44 [9197]~P4(x91972)+~P1(f333(f61(x91971),x91975))+E(f333(f333(f64(x91971,x91972,f333(f333(f8(x91972,f882(x91972,x91972),x91971),f104(x91972)),x91973)),x91974),x91975),f333(f333(f104(x91972),x91974),f333(f333(f42(x91971,x91972),x91975),x91973))) % 183.90/184.44 [9244]E(f333(x92441,x92442),f333(x92441,x92443))+P1(f333(f333(f248(a875),f333(x92441,x92442)),f333(x92441,x92443)))+~P1(f333(f333(f335(f881(x92444,x92444)),f333(f333(f268(x92444,x92444),x92442),x92443)),f154(x92444,f333(f333(f152(f882(x92444,a875)),x92441),x92445)))) % 183.90/184.44 [9275]~E(f333(x92754,x92752),f333(x92754,x92753))+~P1(f333(f333(f335(f881(x92751,x92751)),f333(f333(f268(x92751,x92751),x92752),x92753)),f154(x92751,x92755)))+P1(f333(f333(f335(f881(x92751,x92751)),f333(f333(f268(x92751,x92751),x92752),x92753)),f154(x92751,f333(f333(f152(f882(x92751,a875)),x92754),x92755)))) % 183.90/184.44 [9297]~P25(x92971,x92972,x92973,x92975)+P25(x92971,x92972,x92973,f333(f333(f311(x92971),x92974),x92975))+P1(f333(f333(f335(x92972),f333(x92973,x92974)),f333(f312(x92971,x92972,x92973),f333(f333(f22(f882(x92971,a870)),x92975),f333(f333(f311(x92971),x92974),f196(f882(x92971,a870))))))) % 183.90/184.44 [9301]P1(f333(x93012,x93015))+~P1(f333(f333(f335(x93011),x93015),f333(f174(x93011),x93013)))+E(f333(f333(f139(x93011),f333(f197(f876(x93011)),f179(x93011,x93012,f333(f333(f135(x93011),x93013),x93014)))),f333(f333(f135(x93011),x93013),x93014)),f333(f333(f135(x93011),f333(f333(f139(x93011),f333(f197(f876(x93011)),f179(x93011,x93012,x93013))),x93013)),x93014)) % 183.90/184.44 [9304]~P1(f333(f333(f335(f881(x93041,x93041)),f333(f333(f268(x93041,x93041),x93042),x93043)),f154(x93041,x93045)))+~P1(f333(f333(f247(a875),f333(x93044,x93042)),f333(x93044,x93043)))+P1(f333(f333(f335(f881(x93041,x93041)),f333(f333(f268(x93041,x93041),x93042),x93043)),f154(x93041,f333(f333(f152(f882(x93041,a875)),x93044),x93045)))) % 183.90/184.44 [9369]P1(f333(f333(f335(f881(x93694,x93694)),f333(f333(f268(x93694,x93694),x93692),x93693)),f154(x93694,x93695)))+P1(f333(f333(f248(a875),f333(x93691,x93692)),f333(x93691,x93693)))+~P1(f333(f333(f335(f881(x93694,x93694)),f333(f333(f268(x93694,x93694),x93692),x93693)),f154(x93694,f333(f333(f152(f882(x93694,a875)),x93691),x93695)))) % 183.90/184.44 [9510]~P1(f333(f333(f335(f881(f876(x95101),f876(x95101))),f333(f333(f268(f876(x95101),f876(x95101)),x95102),x95104)),f159(x95101,x95105)))+~P1(f333(f333(f248(a875),x95103),f333(f197(f876(x95101)),x95102)))+P1(f333(f333(f335(f881(x95101,x95101)),f333(f333(f268(x95101,x95101),f333(f333(f166(x95101),x95102),x95103)),f333(f333(f166(x95101),x95104),x95103))),x95105)) % 183.90/184.44 [9752]E(x97521,f2(a1))+~P1(f333(f48(x97523,x97521),f333(f333(f268(a1,a1),x97524),x97525)))+P1(f333(f48(f333(f333(f80(a1),x97522),x97523),x97521),f333(f333(f268(a1,a1),f333(f333(f79(a1),f333(f333(f80(a1),x97522),x97524)),f333(f333(f38(a1),f333(f333(f80(a1),x97522),x97525)),x97521))),f44(a1,f333(f333(f80(a1),x97522),x97525),x97521)))) % 183.90/184.44 [9754]~P1(f333(f333(f248(a875),f2(a875)),x97543))+~P1(f333(f47(x97542,x97543),f333(f333(f268(a875,a875),x97544),x97545)))+P1(f333(f47(f333(f333(f80(a875),x97541),x97542),x97543),f333(f333(f268(a875,a875),f333(f333(f79(a875),f333(f333(f80(a875),x97541),x97544)),f333(f333(f38(a875),f333(f333(f80(a875),x97541),x97545)),x97543))),f44(a875,f333(f333(f80(a875),x97541),x97545),x97543)))) % 183.90/184.44 [10065]~P66(x100652)+~P1(f333(f61(x100651),x100654))+E(f333(f333(f6(x100651,x100652),x100653),f333(f253(x100651),f333(f333(f18(x100651,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100651),a331),f333(f333(f7(x100651,f882(x100651,a870),a870),f335(x100651)),x100654))),f333(f333(f7(x100651,f882(x100651,a870),a870),f335(x100651)),x100655)))),f333(f333(f6(x100651,x100652),f333(f333(f7(x100651,x100652,x100652),f333(f333(f18(x100651,x100652,f882(x100652,x100652)),f333(f333(f8(a870,f882(x100652,f882(x100652,x100652)),x100651),f99(x100652)),f333(f333(f7(x100651,f882(x100651,a870),a870),f335(x100651)),x100655))),x100653)),f2(x100652))),x100654)) % 183.90/184.44 [8254]~E(f333(f333(f135(x82541),x82542),x82545),f333(f333(f135(x82541),x82543),x82544))+E(f333(f333(f135(x82541),f333(f333(f139(x82541),f333(f197(f876(x82541)),x82542)),x82543)),x82544),x82545)+P1(f333(f333(f247(a875),f333(f197(f876(x82541)),x82543)),f333(f197(f876(x82541)),x82542))) % 183.90/184.44 [8454]~E(f333(f333(f135(x84542),x84543),x84541),f333(f333(f135(x84542),x84544),x84545))+E(x84541,f333(f333(f135(x84542),f333(f333(f139(x84542),f333(f197(f876(x84542)),x84543)),x84544)),x84545))+~P1(f333(f333(f247(a875),f333(f197(f876(x84542)),x84543)),f333(f197(f876(x84542)),x84544))) % 183.90/184.44 [8543]~E(f333(f333(f79(a875),f333(f333(f80(a875),x85433),x85434)),x85431),f333(f333(f79(a875),f333(f333(f80(a875),x85432),x85434)),x85435))+~P1(f333(f333(f247(a875),x85433),x85432))+E(x85431,f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x85432),x85433)),x85434)),x85435)) % 183.90/184.44 [8544]~E(f333(f333(f79(a875),f333(f333(f80(a875),x85441),x85443)),x85444),f333(f333(f79(a875),f333(f333(f80(a875),x85442),x85443)),x85445))+~P1(f333(f333(f247(a875),x85442),x85441))+E(f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x85441),x85442)),x85443)),x85444),x85445) % 183.90/184.44 [8699]E(f333(f333(f79(a875),f333(f333(f80(a875),x86991),x86992)),x86993),f333(f333(f79(a875),f333(f333(f80(a875),x86994),x86992)),x86995))+~P1(f333(f333(f247(a875),x86994),x86991))+~E(x86995,f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x86991),x86994)),x86992)),x86993)) % 183.90/184.44 [8700]E(f333(f333(f79(a875),f333(f333(f80(a875),x87001),x87002)),x87003),f333(f333(f79(a875),f333(f333(f80(a875),x87004),x87002)),x87005))+~P1(f333(f333(f247(a875),x87004),x87001))+~E(f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x87001),x87004)),x87002)),x87003),x87005) % 183.90/184.44 [9563]~P58(x95632)+~P1(f333(f61(x95631),x95635))+E(f333(f333(f9(x95631,x95632),f333(f333(f18(x95631,x95632,x95632),f333(f333(f8(x95632,f882(x95632,x95632),x95631),f291(x95632)),x95633)),x95634)),x95635),f333(f333(f291(x95632),f333(f333(f9(x95631,x95632),x95633),x95635)),f333(f333(f9(x95631,x95632),x95634),x95635))) % 183.90/184.44 [9688]~E(f643(x96885,x96884,x96883,x96882,x96881),f644(x96885,x96884,x96883,x96882,x96881))+P1(f333(f333(f335(f881(x96881,x96881)),f333(f333(f268(x96881,x96881),x96882),x96883)),f309(x96881,x96884)))+~P1(f333(f333(f335(f881(x96881,x96881)),f333(f333(f268(x96881,x96881),x96882),x96883)),f309(x96881,f333(f333(f113(f882(f881(x96881,x96881),a870)),x96884),x96885)))) % 183.90/184.44 [9689]~E(f645(x96895,x96894,x96893,x96892,x96891),f646(x96895,x96894,x96893,x96892,x96891))+P1(f333(f333(f335(f881(x96891,x96891)),f333(f333(f268(x96891,x96891),x96892),x96893)),f309(x96891,x96894)))+~P1(f333(f333(f335(f881(x96891,x96891)),f333(f333(f268(x96891,x96891),x96892),x96893)),f309(x96891,f333(f333(f113(f882(f881(x96891,x96891),a870)),x96894),x96895)))) % 183.90/184.44 [9899]P1(f333(f333(f335(f881(x98991,x98991)),f333(f333(f268(x98991,x98991),x98992),f644(x98995,x98994,x98993,x98992,x98991))),f309(x98991,x98994)))+P1(f333(f333(f335(f881(x98991,x98991)),f333(f333(f268(x98991,x98991),x98992),x98993)),f309(x98991,x98994)))+~P1(f333(f333(f335(f881(x98991,x98991)),f333(f333(f268(x98991,x98991),x98992),x98993)),f309(x98991,f333(f333(f113(f882(f881(x98991,x98991),a870)),x98994),x98995)))) % 183.90/184.44 [9978]P1(f333(f333(f335(f881(x99781,x99781)),f333(f333(f268(x99781,x99781),f646(x99785,x99784,x99783,x99782,x99781)),x99783)),f309(x99781,x99784)))+P1(f333(f333(f335(f881(x99781,x99781)),f333(f333(f268(x99781,x99781),x99782),x99783)),f309(x99781,x99784)))+~P1(f333(f333(f335(f881(x99781,x99781)),f333(f333(f268(x99781,x99781),x99782),x99783)),f309(x99781,f333(f333(f113(f882(f881(x99781,x99781),a870)),x99784),x99785)))) % 183.90/184.44 [10014]P1(f333(f333(f335(f881(x100141,x100141)),f333(f333(f268(x100141,x100141),x100142),x100143)),f309(x100141,x100144)))+P1(f333(f333(f335(f881(x100141,x100141)),f333(f333(f268(x100141,x100141),f644(x100145,x100144,x100143,x100142,x100141)),f643(x100145,x100144,x100143,x100142,x100141))),x100145))+~P1(f333(f333(f335(f881(x100141,x100141)),f333(f333(f268(x100141,x100141),x100142),x100143)),f309(x100141,f333(f333(f113(f882(f881(x100141,x100141),a870)),x100144),x100145)))) % 183.90/184.44 [10015]P1(f333(f333(f335(f881(x100151,x100151)),f333(f333(f268(x100151,x100151),x100152),x100153)),f309(x100151,x100154)))+P1(f333(f333(f335(f881(x100151,x100151)),f333(f333(f268(x100151,x100151),f645(x100155,x100154,x100153,x100152,x100151)),f646(x100155,x100154,x100153,x100152,x100151))),x100155))+~P1(f333(f333(f335(f881(x100151,x100151)),f333(f333(f268(x100151,x100151),x100152),x100153)),f309(x100151,f333(f333(f113(f882(f881(x100151,x100151),a870)),x100154),x100155)))) % 183.90/184.44 [10136]~P1(f333(f333(f335(f881(f876(x101361),f876(x101361))),f333(f333(f268(f876(x101361),f876(x101361)),x101364),x101365)),f159(x101361,x101362)))+~P1(f333(f333(f335(f881(x101361,x101361)),x101363),f333(f174(f881(x101361,x101361)),f333(f333(f184(x101361,x101361),x101364),x101365))))+P1(f333(f333(f272(x101361,x101361,a870),f333(f333(f7(x101361,f882(f881(x101361,x101361),a870),f882(x101361,a870)),f333(f333(f8(f882(x101361,f882(f882(f881(x101361,x101361),a870),a870)),f882(f882(f881(x101361,x101361),a870),f882(x101361,a870)),x101361),f7(x101361,f882(f881(x101361,x101361),a870),a870)),f333(f333(f8(f882(x101361,f881(x101361,x101361)),f882(x101361,f882(f882(f881(x101361,x101361),a870),a870)),x101361),f333(f8(f881(x101361,x101361),f882(f882(f881(x101361,x101361),a870),a870),x101361),f335(f881(x101361,x101361)))),f268(x101361,x101361)))),x101362)),x101363)) % 183.90/184.44 [9591]~P1(f333(f333(f247(a875),x95913),x95912))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),x95913),x95914)),x95911)),f333(f333(f79(a875),f333(f333(f80(a875),x95912),x95914)),x95915)))+P1(f333(f333(f248(a875),x95911),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x95912),x95913)),x95914)),x95915))) % 183.90/184.44 [9592]~P1(f333(f333(f247(a875),x95923),x95922))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),x95923),x95924)),x95921)),f333(f333(f79(a875),f333(f333(f80(a875),x95922),x95924)),x95925)))+P1(f333(f333(f247(a875),x95921),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x95922),x95923)),x95924)),x95925))) % 183.90/184.44 [9610]~P1(f333(f333(f247(a875),x96101),x96104))+P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),x96101),x96102)),x96103)),f333(f333(f79(a875),f333(f333(f80(a875),x96104),x96102)),x96105)))+~P1(f333(f333(f248(a875),x96103),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x96104),x96101)),x96102)),x96105))) % 183.90/184.44 [9611]~P1(f333(f333(f247(a875),x96111),x96114))+P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),x96111),x96112)),x96113)),f333(f333(f79(a875),f333(f333(f80(a875),x96114),x96112)),x96115)))+~P1(f333(f333(f247(a875),x96113),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x96114),x96111)),x96112)),x96115))) % 183.90/184.44 [9722]~P1(f333(f333(f247(a875),x97222),x97221))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),x97221),x97223)),x97224)),f333(f333(f79(a875),f333(f333(f80(a875),x97222),x97223)),x97225)))+P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x97221),x97222)),x97223)),x97224)),x97225)) % 183.90/184.44 [9723]~P1(f333(f333(f247(a875),x97232),x97231))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),x97231),x97233)),x97234)),f333(f333(f79(a875),f333(f333(f80(a875),x97232),x97233)),x97235)))+P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x97231),x97232)),x97233)),x97234)),x97235)) % 183.90/184.44 [9776]~P1(f333(f333(f247(a875),x97764),x97761))+P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),x97761),x97762)),x97763)),f333(f333(f79(a875),f333(f333(f80(a875),x97764),x97762)),x97765)))+~P1(f333(f333(f248(a875),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x97761),x97764)),x97762)),x97763)),x97765)) % 183.90/184.44 [9777]~P1(f333(f333(f247(a875),x97774),x97771))+P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),x97771),x97772)),x97773)),f333(f333(f79(a875),f333(f333(f80(a875),x97774),x97772)),x97775)))+~P1(f333(f333(f247(a875),f333(f333(f79(a875),f333(f333(f80(a875),f333(f333(f22(a875),x97771),x97774)),x97772)),x97773)),x97775)) % 183.90/184.44 [9999]~P12(x99991,x99992,x99995,x99993)+~P1(f333(f333(f335(f881(x99991,x99991)),x99994),x99995))+P1(f333(f333(f272(x99991,x99991,a870),f333(f333(f7(x99991,f882(x99991,x99992),f882(x99991,a870)),f333(f333(f8(f882(x99992,a870),f882(f882(x99991,x99992),f882(x99991,a870)),x99991),f8(x99992,a870,x99991)),f333(f333(f8(x99992,f882(x99992,a870),x99991),a330),x99993))),x99993)),x99994)) % 183.90/184.44 [6785]~E(f333(x67854,x67855),f209(x67852))+E(f333(f187(x67851,x67852,x67853,x67854),x67855),f333(f240(x67852),x67856))+~E(f333(x67853,x67855),f333(f240(x67852),x67856)) % 183.90/184.44 [6886]~E(f333(x68863,x68866),f209(x68861))+E(f333(f242(f879(x68861),x68862,f209(x68861),x68863),f333(x68864,x68865)),f209(x68861))+~E(f333(x68864,x68865),f333(f240(x68862),x68866)) % 183.90/184.44 [7471]E(f333(x74711,x74712),f209(x74713))+~E(f333(f187(x74715,x74713,x74716,x74711),x74712),f333(f240(x74713),x74714))+E(f333(x74711,x74712),f333(f240(x74713),x74714)) % 183.90/184.44 [7507]~E(f333(f187(x75076,x75073,x75075,x75071),x75072),f333(f240(x75073),x75074))+E(f333(x75071,x75072),f333(f240(x75073),x75074))+E(f333(x75075,x75072),f333(f240(x75073),x75074)) % 183.90/184.44 [8413]~P19(x84136,x84131,x84132,x84134)+E(f333(f72(x84131,x84131,x84131,f333(x84132,x84133)),f333(x84134,x84135)),f333(f72(x84131,x84131,x84131,f333(x84134,x84135)),f333(x84132,x84133)))+~P1(f333(f61(x84136),x84135)) % 183.90/184.44 [8833]~P25(x88331,x88333,x88335,x88336)+~P25(x88333,x88332,x88334,f333(f312(x88331,x88333,x88335),x88336))+P25(x88331,x88332,f333(f72(x88333,x88332,x88331,x88334),x88335),x88336) % 183.90/184.44 [9401]~P1(f333(f333(x94013,x94012),x94016))+~P1(f333(f333(x94014,x94015),x94012))+P1(f333(f333(f335(x94011),x94012),f301(x94011,x94013,x94014,x94015,x94016))) % 183.90/184.44 [9402]~P1(f333(f333(x94024,x94022),x94026))+~P1(f333(f333(x94023,x94025),x94022))+P1(f333(f333(f335(x94021),x94022),f298(x94021,x94023,x94024,x94025,x94026))) % 183.90/184.44 [9511]E(x95111,x95112)+E(x95113,x95114)+~P1(f333(f333(f335(f881(f876(x95115),f876(x95115))),f333(f333(f268(f876(x95115),f876(x95115)),f333(f333(f152(x95115),x95113),x95111)),f333(f333(f152(x95115),x95114),x95112))),f158(x95115,x95116))) % 183.90/184.44 [9520]~E(x95202,x95204)+P1(f333(f333(f335(f881(f876(x95201),f876(x95201))),f333(f333(f268(f876(x95201),f876(x95201)),f333(f333(f152(x95201),x95202),x95203)),f333(f333(f152(x95201),x95204),x95205))),f146(x95201,x95206)))+~P1(f333(f333(f335(f881(f876(x95201),f876(x95201))),f333(f333(f268(f876(x95201),f876(x95201)),x95203),x95205)),f146(x95201,x95206))) % 183.90/184.44 [9521]~E(x95212,x95214)+P1(f333(f333(f335(f881(f876(x95211),f876(x95211))),f333(f333(f268(f876(x95211),f876(x95211)),f333(f333(f152(x95211),x95212),x95213)),f333(f333(f152(x95211),x95214),x95215))),f148(x95211,x95216)))+~P1(f333(f333(f335(f881(f876(x95211),f876(x95211))),f333(f333(f268(f876(x95211),f876(x95211)),x95213),x95215)),f148(x95211,x95216))) % 183.90/184.44 [9522]~E(x95222,x95224)+P1(f333(f333(f335(f881(f876(x95221),f876(x95221))),f333(f333(f268(f876(x95221),f876(x95221)),f333(f333(f152(x95221),x95222),x95223)),f333(f333(f152(x95221),x95224),x95225))),f158(x95221,x95226)))+~P1(f333(f333(f335(f881(f876(x95221),f876(x95221))),f333(f333(f268(f876(x95221),f876(x95221)),x95223),x95225)),f158(x95221,x95226))) % 183.90/184.44 [9523]~E(x95232,x95234)+P1(f333(f333(f335(f881(f876(x95231),f876(x95231))),f333(f333(f268(f876(x95231),f876(x95231)),f333(f333(f135(x95231),x95232),x95233)),f333(f333(f135(x95231),x95234),x95235))),f158(x95231,x95236)))+~P1(f333(f333(f335(f881(f876(x95231),f876(x95231))),f333(f333(f268(f876(x95231),f876(x95231)),x95233),x95235)),f158(x95231,x95236))) % 183.90/184.44 [9524]~E(x95243,x95245)+P1(f333(f333(f335(f881(f876(x95241),f876(x95241))),f333(f333(f268(f876(x95241),f876(x95241)),f333(f333(f135(x95241),x95242),x95243)),f333(f333(f135(x95241),x95244),x95245))),f158(x95241,x95246)))+~P1(f333(f333(f335(f881(f876(x95241),f876(x95241))),f333(f333(f268(f876(x95241),f876(x95241)),x95242),x95244)),f158(x95241,x95246))) % 183.90/184.44 [9579]E(x95791,x95792)+P1(f333(f333(f335(f881(f876(x95793),f876(x95793))),f333(f333(f268(f876(x95793),f876(x95793)),x95791),x95792)),f158(x95793,x95794)))+~P1(f333(f333(f335(f881(f876(x95793),f876(x95793))),f333(f333(f268(f876(x95793),f876(x95793)),f333(f333(f152(x95793),x95795),x95791)),f333(f333(f152(x95793),x95796),x95792))),f158(x95793,x95794))) % 183.90/184.44 [9726]~E(x97263,x97265)+P1(f333(f333(f335(f881(f876(x97261),f876(x97261))),f333(f333(f268(f876(x97261),f876(x97261)),f333(f333(f135(x97261),x97262),f333(f333(f152(x97261),x97263),f116(x97261)))),f333(f333(f135(x97261),x97264),f333(f333(f152(x97261),x97265),f116(x97261))))),f158(x97261,x97266)))+~P1(f333(f333(f335(f881(f876(x97261),f876(x97261))),f333(f333(f268(f876(x97261),f876(x97261)),x97262),x97264)),f158(x97261,x97266))) % 183.90/184.44 [9742]E(f333(x97421,x97422),f209(x97423))+~E(f333(f242(f879(x97426),x97423,f209(x97426),x97424),f333(x97421,x97422)),f209(x97426))+E(f333(x97424,f767(x97422,x97421,x97424,x97425,x97426,x97423)),f209(x97426)) % 183.90/184.44 [9743]E(f333(x97431,x97432),f209(x97433))+~E(f333(f242(f879(x97436),x97433,f209(x97436),x97434),f333(x97431,x97432)),f209(x97436))+E(f333(f240(x97433),f767(x97432,x97431,x97434,x97435,x97436,x97433)),f333(x97431,x97432)) % 183.90/184.44 [9780]E(x97801,x97802)+E(x97803,x97804)+~P1(f333(f333(f335(f881(f876(x97805),f876(x97805))),f333(f333(f268(f876(x97805),f876(x97805)),f333(f333(f135(x97805),x97803),f333(f333(f152(x97805),x97801),f116(x97805)))),f333(f333(f135(x97805),x97804),f333(f333(f152(x97805),x97802),f116(x97805))))),f158(x97805,x97806))) % 183.90/184.44 [9805]E(x98051,x98052)+~P1(f333(f333(f335(f881(f876(x98053),f876(x98053))),f333(f333(f268(f876(x98053),f876(x98053)),f333(f333(f135(x98053),x98051),f333(f333(f152(x98053),x98055),f116(x98053)))),f333(f333(f135(x98053),x98052),f333(f333(f152(x98053),x98056),f116(x98053))))),f158(x98053,x98054)))+P1(f333(f333(f335(f881(f876(x98053),f876(x98053))),f333(f333(f268(f876(x98053),f876(x98053)),x98051),x98052)),f158(x98053,x98054))) % 183.90/184.44 [9841]~P1(f333(f333(f335(f881(f882(x98411,a870),f882(x98411,a870))),f333(f333(f268(f882(x98411,a870),f882(x98411,a870)),x98412),x98414)),f325(x98411,x98416)))+~P1(f333(f333(f335(f881(f882(x98411,a870),f882(x98411,a870))),f333(f333(f268(f882(x98411,a870),f882(x98411,a870)),x98413),x98415)),f325(x98411,x98416)))+P1(f333(f333(f335(f881(f882(x98411,a870),f882(x98411,a870))),f333(f333(f268(f882(x98411,a870),f882(x98411,a870)),f333(f333(f113(f882(x98411,a870)),x98412),x98413)),f333(f333(f113(f882(x98411,a870)),x98414),x98415))),f325(x98411,x98416))) % 183.90/184.44 [5240]~E(f333(x52403,x52406),x52405)+~E(x52404,f333(f240(x52401),x52406))+E(f333(f333(f210(x52401,x52402),x52403),x52404),f333(f240(x52402),x52405)) % 183.90/184.44 [5655]~E(f333(f333(f135(x56551),x56556),x56553),x56555)+E(f333(f333(f135(x56551),x56552),x56553),f333(f333(f152(x56551),x56554),x56555))+~E(x56552,f333(f333(f152(x56551),x56554),x56556)) % 183.90/184.44 [5656]~E(f333(f333(f135(x56561),x56566),x56563),x56565)+E(f333(f333(f135(x56561),x56562),x56563),f333(f333(f135(x56561),x56564),x56565))+~E(x56562,f333(f333(f135(x56561),x56564),x56566)) % 183.90/184.44 [5658]E(f333(f333(f135(x56581),x56582),x56583),f333(f333(f152(x56581),x56584),x56585))+~E(f333(f333(f152(x56581),x56584),x56586),x56582)+~E(x56585,f333(f333(f135(x56581),x56586),x56583)) % 183.90/184.44 [5660]~E(f333(f333(f135(x56601),x56602),x56606),x56604)+E(f333(f333(f135(x56601),x56602),x56603),f333(f333(f135(x56601),x56604),x56605))+~E(x56603,f333(f333(f135(x56601),x56606),x56605)) % 183.90/184.44 [6779]E(f333(x67791,x67792),f333(x67793,x67792))+~E(f333(f333(f155(x67794,x67795),x67791),x67796),f333(f333(f155(x67794,x67795),x67793),x67796))+~P1(f333(f333(f335(x67794),x67792),f333(f174(x67794),x67796))) % 183.90/184.44 [7165]~P19(x71654,x71655,x71656,x71651)+E(f333(f333(x71651,x71652),x71653),f333(f333(f64(x71654,x71655,x71656),x71653),x71652))+~P1(f333(f61(x71654),x71652)) % 183.90/184.44 [7231]~E(x72312,f333(x72314,x72316))+~P1(f333(f333(f335(x72313),x72316),x72315))+P1(f333(f333(f335(x72311),x72312),f333(f312(x72313,x72311,x72314),x72315))) % 183.90/184.44 [7232]~E(f333(x72324,x72322),x72326)+~P1(f333(f333(f335(x72323),x72326),x72325))+P1(f333(f333(f335(x72321),x72322),f333(f313(x72321,x72323,x72324),x72325))) % 183.90/184.44 [7688]~P32(x76881,x76882,x76884,x76886)+P32(x76881,x76882,f333(f333(f152(x76881),x76883),x76884),f333(f333(f152(x76881),x76885),x76886))+~P1(f333(f333(x76882,x76883),x76885)) % 183.90/184.44 [8707]~P51(x87074,x87075,x87071,x87072,x87076)+E(f333(x87071,f333(x87072,x87073)),x87073)+~P1(f333(f333(f335(x87075),x87073),x87076)) % 183.90/184.44 [9513]E(x95131,x95132)+E(f333(f197(f876(x95133)),x95134),f333(f197(f876(x95133)),x95135))+~P1(f333(f333(f335(f881(f876(x95133),f876(x95133))),f333(f333(f268(f876(x95133),f876(x95133)),f333(f333(f152(x95133),x95131),x95134)),f333(f333(f152(x95133),x95132),x95135))),f146(x95133,x95136))) % 183.90/184.44 [9575]~P16(x95751,x95752,x95753)+E(f333(f333(f64(x95751,x95752,x95753),x95754),x95755),x95756)+~P1(f333(f66(x95751,x95752,x95753,x95754,x95755),x95756)) % 183.90/184.44 [9582]E(f333(f197(f876(x95821)),x95822),f333(f197(f876(x95821)),x95823))+P1(f333(f333(f335(f881(f876(x95821),f876(x95821))),f333(f333(f268(f876(x95821),f876(x95821)),x95822),x95823)),f146(x95821,x95824)))+~P1(f333(f333(f335(f881(f876(x95821),f876(x95821))),f333(f333(f268(f876(x95821),f876(x95821)),f333(f333(f152(x95821),x95825),x95822)),f333(f333(f152(x95821),x95826),x95823))),f146(x95821,x95824))) % 183.90/184.44 [9604]~P1(f333(f333(f335(f881(x96041,x96041)),f333(f333(f268(x96041,x96041),x96042),x96044)),f309(x96041,x96046)))+P1(f333(f333(f335(f881(f876(x96041),f876(x96041))),f333(f333(f268(f876(x96041),f876(x96041)),f333(f333(f152(x96041),x96042),x96043)),f333(f333(f152(x96041),x96044),x96045))),f309(f876(x96041),f158(x96041,x96046))))+~P1(f333(f333(f335(f881(f876(x96041),f876(x96041))),f333(f333(f268(f876(x96041),f876(x96041)),x96043),x96045)),f309(f876(x96041),f158(x96041,x96046)))) % 183.90/184.44 [9786]~P1(f333(x97862,x97866))+~E(f333(f137(x97861,x97862),x97863),f333(f333(f152(x97861),x97864),x97865))+~P1(f333(f333(f335(x97861),x97866),f333(f174(x97861),f787(x97865,x97864,x97863,x97862,x97861)))) % 183.90/184.44 [9787]~P1(f333(x97874,x97876))+~E(f333(f333(f152(x97871),x97872),x97873),f333(f137(x97871,x97874),x97875))+~P1(f333(f333(f335(x97871),x97876),f333(f174(x97871),f784(x97875,x97874,x97873,x97872,x97871)))) % 183.90/184.44 [10093]~P66(x100932)+E(f333(f333(f6(x100931,x100932),f333(f333(f8(f882(x100933,a870),x100932,x100931),f333(f6(x100933,x100932),x100934)),f333(f333(f8(f882(x100933,a870),f882(x100933,a870),x100931),f253(x100933)),f333(f333(f8(f882(x100933,a870),f882(x100933,a870),x100931),f333(f18(x100933,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100933),a331),f333(f333(f7(x100933,f882(x100933,a870),a870),f335(x100933)),x100935)))),f333(f7(x100933,x100931,a870),f333(f333(f8(x100931,f882(x100931,a870),x100933),a330),x100936)))))),f333(f312(x100933,x100931,x100936),x100935)),f333(f333(f6(x100933,x100932),x100934),x100935))+~P1(f333(f61(x100933),x100935)) % 183.90/184.44 [6837]~P106(x68373)+P1(f333(x68372,x68375))+E(f333(f137(x68371,x68372),f333(f333(f149(x68371,x68373,x68374),x68375),x68376)),f333(f137(x68371,x68372),x68376)) % 183.90/184.44 [6839]P1(f333(x68391,x68392))+~E(f168(x68393,x68391,x68394),f333(f333(f268(f876(x68393),f876(x68393)),x68395),x68396))+~P1(f333(f333(f335(x68393),x68392),f333(f174(x68393),x68395))) % 183.90/184.44 [6883]~P1(f333(x68832,x68836))+~E(f168(x68831,x68832,x68833),f333(f333(f268(f876(x68831),f876(x68831)),x68834),x68835))+~P1(f333(f333(f335(x68831),x68836),f333(f174(x68831),x68835))) % 183.90/184.44 [7552]~P15(x75521,x75522,x75523)+~P1(f333(f61(x75521),x75526))+E(f333(f333(f64(x75521,x75522,x75523),x75524),f333(f333(f311(x75521),x75525),x75526)),f333(f333(f64(x75521,x75522,x75523),f333(f333(x75523,x75525),x75524)),x75526)) % 183.90/184.44 [7602]~P106(x76022)+~P1(f333(f333(f247(x76022),f333(x76023,x76024)),f333(x76023,x76025)))+E(f333(f333(f149(x76021,x76022,x76023),x76024),f333(f333(f152(x76021),x76025),x76026)),f333(f333(f152(x76021),x76024),f333(f333(f152(x76021),x76025),x76026))) % 183.90/184.44 [7719]E(x77191,x77192)+~E(f333(f333(f270(x77193,x77194),x77191),f333(f16(f882(x77194,a870),x77193),x77195)),f333(f333(f270(x77193,x77194),x77192),f333(f16(f882(x77194,a870),x77193),x77195)))+~P1(f333(f333(f335(x77194),x77196),x77195)) % 183.90/184.44 [7787]~P15(x77871,x77872,x77873)+~P1(f333(f61(x77871),x77876))+E(f333(f333(f64(x77871,x77872,x77873),x77874),f333(f333(f311(x77871),x77875),x77876)),f333(f333(x77873,x77875),f333(f333(f64(x77871,x77872,x77873),x77874),x77876))) % 183.90/184.44 [7904]~P16(x79041,x79042,x79043)+~P1(f333(f61(x79041),x79046))+E(f333(f333(f64(x79041,x79042,x79043),f333(f333(x79043,x79044),x79045)),x79046),f333(f333(x79043,x79044),f333(f333(f64(x79041,x79042,x79043),x79045),x79046))) % 183.90/184.44 [7974]~P20(x79742,x79745,x79746,x79741)+~P1(f333(f61(x79742),x79744))+E(f333(x79741,f333(f333(f311(x79742),x79743),x79744)),f333(f72(x79745,x79745,x79745,f333(x79741,x79744)),f333(x79746,x79743))) % 183.90/184.44 [8012]~P106(x80122)+P1(f333(f333(f247(x80122),f333(x80123,x80124)),f333(x80123,x80125)))+E(f333(f333(f149(x80121,x80122,x80123),x80124),f333(f333(f152(x80121),x80125),x80126)),f333(f333(f152(x80121),x80125),f333(f333(f149(x80121,x80122,x80123),x80124),x80126))) % 183.90/184.44 [8155]~E(f333(f197(f876(x81551)),x81555),f333(f197(f876(x81552)),x81556))+~E(f333(f197(f876(x81551)),x81553),f333(f197(f876(x81552)),x81554))+E(f333(f333(f135(f881(x81551,x81552)),f333(f333(f184(x81551,x81552),x81553),x81554)),f333(f333(f184(x81551,x81552),x81555),x81556)),f333(f333(f184(x81551,x81552),f333(f333(f135(x81551),x81553),x81555)),f333(f333(f135(x81552),x81554),x81556))) % 183.90/184.44 [8269]~E(x82692,f333(f312(x82693,x82691,x82694),x82696))+P1(f333(f333(f247(f882(x82691,a870)),x82692),f333(f312(x82693,x82691,x82694),x82695)))+~P1(f333(f333(f247(f882(x82693,a870)),x82696),x82695)) % 183.90/184.44 [8370]~P106(x83705)+E(f333(x83701,x83702),f333(x83701,x83703))+E(f333(f333(f149(x83704,x83705,x83701),x83702),f333(f333(f149(x83704,x83705,x83701),x83703),x83706)),f333(f333(f149(x83704,x83705,x83701),x83703),f333(f333(f149(x83704,x83705,x83701),x83702),x83706))) % 183.90/184.44 [8406]~P25(x84063,x84061,x84064,x84065)+P25(x84063,x84061,f333(f333(f333(f71(x84063,x84061),x84064),x84066),x84062),x84065)+P1(f333(f333(f335(x84061),x84062),f333(f312(x84063,x84061,x84064),x84065))) % 183.90/184.44 [8552]~P1(f333(f333(f335(x85522),x85524),f333(x85526,x85523)))+~P1(f333(f333(f335(x85521),x85523),x85525))+P1(f333(f333(f335(f881(x85521,x85522)),f333(f333(f268(x85521,x85522),x85523),x85524)),f333(f333(f270(x85521,x85522),x85525),x85526))) % 183.90/184.44 [9013]~P66(x90132)+~P25(x90134,x90131,x90135,x90136)+E(f333(f333(f6(x90131,x90132),x90133),f333(f312(x90134,x90131,x90135),x90136)),f333(f333(f6(x90134,x90132),f333(f72(x90131,x90132,x90134,x90133),x90135)),x90136)) % 183.90/184.44 [9014]~P73(x90142)+~P25(x90144,x90141,x90145,x90146)+E(f333(f333(f9(x90141,x90142),x90143),f333(f312(x90144,x90141,x90145),x90146)),f333(f333(f9(x90144,x90142),f333(f72(x90141,x90142,x90144,x90143),x90145)),x90146)) % 183.90/184.44 [9062]~P34(x90622,x90625,x90621,x90623,x90626)+P1(f333(f333(x90621,f333(f333(f166(x90622),x90623),x90624)),f333(f333(f166(x90625),x90626),x90624)))+~P1(f333(f333(f248(a875),x90624),f333(f197(f876(x90625)),x90626))) % 183.90/184.44 [9063]~P34(x90632,x90635,x90631,x90633,x90636)+P1(f333(f333(x90631,f333(f333(f166(x90632),x90633),x90634)),f333(f333(f166(x90635),x90636),x90634)))+~P1(f333(f333(f248(a875),x90634),f333(f197(f876(x90632)),x90633))) % 183.90/184.44 [9271]~P19(x92713,x92711,x92716,x92712)+~P1(f333(f61(x92713),x92714))+E(f333(f72(x92711,x92711,x92711,f333(x92712,f333(f333(f22(f882(x92713,a870)),x92714),f333(f333(f311(x92713),x92715),f196(f882(x92713,a870)))))),f333(x92716,x92715)),f333(x92712,f333(f333(f311(x92713),x92715),x92714))) % 183.90/184.44 [9879]~E(f333(f312(x98792,x98794,x98796),f256(f882(x98792,a870))),f256(f882(x98794,a870)))+~E(f333(f312(x98791,x98793,x98795),f256(f882(x98791,a870))),f256(f882(x98793,a870)))+E(f333(f312(f881(x98791,x98792),f881(x98793,x98794),f273(x98791,x98793,x98792,x98794,x98795,x98796)),f256(f882(f881(x98791,x98792),a870))),f256(f882(f881(x98793,x98794),a870))) % 183.90/184.44 [9927]~P25(x99273,x99274,x99275,f333(x99276,f844(x99276,x99275,x99274,x99273,x99272,x99271)))+P25(x99273,x99274,x99275,f333(f333(f42(x99272,f882(x99273,a870)),x99271),x99276))+E(x99271,f196(f882(x99272,a870))) % 183.90/184.44 [9985]P25(x99856,x99855,x99854,f333(f333(f42(x99852,f882(x99856,a870)),x99851),x99853))+E(x99851,f196(f882(x99852,a870)))+P1(f333(f333(f335(x99852),f844(x99853,x99854,x99855,x99856,x99852,x99851)),x99851)) % 183.90/184.44 [9990]P1(f333(f333(f335(x99901),f618(x99902,x99903,x99904,x99905,x99906,x99901)),x99906))+P1(f333(f333(f247(f882(f881(x99901,x99904),a870)),f333(f333(f270(x99901,x99904),x99906),x99903)),f333(f333(f270(x99901,x99904),x99905),x99902)))+~P1(f333(f333(f247(f882(x99901,a870)),x99906),x99905)) % 183.90/184.44 [10028]P24(x100286,x100285,f333(f333(f311(f874(x100286)),f333(f333(f333(f91(x100286),x100281),x100283),x100282)),f196(f882(f874(x100286),a870))))+~P24(x100286,x100285,f333(f333(f311(f874(x100286)),f333(f333(f333(f91(x100286),x100284),x100283),x100282)),f196(f882(f874(x100286),a870))))+P1(f333(f333(x100281,f786(x100281,x100282,x100283,x100284,x100285,x100286)),f830(x100281,x100282,x100283,x100284,x100285,x100286))) % 183.90/184.44 [10029]P24(x100296,x100295,f333(f333(f311(f874(x100296)),f333(f333(f333(f91(x100296),x100294),x100293),x100292)),f196(f882(f874(x100296),a870))))+~P24(x100296,x100295,f333(f333(f311(f874(x100296)),f333(f333(f333(f91(x100296),x100294),x100293),x100291)),f196(f882(f874(x100296),a870))))+P1(f333(f333(x100291,f840(x100292,x100291,x100293,x100294,x100295,x100296)),f856(x100292,x100291,x100293,x100294,x100295,x100296))) % 183.90/184.44 [10068]~P24(x100681,x100682,f333(f333(f311(f874(x100681)),f333(f333(f333(f91(x100681),x100683),x100684),x100686)),f196(f882(f874(x100681),a870))))+P24(x100681,x100682,f333(f333(f311(f874(x100681)),f333(f333(f333(f91(x100681),x100683),x100684),x100685)),f196(f882(f874(x100681),a870))))+~P1(f333(f333(x100685,f840(x100685,x100686,x100684,x100683,x100682,x100681)),f856(x100685,x100686,x100684,x100683,x100682,x100681))) % 183.90/184.44 [10069]~P24(x100691,x100692,f333(f333(f311(f874(x100691)),f333(f333(f333(f91(x100691),x100696),x100694),x100695)),f196(f882(f874(x100691),a870))))+P24(x100691,x100692,f333(f333(f311(f874(x100691)),f333(f333(f333(f91(x100691),x100693),x100694),x100695)),f196(f882(f874(x100691),a870))))+~P1(f333(f333(x100696,f786(x100693,x100695,x100694,x100696,x100692,x100691)),f830(x100693,x100695,x100694,x100696,x100692,x100691))) % 183.90/184.44 [10104]~P1(f333(f333(f247(f882(x101042,a870)),f333(x101044,f618(x101046,x101044,x101042,x101045,x101043,x101041))),f333(x101046,f618(x101046,x101044,x101042,x101045,x101043,x101041))))+~P1(f333(f333(f247(f882(x101041,a870)),x101043),x101045))+P1(f333(f333(f247(f882(f881(x101041,x101042),a870)),f333(f333(f270(x101041,x101042),x101043),x101044)),f333(f333(f270(x101041,x101042),x101045),x101046))) % 183.90/184.44 [7739]~P1(f333(x77391,x77395))+~P1(f333(x77396,x77394))+P1(f333(x77391,f333(f271(x77392,x77393),f333(f333(f268(x77392,x77393),x77394),x77395)))) % 183.90/184.44 [7740]~P1(f333(x77401,x77404))+~P1(f333(x77406,x77405))+P1(f333(x77401,f333(f267(x77402,x77403),f333(f333(f268(x77402,x77403),x77404),x77405)))) % 183.90/184.44 [7763]~E(f333(f197(f876(x77631)),x77633),f333(f197(f876(x77634)),x77635))+~E(f333(f333(f180(x77631,x77634),f333(f333(f184(x77631,x77634),x77633),x77635)),x77632),f333(f240(x77634),x77636))+P1(f333(f333(f335(x77631),x77632),f333(f174(x77631),x77633))) % 183.90/184.44 [7792]~P1(f333(f333(x77924,x77926),x77925))+~P1(f333(f333(f335(x77921),x77926),x77923))+P1(f333(f333(f333(f41(x77921,f882(x77922,a870)),x77923),x77924),x77925)) % 183.90/184.44 [8103]~P1(f333(f333(f335(x81031),x81032),f333(x81035,x81036)))+~P1(f333(f333(f335(x81033),x81036),x81034))+P1(f333(f333(f335(x81031),x81032),f333(f333(f41(x81033,f882(x81031,a870)),x81034),x81035))) % 183.90/184.44 [8147]P1(f333(f333(x81471,x81472),x81473))+~P1(f333(f333(x81474,x81472),x81473))+~P1(f333(f333(f247(f882(x81475,f882(x81476,a870))),x81474),x81471)) % 183.90/184.44 [8293]P1(f333(f333(x82931,x82932),x82933))+~P1(f333(f333(f335(x82934),x82932),x82935))+~P1(f333(f333(f333(f42(x82934,f882(x82936,a870)),x82935),x82931),x82933)) % 183.90/184.44 [8430]P1(f333(f333(f335(x84301),x84302),f333(x84303,x84304)))+~P1(f333(f333(f335(x84305),x84304),x84306))+~P1(f333(f333(f335(x84301),x84302),f333(f333(f42(x84305,f882(x84301,a870)),x84306),x84303))) % 183.90/184.44 [8620]~P1(f333(f333(f333(f333(a204,x86201),x86203),x86204),x86206))+~P1(f333(f333(f333(f333(a204,x86202),x86206),x86204),x86205))+P1(f333(f333(f333(f333(a204,f32(x86201,x86202)),x86203),x86204),x86205)) % 183.90/184.44 [8689]~P12(x86894,x86895,x86896,x86891)+E(f333(x86891,x86892),f333(x86891,x86893))+~P1(f333(f333(f335(f881(x86894,x86894)),f333(f333(f268(x86894,x86894),x86892),x86893)),x86896)) % 183.90/184.44 [8720]P1(f333(f333(f247(f882(x87201,a870)),x87202),f333(x87203,x87204)))+~P1(f333(f333(f335(x87205),x87204),x87206))+~P1(f333(f333(f247(f882(x87201,a870)),x87202),f333(f333(f42(x87205,f882(x87201,a870)),x87206),x87203))) % 183.90/184.44 [8748]~P49(x87483,x87484,f333(f288(x87484,x87483),x87485))+E(x87481,f196(f882(x87482,a870)))+E(f333(f333(f42(x87482,f882(x87483,a870)),x87481),f333(f333(f8(f882(x87484,a870),f882(x87483,a870),x87482),f287(x87484,x87483,x87485)),x87486)),f333(f287(x87484,x87483,x87485),f333(f333(f42(x87482,f882(x87484,a870)),x87481),x87486))) % 183.90/184.44 [8824]P1(f333(f333(f335(x88241),x88242),f333(f287(x88243,x88241,x88244),x88245)))+~P1(f333(f333(f335(x88243),x88246),x88245))+~P1(f333(f333(f335(f881(x88243,x88241)),f333(f333(f268(x88243,x88241),x88246),x88242)),x88244)) % 183.90/184.45 [8944]P1(f333(x89441,x89442))+~P1(f333(f333(f333(f333(a204,x89444),x89442),x89445),x89446))+P1(f333(f333(f333(f333(a204,f29(x89441,x89443,x89444)),x89442),x89445),x89446)) % 183.90/184.45 [8961]~P1(f333(x89611,x89614))+~P1(f333(f333(f333(f333(a204,x89612),x89614),x89615),x89616))+P1(f333(f333(f333(f333(a204,f29(x89611,x89612,x89613)),x89614),x89615),x89616)) % 183.90/184.45 [9135]P1(f333(f333(f247(f882(x91351,a870)),f333(f287(x91352,x91351,x91353),x91354)),f333(f287(x91352,x91351,x91355),x91356)))+~P1(f333(f333(f247(f882(x91352,a870)),x91354),x91356))+~P1(f333(f333(f247(f882(f881(x91352,x91351),a870)),x91353),x91355)) % 183.90/184.45 [9223]P1(f333(x92231,x92232))+P1(f333(f333(f333(f333(a204,x92233),x92232),x92234),x92235))+~P1(f333(f333(f333(f333(a204,f29(x92231,x92236,x92233)),x92232),x92234),x92235)) % 183.90/184.45 [9228]~P1(f333(x92285,x92282))+P1(f333(f333(f333(f333(a204,x92281),x92282),x92283),x92284))+~P1(f333(f333(f333(f333(a204,f29(x92285,x92281,x92286)),x92282),x92283),x92284)) % 183.90/184.45 [9278]P1(f333(f333(f333(f333(a204,x92781),x92782),x92783),x92784))+P1(f333(f333(f333(f333(a204,x92785),x92782),x92783),x92784))+~P1(f333(f333(f333(f333(a204,f29(x92786,x92781,x92785)),x92782),x92783),x92784)) % 183.90/184.45 [9320]~P1(f333(f333(f335(x93202),x93206),x93204))+~P1(f333(f333(f247(f882(x93201,a870)),x93203),x93205))+P1(f333(f333(f247(f882(f881(x93201,x93202),a870)),f333(f333(f270(x93201,x93202),x93203),f333(f16(f882(x93202,a870),x93201),x93204))),f333(f333(f270(x93201,x93202),x93205),f333(f16(f882(x93202,a870),x93201),x93204)))) % 183.90/184.45 [9333]~P34(x93331,x93332,x93333,x93335,x93336)+P1(f333(f333(f272(x93331,x93332,a870),x93333),x93334))+~P1(f333(f333(f335(f881(x93331,x93332)),x93334),f333(f174(f881(x93331,x93332)),f333(f333(f184(x93331,x93332),x93335),x93336)))) % 183.90/184.45 [9467]~E(x94673,x94675)+P1(f333(f333(f335(f881(f876(x94671),f876(x94671))),f333(f333(f268(f876(x94671),f876(x94671)),f333(f333(f152(x94671),x94672),x94673)),f333(f333(f152(x94671),x94674),x94675))),f158(x94671,x94676)))+~P1(f333(f333(f335(f881(x94671,x94671)),f333(f333(f268(x94671,x94671),x94672),x94674)),x94676)) % 183.90/184.45 [9473]~E(f333(f197(f876(x94731)),x94735),f333(f197(f876(x94732)),x94736))+E(f189(x94731,x94732,f190(x94731,x94732,x94733,f333(f333(f22(f882(x94731,a870)),x94734),f333(f174(x94731),x94735))),x94735,x94736),f190(x94731,x94732,f189(x94731,x94732,x94733,x94735,x94736),x94734))+~P1(f333(f333(f247(f882(x94731,a870)),f333(f174(x94731),x94735)),x94734)) % 183.90/184.45 [9474]~E(f333(f197(f876(x94741)),x94743),f333(f197(f876(x94741)),x94745))+P1(f333(f333(f335(f881(f876(x94741),f876(x94741))),f333(f333(f268(f876(x94741),f876(x94741)),f333(f333(f152(x94741),x94742),x94743)),f333(f333(f152(x94741),x94744),x94745))),f146(x94741,x94746)))+~P1(f333(f333(f335(f881(x94741,x94741)),f333(f333(f268(x94741,x94741),x94742),x94744)),x94746)) % 183.90/184.45 [9504]P1(f333(f333(f335(f881(x95041,x95041)),f333(f333(f268(x95041,x95041),x95042),x95043)),f333(f333(f191(f881(x95041,x95041),a870),f333(a115,x95044)),x95045)))+~P1(f333(f333(f335(f881(x95041,x95041)),f333(f333(f268(x95041,x95041),x95046),x95043)),x95045))+~P1(f333(f333(f335(f881(x95041,x95041)),f333(f333(f268(x95041,x95041),x95042),x95046)),f333(f333(f191(f881(x95041,x95041),a870),x95044),x95045))) % 183.90/184.45 [9505]P1(f333(f333(f335(f881(x95051,x95051)),f333(f333(f268(x95051,x95051),x95052),x95053)),f333(f333(f191(f881(x95051,x95051),a870),f333(a115,x95054)),x95055)))+~P1(f333(f333(f335(f881(x95051,x95051)),f333(f333(f268(x95051,x95051),x95052),x95056)),x95055))+~P1(f333(f333(f335(f881(x95051,x95051)),f333(f333(f268(x95051,x95051),x95056),x95053)),f333(f333(f191(f881(x95051,x95051),a870),x95054),x95055))) % 183.90/184.45 [9509]~P1(f333(f333(f335(x95094),x95095),x95096))+P1(f333(f333(f247(f882(x95091,a870)),x95092),x95093))+~P1(f333(f333(f247(f882(f881(x95091,x95094),a870)),f333(f333(f270(x95091,x95094),x95092),f333(f16(f882(x95094,a870),x95091),x95096))),f333(f333(f270(x95091,x95094),x95093),f333(f16(f882(x95094,a870),x95091),x95096)))) % 183.90/184.45 [9553]E(x95531,x95532)+~P1(f333(f333(f335(f881(f876(x95533),f876(x95533))),f333(f333(f268(f876(x95533),f876(x95533)),f333(f333(f152(x95533),x95531),x95535)),f333(f333(f152(x95533),x95532),x95536))),f146(x95533,x95534)))+P1(f333(f333(f335(f881(x95533,x95533)),f333(f333(f268(x95533,x95533),x95531),x95532)),x95534)) % 183.90/184.45 [9554]E(x95541,x95542)+~P1(f333(f333(f335(f881(f876(x95543),f876(x95543))),f333(f333(f268(f876(x95543),f876(x95543)),f333(f333(f152(x95543),x95541),x95545)),f333(f333(f152(x95543),x95542),x95546))),f148(x95543,x95544)))+P1(f333(f333(f335(f881(x95543,x95543)),f333(f333(f268(x95543,x95543),x95541),x95542)),x95544)) % 183.90/184.45 [9555]E(x95551,x95552)+~P1(f333(f333(f335(f881(f876(x95553),f876(x95553))),f333(f333(f268(f876(x95553),f876(x95553)),f333(f333(f152(x95553),x95551),x95555)),f333(f333(f152(x95553),x95552),x95556))),f158(x95553,x95554)))+P1(f333(f333(f335(f881(x95553,x95553)),f333(f333(f268(x95553,x95553),x95551),x95552)),x95554)) % 183.90/184.45 [9590]P1(f333(f333(f335(f881(f876(x95901),f876(x95901))),f333(f333(f268(f876(x95901),f876(x95901)),f333(f333(f152(x95901),x95902),x95903)),f333(f333(f152(x95901),x95904),x95905))),f159(x95901,x95906)))+~P1(f333(f333(f335(f881(f876(x95901),f876(x95901))),f333(f333(f268(f876(x95901),f876(x95901)),x95903),x95905)),f159(x95901,x95906)))+~P1(f333(f333(f335(f881(x95901,x95901)),f333(f333(f268(x95901,x95901),x95902),x95904)),x95906)) % 183.90/184.45 [9608]P1(f333(x96081,x96082))+~P1(f333(x96081,f836(x96081,x96083,x96084,x96085,x96086)))+~P1(f333(f333(f335(x96086),x96082),f333(f333(f41(x96085,f882(x96086,a870)),x96084),x96083))) % 183.90/184.45 [9613]~P1(f333(f333(f335(f881(f876(x96131),f876(x96131))),f333(f333(f268(f876(x96131),f876(x96131)),f333(f333(f152(x96131),x96132),x96135)),f333(f333(f152(x96131),x96133),x96136))),f146(x96131,x96134)))+P1(f333(f333(f335(f881(f876(x96131),f876(x96131))),f333(f333(f268(f876(x96131),f876(x96131)),x96135),x96136)),f146(x96131,x96134)))+P1(f333(f333(f335(f881(x96131,x96131)),f333(f333(f268(x96131,x96131),x96132),x96133)),x96134)) % 183.90/184.45 [9614]~P1(f333(f333(f335(f881(f876(x96141),f876(x96141))),f333(f333(f268(f876(x96141),f876(x96141)),f333(f333(f152(x96141),x96142),x96145)),f333(f333(f152(x96141),x96143),x96146))),f148(x96141,x96144)))+P1(f333(f333(f335(f881(f876(x96141),f876(x96141))),f333(f333(f268(f876(x96141),f876(x96141)),x96145),x96146)),f148(x96141,x96144)))+P1(f333(f333(f335(f881(x96141,x96141)),f333(f333(f268(x96141,x96141),x96142),x96143)),x96144)) % 183.90/184.45 [9615]~P1(f333(f333(f335(f881(f876(x96151),f876(x96151))),f333(f333(f268(f876(x96151),f876(x96151)),f333(f333(f152(x96151),x96152),x96155)),f333(f333(f152(x96151),x96153),x96156))),f158(x96151,x96154)))+P1(f333(f333(f335(f881(f876(x96151),f876(x96151))),f333(f333(f268(f876(x96151),f876(x96151)),x96155),x96156)),f158(x96151,x96154)))+P1(f333(f333(f335(f881(x96151,x96151)),f333(f333(f268(x96151,x96151),x96152),x96153)),x96154)) % 183.90/184.45 [9698]P1(f333(x96981,x96982))+P1(f333(f333(f335(x96983),f837(x96981,x96984,x96985,x96983,x96986)),x96985))+~P1(f333(f333(f335(x96986),x96982),f333(f333(f41(x96983,f882(x96986,a870)),x96985),x96984))) % 183.90/184.45 [9709]~E(x97092,x97094)+P1(f333(f333(f335(f881(f876(x97091),f876(x97091))),f333(f333(f268(f876(x97091),f876(x97091)),f333(f333(f135(x97091),x97092),f333(f333(f152(x97091),x97093),f116(x97091)))),f333(f333(f135(x97091),x97094),f333(f333(f152(x97091),x97095),f116(x97091))))),f158(x97091,x97096)))+~P1(f333(f333(f335(f881(x97091,x97091)),f333(f333(f268(x97091,x97091),x97093),x97095)),x97096)) % 183.90/184.45 [9796]E(x97961,x97962)+~P1(f333(f333(f335(f881(f876(x97963),f876(x97963))),f333(f333(f268(f876(x97963),f876(x97963)),f333(f333(f135(x97963),x97965),f333(f333(f152(x97963),x97961),f116(x97963)))),f333(f333(f135(x97963),x97966),f333(f333(f152(x97963),x97962),f116(x97963))))),f158(x97963,x97964)))+P1(f333(f333(f335(f881(x97963,x97963)),f333(f333(f268(x97963,x97963),x97961),x97962)),x97964)) % 183.90/184.45 [9824]~P1(f333(f333(f335(f881(f876(x98241),f876(x98241))),f333(f333(f268(f876(x98241),f876(x98241)),f333(f333(f135(x98241),x98245),f333(f333(f152(x98241),x98242),f116(x98241)))),f333(f333(f135(x98241),x98246),f333(f333(f152(x98241),x98243),f116(x98241))))),f158(x98241,x98244)))+P1(f333(f333(f335(f881(f876(x98241),f876(x98241))),f333(f333(f268(f876(x98241),f876(x98241)),x98245),x98246)),f158(x98241,x98244)))+P1(f333(f333(f335(f881(x98241,x98241)),f333(f333(f268(x98241,x98241),x98242),x98243)),x98244)) % 183.90/184.45 [9842]P1(f333(x98421,x98422))+P1(f333(f333(f335(x98423),f836(x98421,x98424,x98425,x98426,x98423)),f333(x98424,f837(x98421,x98424,x98425,x98426,x98423))))+~P1(f333(f333(f335(x98423),x98422),f333(f333(f41(x98426,f882(x98423,a870)),x98425),x98424))) % 183.90/184.45 [8839]~P16(x88393,x88394,x88391)+~P1(f333(f61(x88393),x88396))+E(f333(f333(x88391,x88392),f333(f333(f64(x88393,x88394,x88391),x88395),f333(f333(f22(f882(x88393,a870)),x88396),f333(f333(f311(x88393),x88392),f196(f882(x88393,a870)))))),f333(f333(f64(x88393,x88394,x88391),x88395),f333(f333(f311(x88393),x88392),x88396))) % 183.90/184.45 [8927]~E(f333(f333(f180(x89271,x89272),x89274),x89275),f333(f240(x89272),x89276))+~P1(f333(f333(x89273,x89275),x89276))+E(f333(f333(f180(x89271,x89272),f333(f137(f881(x89271,x89272),f333(f272(x89271,x89272,a870),x89273)),x89274)),x89275),f333(f240(x89272),x89276)) % 183.90/184.45 [9142]~P1(f333(f333(f335(x91425),x91423),x91426))+P1(f333(f333(f247(f882(x91421,a870)),f333(x91422,x91423)),x91424))+~P1(f333(f333(f247(f882(x91421,a870)),f333(f333(f41(x91425,f882(x91421,a870)),x91426),x91422)),x91424)) % 183.90/184.45 [9769]~P7(x97691,x97695,x97694)+P1(f333(f333(f335(f881(x97691,x97691)),f333(f333(f268(x97691,x97691),x97692),x97693)),x97694))+~P1(f333(f333(f335(x97691),x97696),f333(f333(f104(f882(x97691,a870)),f333(f287(x97691,x97691,x97694),f333(f333(f311(x97691),x97692),f196(f882(x97691,a870))))),f333(f287(x97691,x97691,x97694),f333(f333(f311(x97691),x97693),f196(f882(x97691,a870))))))) % 183.90/184.45 [8587]~P103(x85872)+~E(f333(f333(f79(x85872),f333(f333(f80(x85872),x85874),x85875)),x85871),f333(f333(f79(x85872),f333(f333(f80(x85872),x85873),x85875)),x85876))+E(x85871,f333(f333(f79(x85872),f333(f333(f80(x85872),f333(f333(f22(x85872),x85873),x85874)),x85875)),x85876)) % 183.90/184.45 [8588]~P103(x85881)+~E(f333(f333(f79(x85881),f333(f333(f80(x85881),x85882),x85884)),x85885),f333(f333(f79(x85881),f333(f333(f80(x85881),x85883),x85884)),x85886))+E(f333(f333(f79(x85881),f333(f333(f80(x85881),f333(f333(f22(x85881),x85882),x85883)),x85884)),x85885),x85886) % 183.90/184.45 [8751]~P103(x87511)+E(f333(f333(f79(x87511),f333(f333(f80(x87511),x87512),x87513)),x87514),f333(f333(f79(x87511),f333(f333(f80(x87511),x87515),x87513)),x87516))+~E(x87516,f333(f333(f79(x87511),f333(f333(f80(x87511),f333(f333(f22(x87511),x87512),x87515)),x87513)),x87514)) % 183.90/184.45 [8752]~P103(x87521)+E(f333(f333(f79(x87521),f333(f333(f80(x87521),x87522),x87523)),x87524),f333(f333(f79(x87521),f333(f333(f80(x87521),x87525),x87523)),x87526))+~E(f333(f333(f79(x87521),f333(f333(f80(x87521),f333(f333(f22(x87521),x87522),x87525)),x87523)),x87524),x87526) % 183.90/184.45 [9082]~P1(f333(f333(x90824,x90825),x90826))+~P1(f333(f333(x90823,x90825),x90826))+P1(f333(f333(f333(f333(f104(f882(x90821,f882(x90822,a870))),x90823),x90824),x90825),x90826)) % 183.90/184.45 [9341]P1(f333(f333(x93411,x93412),x93413))+P1(f333(f333(x93414,x93412),x93413))+~P1(f333(f333(f333(f333(f113(f882(x93415,f882(x93416,a870))),x93414),x93411),x93412),x93413)) % 183.90/184.45 [9628]~P123(x96281)+~P1(f333(f333(f248(x96281),f333(f333(f79(x96281),f333(f333(f80(x96281),x96284),x96285)),x96282)),f333(f333(f79(x96281),f333(f333(f80(x96281),x96283),x96285)),x96286)))+P1(f333(f333(f248(x96281),x96282),f333(f333(f79(x96281),f333(f333(f80(x96281),f333(f333(f22(x96281),x96283),x96284)),x96285)),x96286))) % 183.90/184.45 [9629]~P123(x96291)+~P1(f333(f333(f247(x96291),f333(f333(f79(x96291),f333(f333(f80(x96291),x96294),x96295)),x96292)),f333(f333(f79(x96291),f333(f333(f80(x96291),x96293),x96295)),x96296)))+P1(f333(f333(f247(x96291),x96292),f333(f333(f79(x96291),f333(f333(f80(x96291),f333(f333(f22(x96291),x96293),x96294)),x96295)),x96296))) % 183.90/184.45 [9652]~P123(x96521)+P1(f333(f333(f248(x96521),f333(f333(f79(x96521),f333(f333(f80(x96521),x96522),x96523)),x96524)),f333(f333(f79(x96521),f333(f333(f80(x96521),x96525),x96523)),x96526)))+~P1(f333(f333(f248(x96521),x96524),f333(f333(f79(x96521),f333(f333(f80(x96521),f333(f333(f22(x96521),x96525),x96522)),x96523)),x96526))) % 183.90/184.45 [9653]~P123(x96531)+P1(f333(f333(f247(x96531),f333(f333(f79(x96531),f333(f333(f80(x96531),x96532),x96533)),x96534)),f333(f333(f79(x96531),f333(f333(f80(x96531),x96535),x96533)),x96536)))+~P1(f333(f333(f247(x96531),x96534),f333(f333(f79(x96531),f333(f333(f80(x96531),f333(f333(f22(x96531),x96535),x96532)),x96533)),x96536))) % 183.90/184.45 [9757]~P123(x97571)+~P1(f333(f333(f248(x97571),f333(f333(f79(x97571),f333(f333(f80(x97571),x97572),x97574)),x97575)),f333(f333(f79(x97571),f333(f333(f80(x97571),x97573),x97574)),x97576)))+P1(f333(f333(f248(x97571),f333(f333(f79(x97571),f333(f333(f80(x97571),f333(f333(f22(x97571),x97572),x97573)),x97574)),x97575)),x97576)) % 183.90/184.45 [9758]~P123(x97581)+~P1(f333(f333(f247(x97581),f333(f333(f79(x97581),f333(f333(f80(x97581),x97582),x97584)),x97585)),f333(f333(f79(x97581),f333(f333(f80(x97581),x97583),x97584)),x97586)))+P1(f333(f333(f247(x97581),f333(f333(f79(x97581),f333(f333(f80(x97581),f333(f333(f22(x97581),x97582),x97583)),x97584)),x97585)),x97586)) % 183.90/184.45 [9807]~P123(x98071)+P1(f333(f333(f248(x98071),f333(f333(f79(x98071),f333(f333(f80(x98071),x98072),x98073)),x98074)),f333(f333(f79(x98071),f333(f333(f80(x98071),x98075),x98073)),x98076)))+~P1(f333(f333(f248(x98071),f333(f333(f79(x98071),f333(f333(f80(x98071),f333(f333(f22(x98071),x98072),x98075)),x98073)),x98074)),x98076)) % 183.90/184.45 [9808]~P123(x98081)+P1(f333(f333(f247(x98081),f333(f333(f79(x98081),f333(f333(f80(x98081),x98082),x98083)),x98084)),f333(f333(f79(x98081),f333(f333(f80(x98081),x98085),x98083)),x98086)))+~P1(f333(f333(f247(x98081),f333(f333(f79(x98081),f333(f333(f80(x98081),f333(f333(f22(x98081),x98082),x98085)),x98083)),x98084)),x98086)) % 183.90/184.45 [9979]~P66(x99792)+~P1(f333(f61(x99791),x99796))+E(f333(f333(f6(x99791,x99792),f333(f333(f18(x99791,x99792,x99792),f333(f333(f18(x99791,x99792,f882(x99792,x99792)),f333(f333(f8(a870,f882(x99792,f882(x99792,x99792)),x99791),f99(x99792)),x99793)),x99794)),x99795)),x99796),f333(f333(f79(x99792),f333(f333(f6(x99791,x99792),x99794),f333(f333(f104(f882(x99791,a870)),x99796),f333(f253(x99791),x99793)))),f333(f333(f6(x99791,x99792),x99795),f333(f333(f104(f882(x99791,a870)),x99796),f333(f78(f882(x99791,a870)),f333(f253(x99791),x99793)))))) % 183.90/184.45 [10038]P1(f333(f333(f335(x100382),x100384),x100386))+P1(f333(f333(f335(x100382),x100385),x100386))+E(f333(f313(x100381,x100382,f333(f333(f7(x100381,x100382,x100382),f333(f333(f7(x100381,x100382,f882(x100382,x100382)),f333(f333(f8(a870,f882(x100382,f882(x100382,x100382)),x100381),f99(x100382)),f333(f333(f7(x100381,f882(x100381,a870),a870),f335(x100381)),x100383))),x100384)),x100385)),x100386),f196(f882(x100381,a870))) % 183.90/184.45 [10039]P1(f333(f333(f335(x100392),x100395),x100396))+~P1(f333(f333(f335(x100392),x100394),x100396))+E(f333(f313(x100391,x100392,f333(f333(f7(x100391,x100392,x100392),f333(f333(f7(x100391,x100392,f882(x100392,x100392)),f333(f333(f8(a870,f882(x100392,f882(x100392,x100392)),x100391),f99(x100392)),f333(f333(f7(x100391,f882(x100391,a870),a870),f335(x100391)),x100393))),x100394)),x100395)),x100396),x100393) % 183.90/184.45 [10040]P1(f333(f333(f335(x100402),x100404),x100406))+~P1(f333(f333(f335(x100402),x100405),x100406))+E(f333(f313(x100401,x100402,f333(f333(f7(x100401,x100402,x100402),f333(f333(f7(x100401,x100402,f882(x100402,x100402)),f333(f333(f8(a870,f882(x100402,f882(x100402,x100402)),x100401),f99(x100402)),f333(f333(f7(x100401,f882(x100401,a870),a870),f335(x100401)),x100403))),x100404)),x100405)),x100406),f333(f78(f882(x100401,a870)),x100403)) % 183.90/184.45 [10041]~P1(f333(f333(f335(x100412),x100414),x100416))+~P1(f333(f333(f335(x100412),x100415),x100416))+E(f333(f313(x100411,x100412,f333(f333(f7(x100411,x100412,x100412),f333(f333(f7(x100411,x100412,f882(x100412,x100412)),f333(f333(f8(a870,f882(x100412,f882(x100412,x100412)),x100411),f99(x100412)),f333(f333(f7(x100411,f882(x100411,a870),a870),f335(x100411)),x100413))),x100414)),x100415)),x100416),f256(f882(x100411,a870))) % 183.90/184.45 [10170]P24(x101701,x101702,f333(f333(f311(f874(x101701)),f333(f333(f333(f91(x101701),f333(x101703,x101704)),f333(a25,x101704)),f333(x101705,x101704))),f196(f882(f874(x101701),a870))))+~P1(f333(f333(f335(a873),x101704),x101706))+~P24(x101701,f333(f333(f113(f882(f874(x101701),a870)),x101702),f333(f312(a873,f874(x101701),f333(f333(f18(a873,f882(x101701,f882(a872,a870)),f874(x101701)),f333(f333(f18(a873,a871,f882(f882(x101701,f882(a872,a870)),f874(x101701))),f333(f333(f8(f882(x101701,f882(a872,a870)),f882(a871,f882(f882(x101701,f882(a872,a870)),f874(x101701))),a873),f91(x101701)),x101703)),a25)),x101705)),x101706)),f333(f312(a873,f874(x101701),f333(f333(f18(a873,f882(x101701,f882(a872,a870)),f874(x101701)),f333(f333(f18(a873,a871,f882(f882(x101701,f882(a872,a870)),f874(x101701))),f333(f333(f8(f882(x101701,f882(a872,a870)),f882(a871,f882(f882(x101701,f882(a872,a870)),f874(x101701))),a873),f91(x101701)),x101703)),f333(f333(f8(f879(a871),a871,a873),f244(a871)),a27))),x101705)),x101706)) % 183.90/184.45 [8617]E(x86171,x86172)+~P51(x86174,x86175,x86173,x86176,x86177)+~E(f333(x86173,x86171),f333(x86173,x86172)) % 183.90/184.45 [6991]E(f333(f242(f879(x69911),x69912,f209(x69911),x69913),f333(x69914,x69915)),f333(f240(x69911),x69916))+~E(f333(x69914,x69915),f333(f240(x69912),x69917))+~E(f333(x69913,x69917),f333(f240(x69911),x69916)) % 183.90/184.45 [8645]~P9(x86456,x86455,x86457,x86454,x86451)+E(f333(f333(x86451,x86452),x86453),x86454)+P1(f333(f61(x86455),x86453)) % 183.90/184.45 [9494]P42(x94941,x94942,x94943,x94944,x94945,f333(f333(x94943,x94946),x94947))+~E(f333(f333(x94943,x94946),x94947),x94944)+~E(x94945,f196(f882(x94941,a870))) % 183.90/184.45 [9674]~P1(f333(x96746,x96743))+~P1(f333(f333(f335(f881(x96742,x96742)),f333(f333(f268(x96742,x96742),x96744),x96745)),f333(x96747,x96743)))+P1(f333(f333(f335(f881(f881(x96741,x96742),f881(x96741,x96742))),f333(f333(f268(f881(x96741,x96742),f881(x96741,x96742)),f333(f333(f268(x96741,x96742),x96743),x96744)),f333(f333(f268(x96741,x96742),x96743),x96745))),f285(x96741,x96742,x96746,x96747))) % 183.90/184.45 [10095]~P42(x100952,x100957,x100953,x100956,x100951,f333(f333(x100953,x100955),x100954))+E(f333(f333(x100953,f714(x100954,x100955,x100951,x100956,x100953,x100957,x100952)),f725(x100954,x100955,x100951,x100956,x100953,x100957,x100952)),f333(f333(x100953,x100955),x100954))+E(x100951,f196(f882(x100952,a870))) % 183.90/184.45 [10096]~P42(x100967,x100966,x100961,x100964,x100965,f333(f333(x100961,x100962),x100963))+E(f333(f333(x100961,f714(x100963,x100962,x100965,x100964,x100961,x100966,x100967)),f725(x100963,x100962,x100965,x100964,x100961,x100966,x100967)),f333(f333(x100961,x100962),x100963))+E(f333(f333(x100961,x100962),x100963),x100964) % 183.90/184.45 [9180]~P34(x91801,x91802,x91803,x91805,x91807)+P34(x91801,x91802,x91803,f333(f333(f152(x91801),x91804),x91805),f333(f333(f152(x91802),x91806),x91807))+~P1(f333(f333(x91803,x91804),x91806)) % 183.90/184.45 [9198]P34(x91981,x91982,x91983,x91984,x91985)+~P34(x91981,x91982,x91983,f333(f333(f135(x91981),x91986),x91984),f333(f333(f135(x91982),x91987),x91985))+~E(f333(f197(f876(x91981)),x91986),f333(f197(f876(x91982)),x91987)) % 183.90/184.45 [9199]P34(x91991,x91992,x91993,x91994,x91995)+~P34(x91991,x91992,x91993,f333(f333(f135(x91991),x91994),x91996),f333(f333(f135(x91992),x91995),x91997))+~E(f333(f197(f876(x91991)),x91994),f333(f197(f876(x91992)),x91995)) % 183.90/184.45 [9404]~P34(x94041,x94042,x94043,x94045,x94047)+~P34(x94041,x94042,x94043,x94044,x94046)+P34(x94041,x94042,x94043,f333(f333(f135(x94041),x94044),x94045),f333(f333(f135(x94042),x94046),x94047)) % 183.90/184.45 [9746]~P1(f333(f66(x97461,x97464,x97465,x97466,x97463),x97467))+P1(f333(f66(x97461,x97464,x97465,x97466,f333(f333(f311(x97461),x97462),x97463)),f333(f333(x97465,x97462),x97467)))+P1(f333(f333(f335(x97461),x97462),x97463)) % 183.90/184.45 [9877]~P25(x98773,x98771,x98774,f256(f882(x98773,a870)))+E(f333(f333(f180(x98771,x98772),f333(f333(f155(f881(x98773,x98772),f881(x98771,x98772)),f333(f272(x98773,x98772,f881(x98771,x98772)),f333(f333(f8(x98771,f882(x98772,f881(x98771,x98772)),x98773),f268(x98771,x98772)),x98774))),x98775)),f333(x98774,x98776)),f333(f240(x98772),x98777))+~E(f333(f333(f180(x98773,x98772),x98775),x98776),f333(f240(x98772),x98777)) % 183.90/184.45 [10116]~P42(x101162,x101167,x101166,x101165,x101161,f333(f333(x101166,x101164),x101163))+E(x101161,f196(f882(x101162,a870)))+P1(f333(f333(f335(x101162),f714(x101163,x101164,x101161,x101165,x101166,x101167,x101162)),x101161)) % 183.90/184.45 [10117]~P42(x101175,x101177,x101171,x101174,x101176,f333(f333(x101171,x101172),x101173))+E(f333(f333(x101171,x101172),x101173),x101174)+P1(f333(f333(f335(x101175),f714(x101173,x101172,x101176,x101174,x101171,x101177,x101175)),x101176)) % 183.90/184.45 [6778]~E(x67785,x67787)+~E(x67786,x67784)+E(f333(f333(f333(f333(f71(x67781,f879(x67782)),x67783),x67784),f333(f240(x67782),x67785)),x67786),f333(f240(x67782),x67787)) % 183.90/184.45 [6907]E(x69071,x69072)+~E(f333(x69075,x69071),f333(f240(x69074),x69077))+E(f333(f333(f333(f333(f71(x69073,f879(x69074)),x69075),x69072),f333(f240(x69074),x69076)),x69071),f333(f240(x69074),x69077)) % 183.90/184.45 [7627]E(x76271,x76272)+~E(x76273,x76274)+~E(f333(f333(f333(f333(f71(x76275,f879(x76276)),x76277),x76274),f333(f240(x76276),x76271)),x76273),f333(f240(x76276),x76272)) % 183.90/184.45 [7694]E(x76941,x76942)+E(f333(x76943,x76944),f333(f240(x76945),x76941))+~E(f333(f333(f333(f333(f71(x76946,f879(x76945)),x76943),x76947),f333(f240(x76945),x76942)),x76944),f333(f240(x76945),x76941)) % 183.90/184.45 [7695]E(x76951,x76952)+E(f333(x76953,x76951),f333(f240(x76954),x76955))+~E(f333(f333(f333(f333(f71(x76956,f879(x76954)),x76953),x76952),f333(f240(x76954),x76957)),x76951),f333(f240(x76954),x76955)) % 183.90/184.45 [8864]~P21(x88644,x88645,x88646,x88647,x88641)+~P1(f333(f61(x88645),x88643))+E(f333(f333(x88641,x88642),x88643),f333(f333(f333(f65(x88644,x88645,x88646),x88642),x88647),x88643)) % 183.90/184.45 [8865]~P9(x88654,x88655,x88656,x88657,x88651)+~P1(f333(f61(x88655),x88653))+E(f333(f333(x88651,x88652),x88653),f333(f333(f333(f65(x88654,x88655,x88656),x88652),x88657),x88653)) % 183.90/184.45 [9460]~P24(x94601,x94602,f333(f333(f311(f874(x94601)),f333(f333(f333(f91(x94601),x94603),x94604),x94607)),f196(f882(f874(x94601),a870))))+P24(x94601,x94602,f333(f333(f311(f874(x94601)),f333(f333(f333(f91(x94601),x94603),f32(x94604,x94605)),x94606)),f196(f882(f874(x94601),a870))))+~P24(x94601,x94602,f333(f333(f311(f874(x94601)),f333(f333(f333(f91(x94601),x94607),x94605),x94606)),f196(f882(f874(x94601),a870)))) % 183.90/184.45 [9647]~P23(x96473,x96474,x96475,x96477,x96476,x96471)+~P1(f333(f61(x96474),x96472))+E(f333(x96471,x96472),f333(f333(f333(f65(x96473,x96474,x96475),x96476),x96477),x96472)) % 183.90/184.45 [9802]P42(x98021,x98022,x98023,x98024,x98025,f333(f333(x98023,x98026),x98027))+~P42(x98021,x98022,x98023,x98024,f333(f333(f22(f882(x98021,a870)),x98025),f333(f333(f311(x98021),x98026),f196(f882(x98021,a870)))),x98027)+~P1(f333(f333(f335(x98021),x98026),x98025)) % 183.90/184.45 [10070]~P24(x100701,x100702,f333(f333(f311(f874(x100701)),f333(f333(f333(f91(x100701),f94(x100701,x100703,x100704)),x100705),x100707)),f196(f882(f874(x100701),a870))))+P24(x100701,x100702,f333(f333(f311(f874(x100701)),f333(f333(f333(f91(x100701),x100703),f29(x100704,x100705,x100706)),x100707)),f196(f882(f874(x100701),a870))))+~P24(x100701,x100702,f333(f333(f311(f874(x100701)),f333(f333(f333(f91(x100701),f94(x100701,x100703,f333(f72(a870,a870,a872,a328),x100704))),x100706),x100707)),f196(f882(f874(x100701),a870)))) % 183.90/184.45 [10141]~P42(x101412,x101413,x101414,x101415,x101411,f333(f333(x101414,x101417),x101416))+P42(x101412,x101413,x101414,x101415,f333(f333(f22(f882(x101412,a870)),x101411),f333(f333(f311(x101412),f714(x101416,x101417,x101411,x101415,x101414,x101413,x101412)),f196(f882(x101412,a870)))),f725(x101416,x101417,x101411,x101415,x101414,x101413,x101412))+E(x101411,f196(f882(x101412,a870))) % 183.90/184.45 [10142]~P42(x101425,x101426,x101421,x101424,x101427,f333(f333(x101421,x101422),x101423))+P42(x101425,x101426,x101421,x101424,f333(f333(f22(f882(x101425,a870)),x101427),f333(f333(f311(x101425),f714(x101423,x101422,x101427,x101424,x101421,x101426,x101425)),f196(f882(x101425,a870)))),f725(x101423,x101422,x101427,x101424,x101421,x101426,x101425))+E(f333(f333(x101421,x101422),x101423),x101424) % 183.90/184.45 [9187]E(f189(x91871,x91872,x91873,x91874,f333(f333(f160(x91872,x91875),x91876),x91877)),f189(x91871,x91872,x91873,x91874,x91875))+~P1(f333(f333(f248(a875),x91876),f333(f197(f876(x91872)),x91875)))+~P1(f333(f333(f247(a875),f333(f197(f876(x91871)),x91874)),x91876)) % 183.90/184.45 [9482]P1(f333(f333(f247(f882(f881(x94821,x94822),a870)),f333(f333(f290(x94821,x94823,x94822),x94824),x94825)),f333(f333(f290(x94821,x94823,x94822),x94826),x94827)))+~P1(f333(f333(f247(f882(f881(x94823,x94822),a870)),x94825),x94827))+~P1(f333(f333(f247(f882(f881(x94821,x94823),a870)),x94824),x94826)) % 183.90/184.45 [9813]~P1(f333(f333(f335(x98131),x98136),x98135))+P1(f333(f66(x98131,x98132,x98133,x98134,x98135),f333(f333(x98133,x98136),x98137)))+~P1(f333(f66(x98131,x98132,x98133,x98134,f333(f333(f22(f882(x98131,a870)),x98135),f333(f333(f311(x98131),x98136),f196(f882(x98131,a870))))),x98137)) % 183.90/184.45 [10201]~P134(x102011)+~P25(f881(x102012,x102013),x102011,f333(f272(x102012,x102013,x102011),f333(f333(f7(x102012,f882(x102013,x102011),f882(x102013,x102011)),f333(f333(f8(f882(x102011,x102011),f882(f882(x102013,x102011),f882(x102013,x102011)),x102012),f8(x102011,x102011,x102013)),f333(f333(f8(x102011,f882(x102011,x102011),x102012),f80(x102011)),x102014))),x102015)),f333(f333(f270(x102012,x102013),x102016),f333(f16(f882(x102013,a870),x102012),x102017)))+E(f333(f333(f6(x102011,x102011),f33(x102011)),f333(f253(x102011),f333(f333(f8(f882(x102012,a870),a870,x102011),f86(x102012)),f333(f333(f8(f882(x102012,f882(x102013,a870)),f882(x102012,a870),x102011),f333(f8(f882(x102013,a870),a870,x102012),f86(x102013))),f333(f333(f7(x102011,f882(x102012,f882(x102013,a870)),f882(x102012,f882(x102013,a870))),f333(f333(f8(f882(x102012,f882(f882(x102013,a870),f882(x102013,a870))),f882(f882(x102012,f882(x102013,a870)),f882(x102012,f882(x102013,a870))),x102011),f18(x102012,f882(x102013,a870),f882(x102013,a870))),f333(f333(f8(f882(x102012,f882(x102013,f882(a870,a870))),f882(x102012,f882(f882(x102013,a870),f882(x102013,a870))),x102011),f333(f8(f882(x102013,f882(a870,a870)),f882(f882(x102013,a870),f882(x102013,a870)),x102012),f18(x102013,a870,a870))),f333(f333(f8(f882(x102012,f882(x102013,a870)),f882(x102012,f882(x102013,f882(a870,a870))),x102011),f333(f8(f882(x102013,a870),f882(x102013,f882(a870,a870)),x102012),f333(f8(a870,f882(a870,a870),x102013),a331))),f333(f333(f7(x102011,f882(x102012,f882(x102013,x102011)),f882(x102012,f882(x102013,a870))),f333(f333(f8(f882(f882(x102013,x102011),f882(x102013,a870)),f882(f882(x102012,f882(x102013,x102011)),f882(x102012,f882(x102013,a870))),x102011),f8(f882(x102013,x102011),f882(x102013,a870),x102012)),f333(f333(f8(f882(x102011,a870),f882(f882(x102013,x102011),f882(x102013,a870)),x102011),f8(x102011,a870,x102013)),a330))),f333(f333(f7(x102012,f882(x102013,x102011),f882(x102013,x102011)),f333(f333(f8(f882(x102011,x102011),f882(f882(x102013,x102011),f882(x102013,x102011)),x102012),f8(x102011,x102011,x102013)),f333(f333(f8(x102011,f882(x102011,x102011),x102012),f80(x102011)),x102014))),x102015)))))),f333(f333(f7(x102012,f882(x102013,a870),f882(x102013,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x102013,a870),f882(x102013,a870)),x102012),f8(a870,a870,x102013)),f333(f333(f8(a870,f882(a870,a870),x102012),a331),f333(f333(f7(x102012,f882(x102012,a870),a870),f335(x102012)),x102016)))),f333(f333(f7(x102013,f882(x102013,a870),a870),f335(x102013)),x102017))))))),f333(f333(f80(x102011),f333(f333(f6(x102012,x102011),x102014),x102016)),f333(f333(f6(x102013,x102011),x102015),x102017))) % 183.90/184.45 [9645]~P1(f333(f333(x96454,x96456),x96458))+~P1(f333(f333(x96455,x96458),x96457))+P1(f333(f333(f269(x96451,x96452,x96453,x96454,x96455),x96456),x96457)) % 183.90/184.45 [9248]~P19(x92488,x92481,x92483,x92485)+~P1(f333(f61(x92488),x92486))+E(f333(f72(x92481,x92481,x92482,f333(x92483,x92484)),f333(f72(x92481,x92481,x92482,f333(x92485,x92486)),x92487)),f333(f72(x92481,x92481,x92482,f333(x92485,x92486)),f333(f72(x92481,x92481,x92482,f333(x92483,x92484)),x92487))) % 183.90/184.45 [9635]~P22(x96357,x96352,x96355,x96358,x96356,x96351)+~P1(f333(f61(x96352),x96354))+E(f333(x96351,f333(f333(f311(x96352),x96353),x96354)),f333(f333(x96355,f333(x96356,x96353)),f333(x96351,x96354))) % 183.90/184.45 [9755]~P25(x97552,x97554,x97556,x97558)+~P25(x97551,x97553,x97555,x97557)+P25(f881(x97551,x97552),f881(x97553,x97554),f273(x97551,x97553,x97552,x97554,x97555,x97556),f333(f333(f270(x97551,x97552),x97557),f333(f16(f882(x97552,a870),x97551),x97558))) % 183.90/184.45 [9428]P1(f333(f333(f335(f881(x94281,x94282)),f333(f333(f268(x94281,x94282),x94283),x94284)),f333(f333(f290(x94281,x94285,x94282),x94286),x94287)))+~P1(f333(f333(f335(f881(x94281,x94285)),f333(f333(f268(x94281,x94285),x94283),x94288)),x94286))+~P1(f333(f333(f335(f881(x94285,x94282)),f333(f333(f268(x94285,x94282),x94288),x94284)),x94287)) % 183.90/184.45 [9616]~P1(f333(f333(f247(f882(f881(x96163,x96162),a870)),x96165),f333(f333(f270(x96163,x96162),x96168),f333(f16(f882(x96162,a870),x96163),x96167))))+~P1(f333(f333(f247(f882(f881(x96161,x96163),a870)),x96164),f333(f333(f270(x96161,x96163),x96166),f333(f16(f882(x96163,a870),x96161),x96168))))+P1(f333(f333(f247(f882(f881(x96161,x96162),a870)),f333(f333(f290(x96161,x96163,x96162),x96164),x96165)),f333(f333(f270(x96161,x96162),x96166),f333(f16(f882(x96162,a870),x96161),x96167)))) % 183.90/184.45 [9669]~E(x96693,x96695)+P1(f333(f333(f335(f881(f881(x96691,x96692),f881(x96691,x96692))),f333(f333(f268(f881(x96691,x96692),f881(x96691,x96692)),f333(f333(f268(x96691,x96692),x96693),x96694)),f333(f333(f268(x96691,x96692),x96695),x96696))),f326(x96691,x96692,x96697,x96698)))+~P1(f333(f333(f335(f881(x96692,x96692)),f333(f333(f268(x96692,x96692),x96694),x96696)),x96698)) % 183.90/184.45 [9778]E(x97781,x97782)+~P1(f333(f333(f335(f881(f881(x97783,x97785),f881(x97783,x97785))),f333(f333(f268(f881(x97783,x97785),f881(x97783,x97785)),f333(f333(f268(x97783,x97785),x97781),x97786)),f333(f333(f268(x97783,x97785),x97782),x97787))),f326(x97783,x97785,x97784,x97788)))+P1(f333(f333(f335(f881(x97783,x97783)),f333(f333(f268(x97783,x97783),x97781),x97782)),x97784)) % 183.90/184.45 [9795]~P1(f333(f333(f335(f881(f881(x97951,x97955),f881(x97951,x97955))),f333(f333(f268(f881(x97951,x97955),f881(x97951,x97955)),f333(f333(f268(x97951,x97955),x97952),x97956)),f333(f333(f268(x97951,x97955),x97953),x97957))),f326(x97951,x97955,x97954,x97958)))+P1(f333(f333(f335(f881(x97951,x97951)),f333(f333(f268(x97951,x97951),x97952),x97953)),x97954))+P1(f333(f333(f335(f881(x97955,x97955)),f333(f333(f268(x97955,x97955),x97956),x97957)),x97958)) % 183.90/184.45 [9699]~P23(x96997,x96995,x96991,x96998,x96992,x96994)+~P1(f333(f61(x96995),x96996))+E(f333(f333(x96991,f333(x96992,x96993)),f333(x96994,f333(f333(f22(f882(x96995,a870)),x96996),f333(f333(f311(x96995),x96993),f196(f882(x96995,a870)))))),f333(x96994,f333(f333(f311(x96995),x96993),x96996))) % 183.90/184.45 [9206]~P1(f333(f333(f333(x92065,x92068),x92066),x92067))+~P1(f333(f333(f335(x92061),x92068),x92064))+P1(f333(f333(f333(f333(f41(x92061,f882(x92062,f882(x92063,a870))),x92064),x92065),x92066),x92067)) % 183.90/184.45 [9415]P1(f333(f333(f333(x94151,x94152),x94153),x94154))+~P1(f333(f333(f335(x94155),x94152),x94156))+~P1(f333(f333(f333(f333(f42(x94155,f882(x94157,f882(x94158,a870))),x94156),x94151),x94153),x94154)) % 183.90/184.45 [9609]~P21(x96093,x96092,x96094,x96098,x96091)+~P1(f333(f61(x96092),x96097))+E(f333(f333(x96091,f333(f333(f18(x96092,x96093,x96093),f333(f333(f8(x96093,f882(x96093,x96093),x96092),x96094),x96095)),x96096)),x96097),f333(f333(x96094,f333(f333(x96091,x96095),x96097)),f333(f333(x96091,x96096),x96097))) % 183.90/184.45 [9885]~E(f333(f312(x98852,x98854,x98856),x98858),x988510)+~E(f333(f312(x98851,x98853,x98855),x98857),x98859)+E(f333(f312(f881(x98851,x98852),f881(x98853,x98854),f273(x98851,x98853,x98852,x98854,x98855,x98856)),f333(f333(f270(x98851,x98852),x98857),f333(f16(f882(x98852,a870),x98851),x98858))),f333(f333(f270(x98853,x98854),x98859),f333(f16(f882(x98854,a870),x98853),x988510))) % 183.90/184.45 [4842]~P106(x48422)+~P14(x48422,x48421)+P14(x48422,f117(x48422,x48421))+E(x48421,f116(x48422)) % 183.90/184.45 [4843]~P106(x48432)+~P14(x48432,x48431)+P14(x48432,f742(x48431,x48432))+E(x48431,f116(x48432)) % 183.90/184.45 [5074]~P4(x50742)+E(f10(x50742,x50741),f40(x50742,x50741))+E(x50741,f196(f882(x50742,a870)))+~P1(f333(f61(x50742),x50741)) % 183.90/184.45 [5075]~P4(x50752)+E(f13(x50752,x50751),f39(x50752,x50751))+E(x50751,f196(f882(x50752,a870)))+~P1(f333(f61(x50752),x50751)) % 183.90/184.45 [5228]~P106(x52282)+~P14(x52282,x52281)+E(x52281,f116(x52282))+E(f333(f333(f152(x52282),f761(x52281,x52282)),f742(x52281,x52282)),x52281) % 183.90/184.45 [6022]~P62(x60222)+E(x60221,f196(f882(x60222,a870)))+P1(f333(f333(f247(x60222),f10(x60222,x60221)),f13(x60222,x60221)))+~P1(f333(f61(x60222),x60221)) % 183.90/184.45 [6034]~P38(x60342)+~P38(x60341)+E(x60341,x60342)+~E(f333(f312(a1,a875,a107),x60341),f333(f312(a1,a875,a107),x60342)) % 183.90/184.45 [9064]~P114(x90641)+~P1(f333(f333(f335(x90641),x90642),f112(x90641)))+P1(f333(f333(f248(x90641),f333(f333(f79(x90641),f333(f333(f79(x90641),f77(x90641)),x90642)),x90642)),f2(x90641)))+~P1(f333(f333(f248(x90641),x90642),f2(x90641))) % 183.90/184.45 [9303]~P114(x93031)+~P1(f333(f333(f335(x93031),x93032),f112(x93031)))+~P1(f333(f333(f248(x93031),f333(f333(f79(x93031),f333(f333(f79(x93031),f77(x93031)),x93032)),x93032)),f2(x93031)))+P1(f333(f333(f248(x93031),x93032),f2(x93031))) % 183.90/184.45 [4898]~P134(x48982)+~P111(x48982)+E(x48981,f2(a875))+E(f333(f333(f258(x48982),f2(x48982)),x48981),f2(x48982)) % 183.90/184.45 [4901]~P134(x49011)+~P111(x49011)+~E(x49012,f2(a875))+E(f333(f333(f258(x49011),f2(x49011)),x49012),f77(x49011)) % 183.90/184.45 [5061]~P137(x50612)+E(x50611,f77(x50612))+E(x50611,f333(f78(x50612),f77(x50612)))+~E(f333(f333(f80(x50612),x50611),x50611),f77(x50612)) % 183.90/184.45 [5311]~P87(x53112)+E(x53111,f2(x53112))+E(f81(x53112,x53111),f333(f78(x53112),f77(x53112)))+P1(f333(f333(f248(x53112),f2(x53112)),x53111)) % 183.90/184.45 [5546]~P87(x55462)+E(f81(x55462,x55461),f77(x55462))+E(x55461,f2(x55462))+~P1(f333(f333(f248(x55462),f2(x55462)),x55461)) % 183.90/184.45 [5555]E(x55551,x55552)+~E(f333(f106(a875),x55551),f333(f106(a875),x55552))+P1(f333(a201,f333(f106(a1),x55552)))+P1(f333(a201,f333(f106(a1),x55551))) % 183.90/184.45 [5605]~P89(x56051)+~E(x56052,f2(x56051))+E(f333(f333(f79(x56051),x56052),x56052),f2(x56051))+~P1(f333(f333(f335(x56051),x56052),f112(x56051))) % 183.90/184.45 [5643]E(x56431,f2(a1))+~E(f333(f333(f38(a1),x56432),x56431),f2(a1))+P1(f333(f333(f248(a1),x56431),x56432))+P1(f333(f333(f248(a1),x56432),x56431)) % 183.90/184.45 [5674]E(x56741,f2(a1))+~E(f333(f333(f38(a1),x56742),x56741),f2(a1))+P1(f333(f333(f247(a1),x56742),f2(a1)))+P1(f333(f333(f248(a1),x56742),x56741)) % 183.90/184.45 [5708]E(x57081,f2(a1))+~E(f333(f333(f38(a1),x57082),x57081),f2(a1))+P1(f333(f333(f247(a1),f2(a1)),x57082))+P1(f333(f333(f248(a1),x57081),x57082)) % 183.90/184.45 [5742]~P89(x57422)+E(x57421,f2(x57422))+~E(f333(f333(f79(x57422),x57421),x57421),f2(x57422))+~P1(f333(f333(f335(x57422),x57421),f112(x57422))) % 183.90/184.45 [5802]E(f333(f106(a875),x58021),f333(f106(a875),x58022))+~E(f333(f106(a1),x58022),f2(a1))+P1(f333(a201,f333(f106(a1),x58022)))+~P1(f333(a201,f333(f106(a1),x58021))) % 183.90/184.45 [5829]~E(f333(f106(a875),x58292),f333(f106(a875),x58291))+E(f333(f106(a1),x58291),f2(a1))+P1(f333(a201,f333(f106(a1),x58291)))+~P1(f333(a201,f333(f106(a1),x58292))) % 183.90/184.45 [5838]~P106(x58382)+E(x58381,f196(f882(x58382,a870)))+~P1(f333(f61(x58382),x58381))+P1(f333(f333(f335(x58382),f14(x58382,x58381)),x58381)) % 183.90/184.45 [5839]~P106(x58392)+E(x58391,f196(f882(x58392,a870)))+~P1(f333(f61(x58392),x58391))+P1(f333(f333(f335(x58392),f15(x58392,x58391)),x58391)) % 183.90/184.45 [6002]~P114(x60021)+~P90(x60021)+P1(f333(f333(f248(x60021),f2(x60021)),f333(f106(x60021),x60022)))+~P1(f333(f333(f248(a1),a82),x60022)) % 183.90/184.45 [6003]~P114(x60031)+~P90(x60031)+P1(f333(f333(f247(x60031),f2(x60031)),f333(f106(x60031),x60032)))+~P1(f333(f333(f247(a1),a82),x60032)) % 183.90/184.45 [6021]~P114(x60211)+~P90(x60211)+E(f333(f74(x60211),f333(f106(x60211),x60212)),f333(f106(x60211),x60212))+P1(f333(f333(f248(x60211),f333(f106(x60211),x60212)),f2(x60211))) % 183.90/184.45 [6061]E(x60611,x60612)+~E(f333(a107,x60611),f333(a107,x60612))+~P1(f333(f333(f247(a1),f2(a1)),x60612))+~P1(f333(f333(f247(a1),f2(a1)),x60611)) % 183.90/184.45 [6252]~P90(x62522)+~P114(x62522)+~P1(f333(f333(f248(x62522),f2(x62522)),f333(f106(x62522),x62521)))+P1(f333(f333(f248(a1),a82),x62521)) % 183.90/184.45 [6253]~P90(x62532)+~P114(x62532)+~P1(f333(f333(f247(x62532),f2(x62532)),f333(f106(x62532),x62531)))+P1(f333(f333(f247(a1),a82),x62531)) % 183.90/184.45 [6258]~P114(x62581)+~P90(x62581)+P1(f333(f333(f248(x62581),f333(f106(x62581),x62582)),f2(x62581)))+~P1(f333(f333(f248(a1),x62582),a82)) % 183.90/184.45 [6259]~P114(x62591)+~P90(x62591)+P1(f333(f333(f247(x62591),f333(f106(x62591),x62592)),f2(x62591)))+~P1(f333(f333(f247(a1),x62592),a82)) % 183.90/184.45 [6566]~P90(x65662)+~P114(x65662)+~P1(f333(f333(f248(x65662),f333(f106(x65662),x65661)),f2(x65662)))+P1(f333(f333(f248(a1),x65661),a82)) % 183.90/184.45 [6567]~P90(x65672)+~P114(x65672)+~P1(f333(f333(f247(x65672),f333(f106(x65672),x65671)),f2(x65672)))+P1(f333(f333(f247(a1),x65671),a82)) % 183.90/184.45 [6658]~P114(x66581)+~P90(x66581)+E(f333(f74(x66581),f333(f106(x66581),x66582)),f333(f78(x66581),f333(f106(x66581),x66582)))+~P1(f333(f333(f248(x66581),f333(f106(x66581),x66582)),f2(x66581))) % 183.90/184.45 [6676]E(f333(f106(a875),x66761),f333(f106(a875),x66762))+~E(f333(f106(a1),x66762),f2(a1))+~P1(f333(f333(f247(a1),f333(f106(a1),x66761)),f2(a1)))+~P1(f333(a201,f333(f106(a1),x66761))) % 183.90/184.45 [7558]~P106(x75582)+E(x75581,f196(f882(x75582,a870)))+~P1(f333(f61(x75582),x75581))+P1(f333(f333(f247(x75582),f11(x75582,f245(x75582),x75581)),f12(x75582,f246(x75582),x75581))) % 183.90/184.45 [7880]~P38(x78802)+~P5(x78801)+P1(f333(f333(f335(a1),x78801),x78802))+~P1(f333(f333(f335(a875),f333(a107,x78801)),f333(f312(a1,a875,a107),x78802))) % 183.90/184.45 [8158]~P57(x81582)+P1(f333(x81581,f209(x81582)))+~P1(f333(f57(f879(x81582)),x81581))+P1(f333(f57(x81582),f333(f333(f8(f879(x81582),a870,x81582),x81581),f240(x81582)))) % 183.90/184.45 [8625]~P57(x86251)+~P1(f333(x86252,f209(x86251)))+P1(f333(f58(f879(x86251)),x86252))+~P1(f333(f58(x86251),f333(f333(f8(f879(x86251),a870,x86251),x86252),f240(x86251)))) % 183.90/184.45 [5835]~P138(x58352)+E(x58351,f2(a1))+E(f333(f78(x58352),f333(f105(x58352),f333(f78(a1),x58351))),f333(f105(x58352),x58351))+~P1(f333(f333(f248(a1),x58351),f2(a1))) % 183.90/184.45 [5906]~P89(x59061)+~P90(x59061)+~P30(x59061,f333(f106(x59061),x59062))+P30(x59061,f333(f106(x59061),f333(f333(f79(a1),x59062),x59062))) % 183.90/184.45 [6240]~P74(x62402)+E(x62401,f196(f882(x62402,a870)))+E(f15(x62402,f333(f312(x62402,x62402,f78(x62402)),x62401)),f333(f78(x62402),f14(x62402,x62401)))+~P1(f333(f61(x62402),x62401)) % 183.90/184.45 [6241]~P74(x62412)+E(x62411,f196(f882(x62412,a870)))+E(f14(x62412,f333(f312(x62412,x62412,f78(x62412)),x62411)),f333(f78(x62412),f15(x62412,x62411)))+~P1(f333(f61(x62412),x62411)) % 183.90/184.45 [6273]~P89(x62731)+~P90(x62731)+P30(x62731,f333(f106(x62731),x62732))+~P30(x62731,f333(f106(x62731),f333(f333(f79(a1),x62732),x62732))) % 183.90/184.45 [6362]E(x63621,f2(a1))+E(f333(a50,f49(f333(f78(a1),x63621),f333(f78(a1),x63622))),f45(x63621,x63622))+P1(f333(f333(f247(a1),f2(a1)),x63622))+~P1(f333(f333(f247(a1),f2(a1)),x63621)) % 183.90/184.45 [8668]~P38(x86682)+~P38(x86681)+P1(f333(f333(f248(f882(a875,a870)),f333(f312(a1,a875,a107),x86681)),f333(f312(a1,a875,a107),x86682)))+~P1(f333(f333(f248(f882(a1,a870)),x86681),x86682)) % 183.90/184.45 [8882]~E(f764(x88822,x88821),f765(x88822,x88821))+~P1(f333(f138(x88821),f766(x88822,x88821)))+~P1(f333(f138(f876(x88821)),x88822))+P1(f333(f138(x88821),f333(f143(f876(x88821),f876(x88821),f135(x88821),f116(x88821)),x88822))) % 183.90/184.45 [8982]~P38(x89822)+~P38(x89821)+~P1(f333(f333(f248(f882(a875,a870)),f333(f312(a1,a875,a107),x89821)),f333(f312(a1,a875,a107),x89822)))+P1(f333(f333(f248(f882(a1,a870)),x89821),x89822)) % 183.90/184.45 [8983]~P38(x89832)+~P38(x89831)+~P1(f333(f333(f247(f882(a875,a870)),f333(f312(a1,a875,a107),x89831)),f333(f312(a1,a875,a107),x89832)))+P1(f333(f333(f247(f882(a1,a870)),x89831),x89832)) % 183.90/184.45 [8989]~E(f764(x89892,x89891),f765(x89892,x89891))+~P1(f333(f138(f876(x89891)),x89892))+P1(f333(f138(x89891),f333(f143(f876(x89891),f876(x89891),f135(x89891),f116(x89891)),x89892)))+P1(f333(f333(f335(f876(x89891)),f766(x89892,x89891)),f333(f174(f876(x89891)),x89892))) % 183.90/184.45 [9031]~P1(f333(f138(x90311),f766(x90312,x90311)))+~P1(f333(f138(f876(x90311)),x90312))+P1(f333(f138(x90311),f333(f143(f876(x90311),f876(x90311),f135(x90311),f116(x90311)),x90312)))+P1(f333(f333(f335(f876(x90311)),f765(x90312,x90311)),f333(f174(f876(x90311)),x90312))) % 183.90/184.45 [9032]~P1(f333(f138(x90321),f766(x90322,x90321)))+~P1(f333(f138(f876(x90321)),x90322))+P1(f333(f138(x90321),f333(f143(f876(x90321),f876(x90321),f135(x90321),f116(x90321)),x90322)))+P1(f333(f333(f335(f876(x90321)),f764(x90322,x90321)),f333(f174(f876(x90321)),x90322))) % 183.90/184.45 [9107]~P1(f333(f138(f876(x91071)),x91072))+P1(f333(f138(x91071),f333(f143(f876(x91071),f876(x91071),f135(x91071),f116(x91071)),x91072)))+P1(f333(f333(f335(f876(x91071)),f765(x91072,x91071)),f333(f174(f876(x91071)),x91072)))+P1(f333(f333(f335(f876(x91071)),f766(x91072,x91071)),f333(f174(f876(x91071)),x91072))) % 183.90/184.45 [9108]~P1(f333(f138(f876(x91081)),x91082))+P1(f333(f138(x91081),f333(f143(f876(x91081),f876(x91081),f135(x91081),f116(x91081)),x91082)))+P1(f333(f333(f335(f876(x91081)),f764(x91082,x91081)),f333(f174(f876(x91081)),x91082)))+P1(f333(f333(f335(f876(x91081)),f766(x91082,x91081)),f333(f174(f876(x91081)),x91082))) % 183.90/184.45 [9121]~E(f333(f333(f104(f882(x91211,a870)),f333(f174(x91211),f765(x91212,x91211))),f333(f174(x91211),f764(x91212,x91211))),f196(f882(x91211,a870)))+~P1(f333(f138(x91211),f766(x91212,x91211)))+~P1(f333(f138(f876(x91211)),x91212))+P1(f333(f138(x91211),f333(f143(f876(x91211),f876(x91211),f135(x91211),f116(x91211)),x91212))) % 183.90/184.45 [9183]~E(f333(f333(f104(f882(x91831,a870)),f333(f174(x91831),f765(x91832,x91831))),f333(f174(x91831),f764(x91832,x91831))),f196(f882(x91831,a870)))+~P1(f333(f138(f876(x91831)),x91832))+P1(f333(f138(x91831),f333(f143(f876(x91831),f876(x91831),f135(x91831),f116(x91831)),x91832)))+P1(f333(f333(f335(f876(x91831)),f766(x91832,x91831)),f333(f174(f876(x91831)),x91832))) % 183.90/184.45 [9452]E(x94521,f2(a1))+E(x94522,f2(a1))+E(f333(f333(f85(a1,f881(a1,a1)),f333(f333(a229,x94522),x94521)),f333(f333(f18(a1,a1,f881(a1,a1)),f333(f333(f8(a1,f882(a1,f881(a1,a1)),a1),f268(a1,a1)),f333(f38(a1),x94522))),f333(f38(a1),x94521))),f227(x94522,x94521))+P1(f333(f333(f248(a1),x94521),f2(a1))) % 183.90/184.45 [8219]~P90(x82192)+~P114(x82192)+~P1(f333(f333(f248(x82192),f333(f106(x82192),x82191)),f77(x82192)))+P1(f333(f333(f248(a1),x82191),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))) % 183.90/184.45 [8220]~P90(x82202)+~P114(x82202)+~P1(f333(f333(f247(x82202),f333(f106(x82202),x82201)),f77(x82202)))+P1(f333(f333(f247(a1),x82201),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))) % 183.90/184.45 [8498]~P114(x84981)+~P90(x84981)+P1(f333(f333(f248(x84981),f333(f106(x84981),x84982)),f77(x84981)))+~P1(f333(f333(f248(a1),x84982),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))) % 183.90/184.45 [8499]~P114(x84991)+~P90(x84991)+P1(f333(f333(f247(x84991),f333(f106(x84991),x84992)),f77(x84991)))+~P1(f333(f333(f247(a1),x84992),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))) % 183.90/184.45 [8694]~P90(x86942)+~P114(x86942)+~P1(f333(f333(f248(x86942),f77(x86942)),f333(f106(x86942),x86941)))+P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),x86941)) % 183.90/184.45 [8695]~P90(x86952)+~P114(x86952)+~P1(f333(f333(f247(x86952),f77(x86952)),f333(f106(x86952),x86951)))+P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),x86951)) % 183.90/184.45 [9070]~P114(x90701)+~P90(x90701)+P1(f333(f333(f248(x90701),f77(x90701)),f333(f106(x90701),x90702)))+~P1(f333(f333(f248(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),x90702)) % 183.90/184.45 [9071]~P114(x90711)+~P90(x90711)+P1(f333(f333(f247(x90711),f77(x90711)),f333(f106(x90711),x90712)))+~P1(f333(f333(f247(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),x90712)) % 183.90/184.45 [9581]~P137(x95812)+E(x95811,f77(x95812))+E(x95811,f333(f78(x95812),f77(x95812)))+~E(f333(f333(f258(x95812),x95811),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f77(x95812)) % 183.90/184.45 [9853]~P60(x98531)+~P90(x98531)+~P1(f333(f333(f248(x98531),f2(x98531)),x98532))+P1(f333(f333(f248(x98531),f2(x98531)),f333(f333(f291(x98531),x98532),f333(f106(x98531),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.45 [9915]~P60(x99151)+~P90(x99151)+P1(f333(f333(f248(x99151),f2(x99151)),x99152))+~P1(f333(f333(f248(x99151),f2(x99151)),f333(f333(f291(x99151),x99152),f333(f106(x99151),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.45 [10169]~P138(x101692)+E(x101691,f2(a1))+P1(f333(f333(f248(a1),x101691),f2(a1)))+E(f333(f333(f272(a1,a1,x101692),f333(f333(f7(a1,f882(a1,f882(x101692,x101692)),f882(a1,x101692)),f333(f333(f8(f882(f882(x101692,x101692),x101692),f882(f882(a1,f882(x101692,x101692)),f882(a1,x101692)),a1),f8(f882(x101692,x101692),x101692,a1)),f333(f333(f8(x101692,f882(f882(x101692,x101692),x101692),a1),f85(x101692,x101692)),f105(x101692)))),f333(f333(f7(a1,f882(x101692,x101692),f882(x101692,x101692)),f333(f333(f8(f882(x101692,f882(x101692,x101692)),f882(f882(x101692,x101692),f882(x101692,x101692)),a1),f18(x101692,x101692,x101692)),f333(f333(f7(a1,f882(x101692,x101692),f882(x101692,f882(x101692,x101692))),f333(f333(f8(f882(x101692,f882(x101692,x101692)),f882(f882(x101692,x101692),f882(x101692,f882(x101692,x101692))),a1),f8(x101692,f882(x101692,x101692),x101692)),f333(f333(f8(a870,f882(x101692,f882(x101692,x101692)),a1),f99(x101692)),f333(f333(f7(a1,a1,a870),a330),f2(a1))))),f333(f333(f18(x101692,x101692,x101692),f79(x101692)),f5(x101692))))),f333(f333(f7(x101692,x101692,x101692),f333(f333(f8(x101692,f882(x101692,x101692),x101692),f79(x101692)),f333(f333(f18(x101692,x101692,x101692),f79(x101692)),f5(x101692)))),f77(x101692))))),f45(x101691,f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f105(x101692),x101691)) % 183.90/184.45 [5223]~P57(x52233)+~P35(x52233,x52232,f55(x52233))+E(x52231,f775(x52232,x52233))+~P1(f333(x52232,x52231)) % 183.90/184.45 [5381]~P57(x53811)+P35(x53811,x53812,f55(x53811))+~E(f776(x53812,x53811,x53813),x53813)+~P1(f333(x53812,x53813)) % 183.90/184.45 [4869]~P89(x48693)+~P90(x48693)+E(x48691,x48692)+~E(f333(f106(x48693),x48691),f333(f106(x48693),x48692)) % 183.90/184.45 [6001]~P57(x60011)+P35(x60011,x60012,f55(x60011))+~P1(f333(x60012,x60013))+P1(f333(x60012,f776(x60012,x60011,x60013))) % 183.90/184.45 [6011]~P1(f333(x60111,x60112))+~P1(f333(x60111,x60113))+~P1(f333(f333(f247(a875),x60113),f410(x60112,x60111)))+P1(f333(x60111,f2(a875))) % 183.90/184.45 [6425]P144(x64252,x64251,x64253)+E(x64251,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f813(x64253,x64251,x64252)))+P1(f333(f333(f248(a1),x64251),f2(a1))) % 183.90/184.45 [6426]P143(x64262,x64261,x64263)+E(x64261,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f818(x64263,x64261,x64262)))+P1(f333(f333(f248(a1),x64261),f2(a1))) % 183.90/184.45 [6545]P143(x65451,x65452,x65453)+~P1(f333(x65451,x65453))+P1(f333(f333(f247(a1),f2(a1)),f818(x65453,x65452,x65451)))+P1(f333(f333(f248(a1),x65452),f2(a1))) % 183.90/184.45 [6572]P144(x65721,x65722,x65723)+P1(f333(f333(f247(a1),f2(a1)),f813(x65723,x65722,x65721)))+~P1(f333(x65721,f2(a1)))+P1(f333(f333(f248(a1),x65722),f2(a1))) % 183.90/184.45 [6600]P144(x66002,x66001,x66003)+E(x66001,f2(a1))+~P1(f333(x66002,f814(x66003,x66001,x66002)))+P1(f333(f333(f248(a1),x66001),f2(a1))) % 183.90/184.45 [6601]P143(x66012,x66011,x66013)+E(x66011,f2(a1))+~P1(f333(x66012,f818(x66013,x66011,x66012)))+P1(f333(f333(f248(a1),x66011),f2(a1))) % 183.90/184.45 [6701]~P4(x67011)+~P106(x67011)+~P1(f333(f333(f248(x67011),x67012),f39(x67011,x67013)))+P1(f333(f333(f248(x67011),x67012),f862(x67013,x67012,x67011))) % 183.90/184.45 [6710]P143(x67101,x67102,x67103)+~P1(f333(x67101,x67103))+~P1(f333(x67101,f818(x67103,x67102,x67101)))+P1(f333(f333(f248(a1),x67102),f2(a1))) % 183.90/184.45 [6742]P144(x67421,x67422,x67423)+~P1(f333(x67421,f814(x67423,x67422,x67421)))+~P1(f333(x67421,f2(a1)))+P1(f333(f333(f248(a1),x67422),f2(a1))) % 183.90/184.45 [6996]P144(x69962,x69961,x69963)+E(x69961,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f813(x69963,x69961,x69962)))+P1(f333(f333(f248(a1),x69961),f812(x69963,x69961,x69962))) % 183.90/184.45 [6997]P143(x69972,x69971,x69973)+E(x69971,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f818(x69973,x69971,x69972)))+P1(f333(f333(f248(a1),x69971),f817(x69973,x69971,x69972))) % 183.90/184.45 [7114]P143(x71141,x71142,x71143)+~P1(f333(x71141,x71143))+P1(f333(f333(f247(a1),f2(a1)),f818(x71143,x71142,x71141)))+P1(f333(f333(f248(a1),x71142),f817(x71143,x71142,x71141))) % 183.90/184.45 [7133]P144(x71331,x71332,x71333)+P1(f333(f333(f247(a1),f2(a1)),f813(x71333,x71332,x71331)))+P1(f333(f333(f248(a1),x71332),f812(x71333,x71332,x71331)))+~P1(f333(x71331,f2(a1))) % 183.90/184.45 [7166]P144(x71662,x71661,x71663)+E(x71661,f2(a1))+~P1(f333(x71662,f814(x71663,x71661,x71662)))+P1(f333(f333(f248(a1),x71661),f812(x71663,x71661,x71662))) % 183.90/184.45 [7167]P143(x71672,x71671,x71673)+E(x71671,f2(a1))+~P1(f333(x71672,f818(x71673,x71671,x71672)))+P1(f333(f333(f248(a1),x71671),f817(x71673,x71671,x71672))) % 183.90/184.45 [7208]P144(x72082,x72081,x72083)+E(x72081,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f813(x72083,x72081,x72082)))+~P1(f333(x72082,f815(x72083,x72081,x72082))) % 183.90/184.45 [7209]P143(x72092,x72091,x72093)+E(x72091,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f818(x72093,x72091,x72092)))+~P1(f333(x72092,f817(x72093,x72091,x72092))) % 183.90/184.45 [7297]P143(x72971,x72972,x72973)+~P1(f333(x72971,x72973))+~P1(f333(x72971,f818(x72973,x72972,x72971)))+P1(f333(f333(f248(a1),x72972),f817(x72973,x72972,x72971))) % 183.90/184.45 [7313]P144(x73131,x73132,x73133)+~P1(f333(x73131,f814(x73133,x73132,x73131)))+P1(f333(f333(f248(a1),x73132),f812(x73133,x73132,x73131)))+~P1(f333(x73131,f2(a1))) % 183.90/184.45 [7317]P143(x73171,x73172,x73173)+~P1(f333(x73171,x73173))+P1(f333(f333(f247(a1),f2(a1)),f818(x73173,x73172,x73171)))+~P1(f333(x73171,f817(x73173,x73172,x73171))) % 183.90/184.45 [7335]P144(x73351,x73352,x73353)+P1(f333(f333(f247(a1),f2(a1)),f813(x73353,x73352,x73351)))+~P1(f333(x73351,f815(x73353,x73352,x73351)))+~P1(f333(x73351,f2(a1))) % 183.90/184.45 [7359]P144(x73592,x73591,x73593)+E(x73591,f2(a1))+~P1(f333(x73592,f814(x73593,x73591,x73592)))+~P1(f333(x73592,f815(x73593,x73591,x73592))) % 183.90/184.45 [7360]P143(x73602,x73601,x73603)+E(x73601,f2(a1))+~P1(f333(x73602,f818(x73603,x73601,x73602)))+~P1(f333(x73602,f817(x73603,x73601,x73602))) % 183.90/184.45 [7452]P143(x74521,x74522,x74523)+~P1(f333(x74521,x74523))+~P1(f333(x74521,f818(x74523,x74522,x74521)))+~P1(f333(x74521,f817(x74523,x74522,x74521))) % 183.90/184.45 [7469]P144(x74691,x74692,x74693)+~P1(f333(x74691,f814(x74693,x74692,x74691)))+~P1(f333(x74691,f815(x74693,x74692,x74691)))+~P1(f333(x74691,f2(a1))) % 183.90/184.45 [7518]P144(x75182,x75181,x75183)+E(x75181,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f813(x75183,x75181,x75182)))+P1(f333(f333(f247(a1),f812(x75183,x75181,x75182)),f2(a1))) % 183.90/184.45 [7519]P143(x75192,x75191,x75193)+E(x75191,f2(a1))+P1(f333(f333(f247(a1),f2(a1)),f818(x75193,x75191,x75192)))+P1(f333(f333(f247(a1),f817(x75193,x75191,x75192)),f2(a1))) % 183.90/184.45 [7520]~P138(x75201)+~P1(f333(f333(f335(x75201),x75203),f112(x75201)))+~P1(f333(f333(f335(x75201),x75202),f112(x75201)))+P1(f333(f333(f335(x75201),f333(f333(f22(x75201),x75202),x75203)),f112(x75201))) % 183.90/184.45 [7521]~P138(x75211)+~P1(f333(f333(f335(x75211),x75213),f112(x75211)))+~P1(f333(f333(f335(x75211),x75212),f112(x75211)))+P1(f333(f333(f335(x75211),f333(f333(f79(x75211),x75212),x75213)),f112(x75211))) % 183.90/184.45 [7522]~P141(x75221)+~P1(f333(f333(f335(x75221),x75223),f194(x75221)))+~P1(f333(f333(f335(x75221),x75222),f194(x75221)))+P1(f333(f333(f335(x75221),f333(f333(f79(x75221),x75222),x75223)),f194(x75221))) % 183.90/184.45 [7523]~P138(x75231)+~P1(f333(f333(f335(x75231),x75233),f112(x75231)))+~P1(f333(f333(f335(x75231),x75232),f112(x75231)))+P1(f333(f333(f335(x75231),f333(f333(f80(x75231),x75232),x75233)),f112(x75231))) % 183.90/184.45 [7524]~P141(x75241)+~P1(f333(f333(f335(x75241),x75243),f194(x75241)))+~P1(f333(f333(f335(x75241),x75242),f194(x75241)))+P1(f333(f333(f335(x75241),f333(f333(f80(x75241),x75242),x75243)),f194(x75241))) % 183.90/184.45 [7525]~P85(x75251)+~P1(f333(f333(f248(x75251),x75253),f2(x75251)))+~P1(f333(f333(f248(x75251),x75252),f2(x75251)))+P1(f333(f333(f248(x75251),f333(f333(f79(x75251),x75252),x75253)),f2(x75251))) % 183.90/184.45 [7526]~P85(x75261)+~P1(f333(f333(f247(x75261),x75262),f2(x75261)))+~P1(f333(f333(f248(x75261),x75263),f2(x75261)))+P1(f333(f333(f248(x75261),f333(f333(f79(x75261),x75262),x75263)),f2(x75261))) % 183.90/184.45 [7527]~P85(x75271)+~P1(f333(f333(f247(x75271),x75273),f2(x75271)))+~P1(f333(f333(f248(x75271),x75272),f2(x75271)))+P1(f333(f333(f248(x75271),f333(f333(f79(x75271),x75272),x75273)),f2(x75271))) % 183.90/184.45 [7528]~P85(x75281)+~P1(f333(f333(f247(x75281),x75283),f2(x75281)))+~P1(f333(f333(f247(x75281),x75282),f2(x75281)))+P1(f333(f333(f247(x75281),f333(f333(f79(x75281),x75282),x75283)),f2(x75281))) % 183.90/184.45 [7554]P144(x75543,x75541,x75542)+E(x75541,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x75541),f814(x75542,x75541,x75543))),f813(x75542,x75541,x75543)),x75542)+P1(f333(f333(f248(a1),x75541),f2(a1))) % 183.90/184.45 [7555]P143(x75553,x75551,x75552)+E(x75551,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x75551),f819(x75552,x75551,x75553))),f818(x75552,x75551,x75553)),x75552)+P1(f333(f333(f248(a1),x75551),f2(a1))) % 183.90/184.45 [7637]P143(x76371,x76372,x76373)+~P1(f333(x76371,x76373))+P1(f333(f333(f247(a1),f2(a1)),f818(x76373,x76372,x76371)))+P1(f333(f333(f247(a1),f817(x76373,x76372,x76371)),f2(a1))) % 183.90/184.45 [7666]P144(x76661,x76662,x76663)+P1(f333(f333(f247(a1),f2(a1)),f813(x76663,x76662,x76661)))+~P1(f333(x76661,f2(a1)))+P1(f333(f333(f247(a1),f812(x76663,x76662,x76661)),f2(a1))) % 183.90/184.45 [7676]P143(x76763,x76761,x76762)+~P1(f333(x76763,x76762))+E(f333(f333(f79(a1),f333(f333(f80(a1),x76761),f819(x76762,x76761,x76763))),f818(x76762,x76761,x76763)),x76762)+P1(f333(f333(f248(a1),x76761),f2(a1))) % 183.90/184.45 [7683]P144(x76832,x76831,x76833)+E(x76831,f2(a1))+~P1(f333(x76832,f814(x76833,x76831,x76832)))+P1(f333(f333(f247(a1),f812(x76833,x76831,x76832)),f2(a1))) % 183.90/184.45 [7684]P143(x76842,x76841,x76843)+E(x76841,f2(a1))+~P1(f333(x76842,f818(x76843,x76841,x76842)))+P1(f333(f333(f247(a1),f817(x76843,x76841,x76842)),f2(a1))) % 183.90/184.45 [7689]P144(x76893,x76891,x76892)+E(f333(f333(f79(a1),f333(f333(f80(a1),x76891),f814(x76892,x76891,x76893))),f813(x76892,x76891,x76893)),x76892)+~P1(f333(x76893,f2(a1)))+P1(f333(f333(f248(a1),x76891),f2(a1))) % 183.90/184.45 [7746]P143(x77461,x77462,x77463)+~P1(f333(x77461,x77463))+~P1(f333(x77461,f818(x77463,x77462,x77461)))+P1(f333(f333(f247(a1),f817(x77463,x77462,x77461)),f2(a1))) % 183.90/184.45 [7750]P144(x77501,x77502,x77503)+~P1(f333(x77501,f814(x77503,x77502,x77501)))+~P1(f333(x77501,f2(a1)))+P1(f333(f333(f247(a1),f812(x77503,x77502,x77501)),f2(a1))) % 183.90/184.45 [7822]~P60(x78221)+~P1(f333(f333(f248(x78221),f333(f333(f291(x78221),x78223),x78222)),f2(x78221)))+P1(f333(f333(f248(x78221),x78222),f2(x78221)))+P1(f333(f333(f248(x78221),x78223),f2(x78221))) % 183.90/184.45 [7823]~P122(x78231)+~P1(f333(f333(f247(x78231),f333(f333(f80(x78231),x78233),x78232)),f2(x78231)))+P1(f333(f333(f247(x78231),x78232),f2(x78231)))+P1(f333(f333(f247(x78231),x78233),f2(x78231))) % 183.90/184.45 [7824]~P60(x78241)+~P1(f333(f333(f247(x78241),f333(f333(f291(x78241),x78243),x78242)),f2(x78241)))+P1(f333(f333(f247(x78241),x78242),f2(x78241)))+P1(f333(f333(f247(x78241),x78243),f2(x78241))) % 183.90/184.45 [7938]P144(x79383,x79381,x79382)+E(x79381,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x79381),f814(x79382,x79381,x79383))),f813(x79382,x79381,x79383)),x79382)+P1(f333(f333(f248(a1),x79381),f812(x79382,x79381,x79383))) % 183.90/184.45 [7939]P143(x79393,x79391,x79392)+E(x79391,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x79391),f819(x79392,x79391,x79393))),f818(x79392,x79391,x79393)),x79392)+P1(f333(f333(f248(a1),x79391),f817(x79392,x79391,x79393))) % 183.90/184.45 [7951]P144(x79513,x79511,x79512)+E(x79511,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x79511),f815(x79512,x79511,x79513))),f812(x79512,x79511,x79513)),x79512)+P1(f333(f333(f247(a1),f2(a1)),f813(x79512,x79511,x79513))) % 183.90/184.45 [7952]P143(x79523,x79521,x79522)+E(x79521,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x79521),f820(x79522,x79521,x79523))),f817(x79522,x79521,x79523)),x79522)+P1(f333(f333(f247(a1),f2(a1)),f818(x79522,x79521,x79523))) % 183.90/184.45 [7997]P143(x79973,x79971,x79972)+~P1(f333(x79973,x79972))+E(f333(f333(f79(a1),f333(f333(f80(a1),x79971),f819(x79972,x79971,x79973))),f818(x79972,x79971,x79973)),x79972)+P1(f333(f333(f248(a1),x79971),f817(x79972,x79971,x79973))) % 183.90/184.45 [8009]P144(x80093,x80091,x80092)+E(f333(f333(f79(a1),f333(f333(f80(a1),x80091),f814(x80092,x80091,x80093))),f813(x80092,x80091,x80093)),x80092)+P1(f333(f333(f248(a1),x80091),f812(x80092,x80091,x80093)))+~P1(f333(x80093,f2(a1))) % 183.90/184.45 [8015]P143(x80153,x80151,x80152)+~P1(f333(x80153,x80152))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80151),f820(x80152,x80151,x80153))),f817(x80152,x80151,x80153)),x80152)+P1(f333(f333(f247(a1),f2(a1)),f818(x80152,x80151,x80153))) % 183.90/184.45 [8023]P144(x80233,x80231,x80232)+E(f333(f333(f79(a1),f333(f333(f80(a1),x80231),f815(x80232,x80231,x80233))),f812(x80232,x80231,x80233)),x80232)+P1(f333(f333(f247(a1),f2(a1)),f813(x80232,x80231,x80233)))+~P1(f333(x80233,f2(a1))) % 183.90/184.45 [8034]P144(x80343,x80341,x80342)+E(x80341,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80341),f814(x80342,x80341,x80343))),f813(x80342,x80341,x80343)),x80342)+~P1(f333(x80343,f815(x80342,x80341,x80343))) % 183.90/184.45 [8035]P143(x80353,x80351,x80352)+E(x80351,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80351),f819(x80352,x80351,x80353))),f818(x80352,x80351,x80353)),x80352)+~P1(f333(x80353,f817(x80352,x80351,x80353))) % 183.90/184.45 [8036]P144(x80363,x80361,x80362)+E(x80361,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80361),f815(x80362,x80361,x80363))),f812(x80362,x80361,x80363)),x80362)+~P1(f333(x80363,f814(x80362,x80361,x80363))) % 183.90/184.45 [8037]P143(x80373,x80371,x80372)+E(x80371,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80371),f820(x80372,x80371,x80373))),f817(x80372,x80371,x80373)),x80372)+~P1(f333(x80373,f818(x80372,x80371,x80373))) % 183.90/184.45 [8095]P143(x80953,x80951,x80952)+~P1(f333(x80953,x80952))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80951),f819(x80952,x80951,x80953))),f818(x80952,x80951,x80953)),x80952)+~P1(f333(x80953,f817(x80952,x80951,x80953))) % 183.90/184.45 [8096]P143(x80963,x80961,x80962)+~P1(f333(x80963,x80962))+E(f333(f333(f79(a1),f333(f333(f80(a1),x80961),f820(x80962,x80961,x80963))),f817(x80962,x80961,x80963)),x80962)+~P1(f333(x80963,f818(x80962,x80961,x80963))) % 183.90/184.45 [8106]P144(x81063,x81061,x81062)+E(f333(f333(f79(a1),f333(f333(f80(a1),x81061),f814(x81062,x81061,x81063))),f813(x81062,x81061,x81063)),x81062)+~P1(f333(x81063,f815(x81062,x81061,x81063)))+~P1(f333(x81063,f2(a1))) % 183.90/184.45 [8107]P144(x81073,x81071,x81072)+E(f333(f333(f79(a1),f333(f333(f80(a1),x81071),f815(x81072,x81071,x81073))),f812(x81072,x81071,x81073)),x81072)+~P1(f333(x81073,f814(x81072,x81071,x81073)))+~P1(f333(x81073,f2(a1))) % 183.90/184.45 [8212]P144(x82123,x82121,x82122)+E(x82121,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82121),f814(x82122,x82121,x82123))),f813(x82122,x82121,x82123)),x82122)+P1(f333(f333(f247(a1),f812(x82122,x82121,x82123)),f2(a1))) % 183.90/184.45 [8213]P143(x82133,x82131,x82132)+E(x82131,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82131),f819(x82132,x82131,x82133))),f818(x82132,x82131,x82133)),x82132)+P1(f333(f333(f247(a1),f817(x82132,x82131,x82133)),f2(a1))) % 183.90/184.45 [8253]P143(x82533,x82531,x82532)+~P1(f333(x82533,x82532))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82531),f819(x82532,x82531,x82533))),f818(x82532,x82531,x82533)),x82532)+P1(f333(f333(f247(a1),f817(x82532,x82531,x82533)),f2(a1))) % 183.90/184.45 [8258]P144(x82583,x82581,x82582)+E(f333(f333(f79(a1),f333(f333(f80(a1),x82581),f814(x82582,x82581,x82583))),f813(x82582,x82581,x82583)),x82582)+~P1(f333(x82583,f2(a1)))+P1(f333(f333(f247(a1),f812(x82582,x82581,x82583)),f2(a1))) % 183.90/184.45 [8387]P144(x83873,x83871,x83872)+E(x83871,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x83871),f815(x83872,x83871,x83873))),f812(x83872,x83871,x83873)),x83872)+E(f333(f333(f79(a1),f333(f333(f80(a1),x83871),f814(x83872,x83871,x83873))),f813(x83872,x83871,x83873)),x83872) % 183.90/184.45 [8388]P143(x83883,x83881,x83882)+E(x83881,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x83881),f820(x83882,x83881,x83883))),f817(x83882,x83881,x83883)),x83882)+E(f333(f333(f79(a1),f333(f333(f80(a1),x83881),f819(x83882,x83881,x83883))),f818(x83882,x83881,x83883)),x83882) % 183.90/184.45 [8412]P143(x84123,x84121,x84122)+~P1(f333(x84123,x84122))+E(f333(f333(f79(a1),f333(f333(f80(a1),x84121),f820(x84122,x84121,x84123))),f817(x84122,x84121,x84123)),x84122)+E(f333(f333(f79(a1),f333(f333(f80(a1),x84121),f819(x84122,x84121,x84123))),f818(x84122,x84121,x84123)),x84122) % 183.90/184.45 [8425]P144(x84253,x84251,x84252)+E(f333(f333(f79(a1),f333(f333(f80(a1),x84251),f815(x84252,x84251,x84253))),f812(x84252,x84251,x84253)),x84252)+E(f333(f333(f79(a1),f333(f333(f80(a1),x84251),f814(x84252,x84251,x84253))),f813(x84252,x84251,x84253)),x84252)+~P1(f333(x84253,f2(a1))) % 183.90/184.45 [9075]~P122(x90751)+~E(x90753,f2(x90751))+~E(x90752,f2(x90751))+P1(f333(f333(f247(x90751),f333(f333(f79(x90751),f333(f333(f80(x90751),x90752),x90752)),f333(f333(f80(x90751),x90753),x90753))),f2(x90751))) % 183.90/184.45 [10119]~P114(x101191)+~E(x101193,f2(x101191))+~E(x101192,f2(x101191))+P1(f333(f333(f247(x101191),f333(f333(f79(x101191),f333(f333(f258(x101191),x101192),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x101191),x101193),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))),f2(x101191))) % 183.90/184.45 [4818]~E(x48183,x48181)+~P117(x48182)+E(x48181,f2(x48182))+E(f333(f333(f291(x48182),x48183),x48181),f77(x48182)) % 183.90/184.45 [4870]~P63(x48701)+~E(x48703,f196(x48701))+~E(x48702,f196(x48701))+E(f333(f333(f113(x48701),x48702),x48703),f196(x48701)) % 183.90/184.45 [4871]~P97(x48711)+~E(x48713,f256(x48711))+~E(x48712,f256(x48711))+E(f333(f333(f104(x48711),x48712),x48713),f256(x48711)) % 183.90/184.45 [4958]~P117(x49583)+E(x49581,x49582)+E(x49582,f2(x49583))+~E(f333(f333(f291(x49583),x49581),x49582),f77(x49583)) % 183.90/184.45 [4977]~P129(x49772)+E(x49771,f2(x49772))+E(x49773,f2(x49772))+~E(f333(f333(f80(x49772),x49773),x49771),f2(x49772)) % 183.90/184.45 [4978]~P136(x49782)+E(x49781,f2(x49782))+E(x49783,f2(x49782))+~E(f333(f333(f80(x49782),x49783),x49781),f2(x49782)) % 183.90/184.45 [5348]~P116(x53483)+E(x53481,x53482)+E(x53481,f333(f78(x53483),x53482))+~E(f333(f333(f80(x53483),x53481),x53481),f333(f333(f80(x53483),x53482),x53482)) % 183.90/184.45 [5388]~P93(x53881)+E(f333(f78(x53881),x53882),x53883)+~E(f333(f333(f113(x53881),x53882),x53883),f256(x53881))+~E(f333(f333(f104(x53881),x53882),x53883),f196(x53881)) % 183.90/184.45 [5462]~P114(x54623)+E(x54621,x54622)+P1(f333(f333(f248(x54623),x54622),x54621))+P1(f333(f333(f248(x54623),x54621),x54622)) % 183.90/184.45 [5468]~P106(x54683)+E(x54681,x54682)+P1(f333(f333(f248(x54683),x54682),x54681))+P1(f333(f333(f248(x54683),x54681),x54682)) % 183.90/184.45 [5469]~E(x54692,x54693)+~P106(x54691)+P1(f333(f333(f247(x54691),x54692),x54693))+P1(f333(f333(f248(x54691),x54692),x54693)) % 183.90/184.45 [5724]~P108(x57243)+E(x57241,x57242)+~P1(f333(f333(f247(x57243),x57242),x57241))+P1(f333(f333(f248(x57243),x57242),x57241)) % 183.90/184.45 [5726]~P106(x57263)+E(x57261,x57262)+~P1(f333(f333(f247(x57263),x57261),x57262))+P1(f333(f333(f248(x57263),x57261),x57262)) % 183.90/184.45 [5732]~P108(x57323)+E(x57321,x57322)+~P1(f333(f333(f247(x57323),x57321),x57322))+P1(f333(f333(f248(x57323),x57321),x57322)) % 183.90/184.45 [5832]P143(x58321,x58322,x58323)+~P1(f333(x58321,x58323))+P1(f333(f333(f248(a1),x58322),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x58322)) % 183.90/184.45 [5879]P144(x58791,x58792,x58793)+~P1(f333(x58791,f2(a1)))+P1(f333(f333(f248(a1),x58792),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x58792)) % 183.90/184.45 [5883]~P62(x58831)+E(f333(f333(f113(x58831),x58832),f10(x58831,x58833)),x58832)+~P1(f333(f61(x58831),x58833))+~P1(f333(f333(f335(x58831),x58832),x58833)) % 183.90/184.45 [5884]~P62(x58841)+E(f333(f333(f104(x58841),x58842),f13(x58841,x58843)),x58842)+~P1(f333(f61(x58841),x58843))+~P1(f333(f333(f335(x58841),x58842),x58843)) % 183.90/184.45 [5918]~P62(x59181)+E(f333(f333(f113(x59181),x59182),f13(x59181,x59183)),f13(x59181,x59183))+~P1(f333(f61(x59181),x59183))+~P1(f333(f333(f335(x59181),x59182),x59183)) % 183.90/184.45 [5919]~P62(x59191)+E(f333(f333(f104(x59191),x59192),f10(x59191,x59193)),f10(x59191,x59193))+~P1(f333(f61(x59191),x59193))+~P1(f333(f333(f335(x59191),x59192),x59193)) % 183.90/184.45 [5920]~P106(x59201)+E(f333(f333(f245(x59201),x59202),f14(x59201,x59203)),f14(x59201,x59203))+~P1(f333(f61(x59201),x59203))+~P1(f333(f333(f335(x59201),x59202),x59203)) % 183.90/184.45 [5921]~P106(x59211)+E(f333(f333(f246(x59211),x59212),f15(x59211,x59213)),f15(x59211,x59213))+~P1(f333(f61(x59211),x59213))+~P1(f333(f333(f335(x59211),x59212),x59213)) % 183.90/184.45 [5966]E(x59661,x59662)+~P108(x59663)+~P1(f333(f333(f247(x59663),x59662),x59661))+~P1(f333(f333(f247(x59663),x59661),x59662)) % 183.90/184.45 [6106]~P105(x61061)+P1(f333(f333(f247(x61061),x61063),x61062))+~P1(f333(f333(f247(x61061),x61062),x61063))+P1(f333(f333(f248(x61061),x61062),x61063)) % 183.90/184.45 [6127]~P106(x61271)+~P1(f333(f61(x61271),x61273))+P1(f333(f333(f247(x61271),x61272),f15(x61271,x61273)))+~P1(f333(f333(f335(x61271),x61272),x61273)) % 183.90/184.45 [6175]~P106(x61751)+E(f333(f333(f245(x61751),x61752),f12(x61751,f246(x61751),x61753)),x61752)+~P1(f333(f61(x61751),x61753))+~P1(f333(f333(f335(x61751),x61752),x61753)) % 183.90/184.45 [6176]~P106(x61761)+E(f333(f333(f246(x61761),x61762),f11(x61761,f245(x61761),x61763)),x61762)+~P1(f333(f61(x61761),x61763))+~P1(f333(f333(f335(x61761),x61762),x61763)) % 183.90/184.45 [6314]E(x63141,x63142)+~E(f333(f333(f22(a875),x63141),x63143),f333(f333(f22(a875),x63142),x63143))+~P1(f333(f333(f247(a875),x63143),x63141))+~P1(f333(f333(f247(a875),x63143),x63142)) % 183.90/184.45 [6341]~P106(x63411)+~P1(f333(f61(x63411),x63412))+~P1(f333(f333(f335(x63411),x63413),x63412))+P1(f333(f333(f247(x63411),f14(x63411,x63412)),x63413)) % 183.90/184.45 [6404]P144(x64042,x64041,x64043)+E(x64041,f2(a1))+P1(f333(f333(f248(a1),x64041),f812(x64043,x64041,x64042)))+P1(f333(f333(f248(a1),f2(a1)),x64041)) % 183.90/184.45 [6405]P143(x64052,x64051,x64053)+E(x64051,f2(a1))+P1(f333(f333(f248(a1),x64051),f817(x64053,x64051,x64052)))+P1(f333(f333(f248(a1),f2(a1)),x64051)) % 183.90/184.45 [6406]~P106(x64061)+E(f333(f333(f245(x64061),x64062),f11(x64061,f245(x64061),x64063)),f11(x64061,f245(x64061),x64063))+~P1(f333(f61(x64061),x64063))+~P1(f333(f333(f335(x64061),x64062),x64063)) % 183.90/184.45 [6407]~P106(x64071)+E(f333(f333(f246(x64071),x64072),f12(x64071,f246(x64071),x64073)),f12(x64071,f246(x64071),x64073))+~P1(f333(f61(x64071),x64073))+~P1(f333(f333(f335(x64071),x64072),x64073)) % 183.90/184.45 [6413]~P1(f333(x64131,x64132))+P1(f333(x64131,f522(x64132,x64131,x64133)))+P1(f333(x64131,f2(a875)))+~P1(f333(f333(f248(a875),x64132),x64133)) % 183.90/184.45 [6467]~P1(f333(x64671,x64672))+~P1(f333(f61(x64673),x64672))+P1(f333(x64671,f615(x64671,x64672,x64673)))+P1(f333(x64671,f196(f882(x64673,a870)))) % 183.90/184.45 [6480]~P114(x64801)+~P90(x64801)+P1(f333(f333(f248(x64801),f333(f106(x64801),x64802)),f333(f106(x64801),x64803)))+~P1(f333(f333(f248(a1),x64802),x64803)) % 183.90/184.45 [6481]~P114(x64811)+~P90(x64811)+P1(f333(f333(f247(x64811),f333(f106(x64811),x64812)),f333(f106(x64811),x64813)))+~P1(f333(f333(f247(a1),x64812),x64813)) % 183.90/184.45 [6484]~P1(f333(x64841,x64843))+~P1(f333(f61(x64842),x64843))+P1(f333(f61(x64842),f615(x64841,x64843,x64842)))+P1(f333(x64841,f196(f882(x64842,a870)))) % 183.90/184.45 [6517]P143(x65171,x65172,x65173)+~P1(f333(x65171,x65173))+P1(f333(f333(f248(a1),x65172),f817(x65173,x65172,x65171)))+P1(f333(f333(f248(a1),f2(a1)),x65172)) % 183.90/184.45 [6552]P144(x65521,x65522,x65523)+P1(f333(f333(f248(a1),x65522),f812(x65523,x65522,x65521)))+~P1(f333(x65521,f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x65522)) % 183.90/184.45 [6583]~P107(x65831)+~P91(x65831)+E(f333(f333(f245(x65831),f333(f106(x65831),x65832)),f333(f106(x65831),x65833)),f333(f106(x65831),x65833))+P1(f333(f333(f247(x65831),f333(f106(x65831),x65832)),f333(f106(x65831),x65833))) % 183.90/184.45 [6584]~P107(x65841)+~P91(x65841)+E(f333(f333(f246(x65841),f333(f106(x65841),x65842)),f333(f106(x65841),x65843)),f333(f106(x65841),x65842))+P1(f333(f333(f247(x65841),f333(f106(x65841),x65842)),f333(f106(x65841),x65843))) % 183.90/184.45 [6642]P144(x66422,x66421,x66423)+E(x66421,f2(a1))+~P1(f333(x66422,f815(x66423,x66421,x66422)))+P1(f333(f333(f248(a1),f2(a1)),x66421)) % 183.90/184.45 [6643]P143(x66432,x66431,x66433)+E(x66431,f2(a1))+~P1(f333(x66432,f817(x66433,x66431,x66432)))+P1(f333(f333(f248(a1),f2(a1)),x66431)) % 183.90/184.45 [6647]P1(f333(x66471,x66472))+~P1(f333(f61(x66473),x66472))+P1(f333(x66471,f487(x66471,x66472,x66473)))+~P1(f333(x66471,f196(f882(x66473,a870)))) % 183.90/184.45 [6666]P1(f333(x66661,x66662))+P1(f333(f61(x66663),f487(x66661,x66662,x66663)))+~P1(f333(f61(x66663),x66662))+~P1(f333(x66661,f196(f882(x66663,a870)))) % 183.90/184.45 [6731]P143(x67311,x67312,x67313)+~P1(f333(x67311,x67313))+~P1(f333(x67311,f817(x67313,x67312,x67311)))+P1(f333(f333(f248(a1),f2(a1)),x67312)) % 183.90/184.45 [6761]P144(x67611,x67612,x67613)+~P1(f333(x67611,f815(x67613,x67612,x67611)))+~P1(f333(x67611,f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x67612)) % 183.90/184.45 [6869]~P90(x68693)+~P114(x68693)+~P1(f333(f333(f248(x68693),f333(f106(x68693),x68691)),f333(f106(x68693),x68692)))+P1(f333(f333(f248(a1),x68691),x68692)) % 183.90/184.45 [6870]~P90(x68703)+~P114(x68703)+~P1(f333(f333(f247(x68703),f333(f106(x68703),x68701)),f333(f106(x68703),x68702)))+P1(f333(f333(f247(a1),x68701),x68702)) % 183.90/184.45 [6899]~P106(x68991)+~P14(x68991,x68993)+P14(x68991,f333(f333(f152(x68991),x68992),x68993))+~P1(f333(f333(f247(x68991),x68992),f745(x68993,x68992,x68991))) % 183.90/184.45 [6900]~P106(x69001)+~P14(x69001,x69003)+P14(x69001,f333(f333(f152(x69001),x69002),x69003))+~P1(f333(f333(f247(x69001),x69002),f747(x69003,x69002,x69001))) % 183.90/184.45 [6901]~P106(x69011)+~P14(x69011,x69013)+P14(x69011,f333(f333(f152(x69011),x69012),x69013))+~P1(f333(f333(f247(x69011),x69012),f778(x69012,x69013,x69011))) % 183.90/184.45 [6985]P144(x69852,x69851,x69853)+E(x69851,f2(a1))+P1(f333(f333(f248(a1),x69851),f2(a1)))+P1(f333(f333(f248(a1),f813(x69853,x69851,x69852)),x69851)) % 183.90/184.45 [6986]P143(x69862,x69861,x69863)+E(x69861,f2(a1))+P1(f333(f333(f248(a1),x69861),f2(a1)))+P1(f333(f333(f248(a1),f818(x69863,x69861,x69862)),x69861)) % 183.90/184.45 [7027]P144(x70272,x70271,x70273)+E(x70271,f2(a1))+P1(f333(f333(f247(a1),f812(x70273,x70271,x70272)),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x70271)) % 183.90/184.45 [7028]P143(x70282,x70281,x70283)+E(x70281,f2(a1))+P1(f333(f333(f247(a1),f817(x70283,x70281,x70282)),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x70281)) % 183.90/184.45 [7050]~P106(x70501)+~P14(x70501,x70503)+E(f333(f333(f149(x70501,x70501,f5(x70501)),x70502),f172(x70501,x70502,x70503)),x70503)+~P1(f333(f333(f335(x70501),x70502),f333(f174(x70501),x70503))) % 183.90/184.45 [7097]P143(x70971,x70972,x70973)+~P1(f333(x70971,x70973))+P1(f333(f333(f248(a1),x70972),f2(a1)))+P1(f333(f333(f248(a1),f818(x70973,x70972,x70971)),x70972)) % 183.90/184.45 [7103]~P107(x71031)+~P91(x71031)+E(f333(f333(f245(x71031),f333(f106(x71031),x71032)),f333(f106(x71031),x71033)),f333(f106(x71031),x71032))+~P1(f333(f333(f247(x71031),f333(f106(x71031),x71032)),f333(f106(x71031),x71033))) % 183.90/184.45 [7104]~P107(x71041)+~P91(x71041)+E(f333(f333(f246(x71041),f333(f106(x71041),x71042)),f333(f106(x71041),x71043)),f333(f106(x71041),x71043))+~P1(f333(f333(f247(x71041),f333(f106(x71041),x71042)),f333(f106(x71041),x71043))) % 183.90/184.45 [7118]P144(x71181,x71182,x71183)+~P1(f333(x71181,f2(a1)))+P1(f333(f333(f248(a1),x71182),f2(a1)))+P1(f333(f333(f248(a1),f813(x71183,x71182,x71181)),x71182)) % 183.90/184.45 [7126]P143(x71261,x71262,x71263)+~P1(f333(x71261,x71263))+P1(f333(f333(f247(a1),f817(x71263,x71262,x71261)),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x71262)) % 183.90/184.45 [7150]P144(x71501,x71502,x71503)+~P1(f333(x71501,f2(a1)))+P1(f333(f333(f247(a1),f812(x71503,x71502,x71501)),f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x71502)) % 183.90/184.45 [7178]~P1(f333(x71781,x71782))+P1(f333(x71781,f2(a875)))+~P1(f333(f333(f248(a875),x71782),x71783))+P1(f333(f333(f248(a875),f522(x71782,x71781,x71783)),x71783)) % 183.90/184.45 [7195]~P106(x71951)+~P14(x71951,x71953)+P14(x71951,f333(f333(f152(x71951),x71952),x71953))+P1(f333(f333(f335(x71951),f745(x71953,x71952,x71951)),f333(f174(x71951),x71953))) % 183.90/184.45 [7196]~P106(x71961)+~P14(x71961,x71963)+P14(x71961,f333(f333(f152(x71961),x71962),x71963))+P1(f333(f333(f335(x71961),f747(x71963,x71962,x71961)),f333(f174(x71961),x71963))) % 183.90/184.45 [7197]~P106(x71971)+~P14(x71971,x71973)+P14(x71971,f333(f333(f152(x71971),x71972),x71973))+P1(f333(f333(f335(x71971),f778(x71972,x71973,x71971)),f333(f174(x71971),x71973))) % 183.90/184.45 [7301]~P4(x73011)+~P106(x73011)+~P1(f333(f333(f248(x73011),x73013),f39(x73011,x73012)))+P1(f333(f333(f335(x73011),f862(x73012,x73013,x73011)),x73012)) % 183.90/184.45 [7467]~P4(x74671)+~P106(x74671)+~P1(f333(f333(f248(x74671),f40(x74671,x74673)),x74672))+P1(f333(f333(f335(x74671),f865(x74672,x74673,x74671)),x74673)) % 183.90/184.45 [7468]~P4(x74681)+~P106(x74681)+~P1(f333(f333(f248(x74681),f40(x74681,x74683)),x74682))+P1(f333(f333(f248(x74681),f865(x74682,x74683,x74681)),x74682)) % 183.90/184.45 [7483]P144(x74832,x74831,x74833)+E(x74831,f2(a1))+P1(f333(f333(f248(a1),x74831),f812(x74833,x74831,x74832)))+P1(f333(f333(f248(a1),f813(x74833,x74831,x74832)),x74831)) % 183.90/184.45 [7484]P143(x74842,x74841,x74843)+E(x74841,f2(a1))+P1(f333(f333(f248(a1),x74841),f817(x74843,x74841,x74842)))+P1(f333(f333(f248(a1),f818(x74843,x74841,x74842)),x74841)) % 183.90/184.45 [7575]P144(x75753,x75751,x75752)+E(x75751,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x75751),f815(x75752,x75751,x75753))),f812(x75752,x75751,x75753)),x75752)+P1(f333(f333(f248(a1),f2(a1)),x75751)) % 183.90/184.45 [7576]P143(x75763,x75761,x75762)+E(x75761,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x75761),f820(x75762,x75761,x75763))),f817(x75762,x75761,x75763)),x75762)+P1(f333(f333(f248(a1),f2(a1)),x75761)) % 183.90/184.45 [7578]~P125(x75781)+~P1(f333(f333(f248(x75781),x75783),f2(x75781)))+P1(f333(f333(f248(x75781),f333(f333(f80(x75781),x75782),x75783)),f2(x75781)))+~P1(f333(f333(f248(x75781),f2(x75781)),x75782)) % 183.90/184.45 [7579]~P125(x75791)+~P1(f333(f333(f248(x75791),x75792),f2(x75791)))+P1(f333(f333(f248(x75791),f333(f333(f80(x75791),x75792),x75793)),f2(x75791)))+~P1(f333(f333(f248(x75791),f2(x75791)),x75793)) % 183.90/184.45 [7580]~P60(x75801)+~P1(f333(f333(f248(x75801),x75803),f2(x75801)))+P1(f333(f333(f248(x75801),f333(f333(f291(x75801),x75802),x75803)),f2(x75801)))+~P1(f333(f333(f248(x75801),f2(x75801)),x75802)) % 183.90/184.45 [7581]~P60(x75811)+~P1(f333(f333(f248(x75811),x75812),f2(x75811)))+P1(f333(f333(f248(x75811),f333(f333(f291(x75811),x75812),x75813)),f2(x75811)))+~P1(f333(f333(f248(x75811),f2(x75811)),x75813)) % 183.90/184.45 [7582]~P61(x75821)+~P1(f333(f333(f248(x75821),x75823),f2(x75821)))+P1(f333(f333(f248(x75821),f333(f333(f291(x75821),x75822),x75823)),f2(x75821)))+~P1(f333(f333(f248(x75821),f2(x75821)),x75822)) % 183.90/184.45 [7583]~P61(x75831)+~P1(f333(f333(f248(x75831),x75832),f2(x75831)))+P1(f333(f333(f248(x75831),f333(f333(f291(x75831),x75832),x75833)),f2(x75831)))+~P1(f333(f333(f248(x75831),f2(x75831)),x75833)) % 183.90/184.45 [7585]~P122(x75851)+~P1(f333(f333(f247(x75851),x75853),f2(x75851)))+P1(f333(f333(f247(x75851),f333(f333(f80(x75851),x75852),x75853)),f2(x75851)))+~P1(f333(f333(f247(x75851),f2(x75851)),x75852)) % 183.90/184.45 [7586]~P122(x75861)+~P1(f333(f333(f247(x75861),x75862),f2(x75861)))+P1(f333(f333(f247(x75861),f333(f333(f80(x75861),x75862),x75863)),f2(x75861)))+~P1(f333(f333(f247(x75861),f2(x75861)),x75863)) % 183.90/184.45 [7588]~P130(x75881)+~P1(f333(f333(f247(x75881),x75883),f2(x75881)))+P1(f333(f333(f247(x75881),f333(f333(f80(x75881),x75882),x75883)),f2(x75881)))+~P1(f333(f333(f247(x75881),f2(x75881)),x75882)) % 183.90/184.45 [7590]~P130(x75901)+~P1(f333(f333(f247(x75901),x75902),f2(x75901)))+P1(f333(f333(f247(x75901),f333(f333(f80(x75901),x75902),x75903)),f2(x75901)))+~P1(f333(f333(f247(x75901),f2(x75901)),x75903)) % 183.90/184.45 [7591]~P60(x75911)+~P1(f333(f333(f247(x75911),x75913),f2(x75911)))+P1(f333(f333(f247(x75911),f333(f333(f291(x75911),x75912),x75913)),f2(x75911)))+~P1(f333(f333(f247(x75911),f2(x75911)),x75912)) % 183.90/184.45 [7592]~P60(x75921)+~P1(f333(f333(f247(x75921),x75922),f2(x75921)))+P1(f333(f333(f247(x75921),f333(f333(f291(x75921),x75922),x75923)),f2(x75921)))+~P1(f333(f333(f247(x75921),f2(x75921)),x75923)) % 183.90/184.45 [7593]~P61(x75931)+~P1(f333(f333(f248(x75931),x75933),f2(x75931)))+P1(f333(f333(f247(x75931),f333(f333(f291(x75931),x75932),x75933)),f2(x75931)))+~P1(f333(f333(f247(x75931),f2(x75931)),x75932)) % 183.90/184.45 [7594]~P61(x75941)+~P1(f333(f333(f247(x75941),x75942),f2(x75941)))+P1(f333(f333(f247(x75941),f333(f333(f291(x75941),x75942),x75943)),f2(x75941)))+~P1(f333(f333(f248(x75941),f2(x75941)),x75943)) % 183.90/184.45 [7609]P143(x76091,x76092,x76093)+~P1(f333(x76091,x76093))+P1(f333(f333(f248(a1),x76092),f817(x76093,x76092,x76091)))+P1(f333(f333(f248(a1),f818(x76093,x76092,x76091)),x76092)) % 183.90/184.45 [7622]P144(x76221,x76222,x76223)+P1(f333(f333(f248(a1),x76222),f812(x76223,x76222,x76221)))+~P1(f333(x76221,f2(a1)))+P1(f333(f333(f248(a1),f813(x76223,x76222,x76221)),x76222)) % 183.90/184.45 [7673]P144(x76732,x76731,x76733)+E(x76731,f2(a1))+~P1(f333(x76732,f815(x76733,x76731,x76732)))+P1(f333(f333(f248(a1),f813(x76733,x76731,x76732)),x76731)) % 183.90/184.45 [7674]P143(x76742,x76741,x76743)+E(x76741,f2(a1))+~P1(f333(x76742,f817(x76743,x76741,x76742)))+P1(f333(f333(f248(a1),f818(x76743,x76741,x76742)),x76741)) % 183.90/184.45 [7686]P143(x76863,x76861,x76862)+~P1(f333(x76863,x76862))+E(f333(f333(f79(a1),f333(f333(f80(a1),x76861),f820(x76862,x76861,x76863))),f817(x76862,x76861,x76863)),x76862)+P1(f333(f333(f248(a1),f2(a1)),x76861)) % 183.90/184.45 [7704]P144(x77043,x77041,x77042)+E(f333(f333(f79(a1),f333(f333(f80(a1),x77041),f815(x77042,x77041,x77043))),f812(x77042,x77041,x77043)),x77042)+~P1(f333(x77043,f2(a1)))+P1(f333(f333(f248(a1),f2(a1)),x77041)) % 183.90/184.45 [7730]~P1(f333(x77301,x77303))+~P1(f333(f61(x77302),x77303))+P1(f333(f333(f335(x77302),f616(x77301,x77303,x77302)),f615(x77301,x77303,x77302)))+P1(f333(x77301,f196(f882(x77302,a870)))) % 183.90/184.45 [7741]P143(x77411,x77412,x77413)+~P1(f333(x77411,x77413))+~P1(f333(x77411,f817(x77413,x77412,x77411)))+P1(f333(f333(f248(a1),f818(x77413,x77412,x77411)),x77412)) % 183.90/184.45 [7747]P144(x77471,x77472,x77473)+~P1(f333(x77471,f815(x77473,x77472,x77471)))+~P1(f333(x77471,f2(a1)))+P1(f333(f333(f248(a1),f813(x77473,x77472,x77471)),x77472)) % 183.90/184.45 [7853]~P60(x78531)+~P1(f333(f333(f248(x78531),f333(f333(f291(x78531),x78533),x78532)),f2(x78531)))+P1(f333(f333(f248(x78531),x78532),f2(x78531)))+P1(f333(f333(f248(x78531),f2(x78531)),x78532)) % 183.90/184.45 [7854]~P60(x78541)+~P1(f333(f333(f248(x78541),f333(f333(f291(x78541),x78542),x78543)),f2(x78541)))+P1(f333(f333(f248(x78541),x78542),f2(x78541)))+P1(f333(f333(f248(x78541),f2(x78541)),x78542)) % 183.90/184.45 [7855]~P122(x78551)+~P1(f333(f333(f247(x78551),f333(f333(f80(x78551),x78553),x78552)),f2(x78551)))+P1(f333(f333(f247(x78551),x78552),f2(x78551)))+P1(f333(f333(f247(x78551),f2(x78551)),x78552)) % 183.90/184.45 [7856]~P122(x78561)+~P1(f333(f333(f247(x78561),f333(f333(f80(x78561),x78562),x78563)),f2(x78561)))+P1(f333(f333(f247(x78561),x78562),f2(x78561)))+P1(f333(f333(f247(x78561),f2(x78561)),x78562)) % 183.90/184.45 [7857]~P60(x78571)+~P1(f333(f333(f247(x78571),f333(f333(f291(x78571),x78573),x78572)),f2(x78571)))+P1(f333(f333(f247(x78571),x78572),f2(x78571)))+P1(f333(f333(f247(x78571),f2(x78571)),x78572)) % 183.90/184.45 [7858]~P60(x78581)+~P1(f333(f333(f247(x78581),f333(f333(f291(x78581),x78582),x78583)),f2(x78581)))+P1(f333(f333(f247(x78581),x78582),f2(x78581)))+P1(f333(f333(f247(x78581),f2(x78581)),x78582)) % 183.90/184.45 [7882]~P60(x78821)+~P1(f333(f333(f248(x78821),f333(f333(f291(x78821),x78822),x78823)),f2(x78821)))+P1(f333(f333(f248(x78821),f2(x78821)),x78822))+P1(f333(f333(f248(x78821),f2(x78821)),x78823)) % 183.90/184.45 [7883]~P122(x78831)+~P1(f333(f333(f247(x78831),f333(f333(f80(x78831),x78832),x78833)),f2(x78831)))+P1(f333(f333(f247(x78831),f2(x78831)),x78832))+P1(f333(f333(f247(x78831),f2(x78831)),x78833)) % 183.90/184.45 [7884]~P60(x78841)+~P1(f333(f333(f247(x78841),f333(f333(f291(x78841),x78842),x78843)),f2(x78841)))+P1(f333(f333(f247(x78841),f2(x78841)),x78842))+P1(f333(f333(f247(x78841),f2(x78841)),x78843)) % 183.90/184.45 [7905]P144(x79052,x79051,x79053)+E(x79051,f2(a1))+P1(f333(f333(f247(a1),f812(x79053,x79051,x79052)),f2(a1)))+P1(f333(f333(f248(a1),f813(x79053,x79051,x79052)),x79051)) % 183.90/184.45 [7906]P143(x79062,x79061,x79063)+E(x79061,f2(a1))+P1(f333(f333(f247(a1),f817(x79063,x79061,x79062)),f2(a1)))+P1(f333(f333(f248(a1),f818(x79063,x79061,x79062)),x79061)) % 183.90/184.45 [7913]~P120(x79131)+~P1(f333(f333(f248(x79131),x79132),f77(x79131)))+P1(f333(f333(f248(x79131),f333(f333(f258(x79131),x79132),f333(a115,x79133))),f77(x79131)))+~P1(f333(f333(f248(x79131),f2(x79131)),x79132)) % 183.90/184.45 [7968]~P106(x79681)+~E(x79683,f116(x79681))+~P14(x79681,f333(f170(x79681),x79683))+E(f333(f143(x79681,x79681,f333(f7(x79681,x79681,x79681),f246(x79681)),x79682),f333(f170(x79681),x79683)),x79682) % 183.90/184.45 [7971]P143(x79711,x79712,x79713)+~P1(f333(x79711,x79713))+P1(f333(f333(f247(a1),f817(x79713,x79712,x79711)),f2(a1)))+P1(f333(f333(f248(a1),f818(x79713,x79712,x79711)),x79712)) % 183.90/184.45 [7981]P144(x79811,x79812,x79813)+~P1(f333(x79811,f2(a1)))+P1(f333(f333(f247(a1),f812(x79813,x79812,x79811)),f2(a1)))+P1(f333(f333(f248(a1),f813(x79813,x79812,x79811)),x79812)) % 183.90/184.45 [8207]P144(x82073,x82071,x82072)+E(x82071,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82071),f815(x82072,x82071,x82073))),f812(x82072,x82071,x82073)),x82072)+P1(f333(f333(f248(a1),f813(x82072,x82071,x82073)),x82071)) % 183.90/184.45 [8208]P143(x82083,x82081,x82082)+E(x82081,f2(a1))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82081),f820(x82082,x82081,x82083))),f817(x82082,x82081,x82083)),x82082)+P1(f333(f333(f248(a1),f818(x82082,x82081,x82083)),x82081)) % 183.90/184.45 [8244]P143(x82443,x82441,x82442)+~P1(f333(x82443,x82442))+E(f333(f333(f79(a1),f333(f333(f80(a1),x82441),f820(x82442,x82441,x82443))),f817(x82442,x82441,x82443)),x82442)+P1(f333(f333(f248(a1),f818(x82442,x82441,x82443)),x82441)) % 183.90/184.45 [8245]~P66(x82451)+~P73(x82451)+~P38(x82453)+E(f333(f333(f6(a875,x82451),f333(f333(f8(a1,x82451,a875),x82452),f103(a1))),f333(f312(a1,a875,a107),x82453)),f333(f333(f6(a1,x82451),x82452),x82453)) % 183.90/184.45 [8246]~P66(x82461)+~P73(x82461)+~P38(x82463)+E(f333(f333(f9(a875,x82461),f333(f333(f8(a1,x82461,a875),x82462),f103(a1))),f333(f312(a1,a875,a107),x82463)),f333(f333(f9(a1,x82461),x82462),x82463)) % 183.90/184.45 [8255]P144(x82553,x82551,x82552)+E(f333(f333(f79(a1),f333(f333(f80(a1),x82551),f815(x82552,x82551,x82553))),f812(x82552,x82551,x82553)),x82552)+~P1(f333(x82553,f2(a1)))+P1(f333(f333(f248(a1),f813(x82552,x82551,x82553)),x82551)) % 183.90/184.45 [8274]~E(x82742,f2(a875))+~E(f333(f267(a875,a875),x82743),f2(a875))+~E(x82741,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x82743)),x82742)),f333(f271(a875,a875),x82743)))+P1(f333(f47(x82741,x82742),x82743)) % 183.90/184.45 [8328]P1(f333(x83281,x83282))+~P1(f333(f333(f335(x83283),f500(x83281,x83282,x83283)),f487(x83281,x83282,x83283)))+~P1(f333(f61(x83283),x83282))+~P1(f333(x83281,f196(f882(x83283,a870)))) % 183.90/184.45 [8946]P1(f333(x89461,x89462))+~P1(f333(f61(x89463),x89462))+~P1(f333(x89461,f333(f333(f311(x89463),f500(x89461,x89462,x89463)),f487(x89461,x89462,x89463))))+~P1(f333(x89461,f196(f882(x89463,a870)))) % 183.90/184.45 [9179]P1(f333(f333(f247(a1),x91791),f2(a1)))+~P1(f333(f333(f248(a1),f333(f333(f79(a1),f333(f333(f80(a1),x91792),x91791)),x91793)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x91792))+~P1(f333(f333(f247(a1),f2(a1)),x91793)) % 183.90/184.45 [5793]~P62(x57932)+E(x57931,f196(f882(x57932,a870)))+~P1(f333(f61(x57932),x57931))+E(f13(x57932,f333(f333(f311(x57932),x57933),x57931)),f333(f333(f113(x57932),x57933),f13(x57932,x57931))) % 183.90/184.45 [5794]~P62(x57942)+E(x57941,f196(f882(x57942,a870)))+~P1(f333(f61(x57942),x57941))+E(f10(x57942,f333(f333(f311(x57942),x57943),x57941)),f333(f333(f104(x57942),x57943),f10(x57942,x57941))) % 183.90/184.45 [5795]~P106(x57952)+E(x57951,f196(f882(x57952,a870)))+~P1(f333(f61(x57952),x57951))+E(f14(x57952,f333(f333(f311(x57952),x57953),x57951)),f333(f333(f245(x57952),x57953),f14(x57952,x57951))) % 183.90/184.45 [5796]~P106(x57962)+E(x57961,f196(f882(x57962,a870)))+~P1(f333(f61(x57962),x57961))+E(f15(x57962,f333(f333(f311(x57962),x57963),x57961)),f333(f333(f246(x57962),x57963),f15(x57962,x57961))) % 183.90/184.45 [6103]~P122(x61031)+~E(x61033,f2(x61031))+~E(x61032,f2(x61031))+E(f333(f333(f79(x61031),f333(f333(f80(x61031),x61032),x61032)),f333(f333(f80(x61031),x61033),x61033)),f2(x61031)) % 183.90/184.45 [6168]~P94(x61682)+E(x61681,f196(f882(x61682,a870)))+~P1(f333(f61(x61682),x61681))+E(f333(f63(x61682,f80(x61682)),f333(f333(f311(x61682),x61683),x61681)),f333(f333(f80(x61682),x61683),f333(f63(x61682,f80(x61682)),x61681))) % 183.90/184.45 [6293]~P106(x62932)+E(x62931,f196(f882(x62932,a870)))+~P1(f333(f61(x62932),x62931))+E(f11(x62932,f245(x62932),f333(f333(f311(x62932),x62933),x62931)),f333(f333(f245(x62932),x62933),f11(x62932,f245(x62932),x62931))) % 183.90/184.45 [6294]~P106(x62942)+E(x62941,f196(f882(x62942,a870)))+~P1(f333(f61(x62942),x62941))+E(f12(x62942,f246(x62942),f333(f333(f311(x62942),x62943),x62941)),f333(f333(f246(x62942),x62943),f12(x62942,f246(x62942),x62941))) % 183.90/184.45 [6796]~P67(x67961)+~P1(f333(f61(x67961),x67963))+E(f333(f63(x67961,f80(x67961)),f333(f333(f311(x67961),x67962),x67963)),f333(f333(f64(x67961,x67961,f80(x67961)),x67962),x67963))+P1(f333(f333(f335(x67961),x67962),x67963)) % 183.90/184.45 [6877]~E(f333(f333(f79(a1),x68772),f333(f333(f80(a1),x68773),x68771)),x68773)+~P1(f333(f333(f248(a1),f2(a1)),x68773))+P1(f333(f333(f247(a1),f77(a1)),x68771))+~P1(f333(f333(f248(a1),x68772),x68773)) % 183.90/184.45 [6906]~E(f333(f333(f79(a1),x69062),f333(f333(f80(a1),x69063),x69061)),x69063)+P1(f333(f333(f247(a1),x69061),f77(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x69063))+~P1(f333(f333(f247(a1),f2(a1)),x69062)) % 183.90/184.45 [6922]E(x69221,f2(a875))+~P1(f333(f47(x69223,x69221),x69222))+~P1(f333(f333(f248(a875),f2(a875)),x69221))+P1(f333(f333(f248(a875),f333(f271(a875,a875),x69222)),x69221)) % 183.90/184.45 [6952]~P133(x69521)+~P1(f333(f333(f247(x69521),x69522),f2(x69521)))+~P1(f333(f333(f247(x69521),x69523),f2(x69521)))+E(f333(f333(f80(x69521),f333(f74(x69521),x69522)),f333(f74(x69521),x69523)),f333(f74(x69521),f333(f333(f80(x69521),x69522),x69523))) % 183.90/184.45 [7004]~P133(x70041)+~P1(f333(f333(f247(x70041),x70042),f2(x70041)))+E(f333(f333(f80(x70041),f333(f74(x70041),x70042)),f333(f74(x70041),x70043)),f333(f74(x70041),f333(f333(f80(x70041),x70042),x70043)))+~P1(f333(f333(f247(x70041),f2(x70041)),x70043)) % 183.90/184.45 [7005]~P133(x70051)+~P1(f333(f333(f247(x70051),x70053),f2(x70051)))+E(f333(f333(f80(x70051),f333(f74(x70051),x70052)),f333(f74(x70051),x70053)),f333(f74(x70051),f333(f333(f80(x70051),x70052),x70053)))+~P1(f333(f333(f247(x70051),f2(x70051)),x70052)) % 183.90/184.45 [7059]~P133(x70591)+E(f333(f333(f80(x70591),f333(f74(x70591),x70592)),f333(f74(x70591),x70593)),f333(f74(x70591),f333(f333(f80(x70591),x70592),x70593)))+~P1(f333(f333(f247(x70591),f2(x70591)),x70592))+~P1(f333(f333(f247(x70591),f2(x70591)),x70593)) % 183.90/184.45 [7075]~P122(x70751)+~P1(f333(f333(f248(x70751),x70753),f2(x70751)))+~P1(f333(f333(f248(x70751),x70752),f2(x70751)))+P1(f333(f333(f248(x70751),f2(x70751)),f333(f333(f80(x70751),x70752),x70753))) % 183.90/184.45 [7076]~P60(x70761)+~P1(f333(f333(f248(x70761),x70763),f2(x70761)))+~P1(f333(f333(f248(x70761),x70762),f2(x70761)))+P1(f333(f333(f248(x70761),f2(x70761)),f333(f333(f291(x70761),x70762),x70763))) % 183.90/184.45 [7077]~P61(x70771)+~P1(f333(f333(f248(x70771),x70773),f2(x70771)))+~P1(f333(f333(f248(x70771),x70772),f2(x70771)))+P1(f333(f333(f248(x70771),f2(x70771)),f333(f333(f291(x70771),x70772),x70773))) % 183.90/184.45 [7079]~P123(x70791)+~P1(f333(f333(f247(x70791),x70793),f2(x70791)))+~P1(f333(f333(f247(x70791),x70792),f2(x70791)))+P1(f333(f333(f247(x70791),f2(x70791)),f333(f333(f80(x70791),x70792),x70793))) % 183.90/184.45 [7080]~P122(x70801)+~P1(f333(f333(f247(x70801),x70803),f2(x70801)))+~P1(f333(f333(f247(x70801),x70802),f2(x70801)))+P1(f333(f333(f247(x70801),f2(x70801)),f333(f333(f80(x70801),x70802),x70803))) % 183.90/184.45 [7081]~P60(x70811)+~P1(f333(f333(f247(x70811),x70813),f2(x70811)))+~P1(f333(f333(f247(x70811),x70812),f2(x70811)))+P1(f333(f333(f247(x70811),f2(x70811)),f333(f333(f291(x70811),x70812),x70813))) % 183.90/184.45 [7082]~P61(x70821)+~P1(f333(f333(f248(x70821),x70823),f2(x70821)))+~P1(f333(f333(f247(x70821),x70822),f2(x70821)))+P1(f333(f333(f247(x70821),f2(x70821)),f333(f333(f291(x70821),x70822),x70823))) % 183.90/184.45 [7083]~P120(x70831)+~P1(f333(f333(f248(a875),f2(a875)),x70833))+~P1(f333(f333(f248(x70831),f77(x70831)),x70832))+P1(f333(f333(f248(x70831),f77(x70831)),f333(f333(f258(x70831),x70832),x70833))) % 183.90/184.45 [7179]~P120(x71791)+~P1(f333(f333(f248(x71791),f77(x71791)),x71793))+~P1(f333(f333(f248(x71791),f77(x71791)),x71792))+P1(f333(f333(f248(x71791),f77(x71791)),f333(f333(f80(x71791),x71792),x71793))) % 183.90/184.45 [7180]~P85(x71801)+~P1(f333(f333(f248(x71801),f2(x71801)),x71803))+~P1(f333(f333(f248(x71801),f2(x71801)),x71802))+P1(f333(f333(f248(x71801),f2(x71801)),f333(f333(f79(x71801),x71802),x71803))) % 183.90/184.45 [7183]~P125(x71831)+~P1(f333(f333(f248(x71831),f2(x71831)),x71833))+~P1(f333(f333(f248(x71831),f2(x71831)),x71832))+P1(f333(f333(f248(x71831),f2(x71831)),f333(f333(f80(x71831),x71832),x71833))) % 183.90/184.45 [7184]~P60(x71841)+~P1(f333(f333(f248(x71841),f2(x71841)),x71843))+~P1(f333(f333(f248(x71841),f2(x71841)),x71842))+P1(f333(f333(f248(x71841),f2(x71841)),f333(f333(f291(x71841),x71842),x71843))) % 183.90/184.45 [7185]~P61(x71851)+~P1(f333(f333(f248(x71851),f2(x71851)),x71853))+~P1(f333(f333(f248(x71851),f2(x71851)),x71852))+P1(f333(f333(f248(x71851),f2(x71851)),f333(f333(f291(x71851),x71852),x71853))) % 183.90/184.45 [7187]~P123(x71871)+~P1(f333(f333(f247(x71871),f2(x71871)),x71873))+~P1(f333(f333(f247(x71871),f2(x71871)),x71872))+P1(f333(f333(f247(x71871),f2(x71871)),f333(f333(f80(x71871),x71872),x71873))) % 183.90/184.45 [7188]~P122(x71881)+~P1(f333(f333(f247(x71881),f2(x71881)),x71883))+~P1(f333(f333(f247(x71881),f2(x71881)),x71882))+P1(f333(f333(f247(x71881),f2(x71881)),f333(f333(f80(x71881),x71882),x71883))) % 183.90/184.45 [7189]~P130(x71891)+~P1(f333(f333(f247(x71891),f2(x71891)),x71893))+~P1(f333(f333(f247(x71891),f2(x71891)),x71892))+P1(f333(f333(f247(x71891),f2(x71891)),f333(f333(f80(x71891),x71892),x71893))) % 183.90/184.45 [7190]~P60(x71901)+~P1(f333(f333(f247(x71901),f2(x71901)),x71903))+~P1(f333(f333(f247(x71901),f2(x71901)),x71902))+P1(f333(f333(f247(x71901),f2(x71901)),f333(f333(f291(x71901),x71902),x71903))) % 183.90/184.45 [7191]~P61(x71911)+~P1(f333(f333(f248(x71911),f2(x71911)),x71913))+~P1(f333(f333(f247(x71911),f2(x71911)),x71912))+P1(f333(f333(f247(x71911),f2(x71911)),f333(f333(f291(x71911),x71912),x71913))) % 183.90/184.45 [7262]~P62(x72621)+~P1(f333(f61(x72621),x72623))+E(f13(x72621,f333(f333(f311(x72621),x72622),x72623)),x72622)+~E(f333(f333(f22(f882(x72621,a870)),x72623),f333(f333(f311(x72621),x72622),f196(f882(x72621,a870)))),f196(f882(x72621,a870))) % 183.90/184.45 [7263]~P62(x72631)+~P1(f333(f61(x72631),x72633))+E(f10(x72631,f333(f333(f311(x72631),x72632),x72633)),x72632)+~E(f333(f333(f22(f882(x72631,a870)),x72633),f333(f333(f311(x72631),x72632),f196(f882(x72631,a870)))),f196(f882(x72631,a870))) % 183.90/184.45 [7264]~P106(x72641)+~P1(f333(f61(x72641),x72643))+E(f14(x72641,f333(f333(f311(x72641),x72642),x72643)),x72642)+~E(f333(f333(f22(f882(x72641,a870)),x72643),f333(f333(f311(x72641),x72642),f196(f882(x72641,a870)))),f196(f882(x72641,a870))) % 183.90/184.45 [7265]~P106(x72651)+~P1(f333(f61(x72651),x72653))+E(f15(x72651,f333(f333(f311(x72651),x72652),x72653)),x72652)+~E(f333(f333(f22(f882(x72651,a870)),x72653),f333(f333(f311(x72651),x72652),f196(f882(x72651,a870)))),f196(f882(x72651,a870))) % 183.90/184.45 [7266]~P60(x72661)+P1(f333(f333(f248(x72661),x72662),f2(x72661)))+P1(f333(f333(f248(x72661),f2(x72661)),x72663))+~P1(f333(f333(f248(x72661),f2(x72661)),f333(f333(f291(x72661),x72663),x72662))) % 183.90/184.45 [7267]~P60(x72671)+P1(f333(f333(f248(x72671),x72672),f2(x72671)))+P1(f333(f333(f248(x72671),f2(x72671)),x72673))+~P1(f333(f333(f248(x72671),f2(x72671)),f333(f333(f291(x72671),x72672),x72673))) % 183.90/184.45 [7268]~P60(x72681)+P1(f333(f333(f248(x72681),x72682),f2(x72681)))+P1(f333(f333(f248(x72681),f2(x72681)),x72682))+~P1(f333(f333(f248(x72681),f2(x72681)),f333(f333(f291(x72681),x72683),x72682))) % 183.90/184.45 [7269]~P60(x72691)+P1(f333(f333(f248(x72691),x72692),f2(x72691)))+P1(f333(f333(f248(x72691),f2(x72691)),x72692))+~P1(f333(f333(f248(x72691),f2(x72691)),f333(f333(f291(x72691),x72692),x72693))) % 183.90/184.45 [7270]~P122(x72701)+P1(f333(f333(f247(x72701),x72702),f2(x72701)))+P1(f333(f333(f247(x72701),f2(x72701)),x72703))+~P1(f333(f333(f247(x72701),f2(x72701)),f333(f333(f80(x72701),x72703),x72702))) % 183.90/184.45 [7271]~P122(x72711)+P1(f333(f333(f247(x72711),x72712),f2(x72711)))+P1(f333(f333(f247(x72711),f2(x72711)),x72713))+~P1(f333(f333(f247(x72711),f2(x72711)),f333(f333(f80(x72711),x72712),x72713))) % 183.90/184.45 [7272]~P60(x72721)+P1(f333(f333(f247(x72721),x72722),f2(x72721)))+P1(f333(f333(f247(x72721),f2(x72721)),x72723))+~P1(f333(f333(f247(x72721),f2(x72721)),f333(f333(f291(x72721),x72723),x72722))) % 183.90/184.45 [7273]~P60(x72731)+P1(f333(f333(f247(x72731),x72732),f2(x72731)))+P1(f333(f333(f247(x72731),f2(x72731)),x72733))+~P1(f333(f333(f247(x72731),f2(x72731)),f333(f333(f291(x72731),x72732),x72733))) % 183.90/184.45 [7274]~P122(x72741)+P1(f333(f333(f247(x72741),x72742),f2(x72741)))+P1(f333(f333(f247(x72741),f2(x72741)),x72742))+~P1(f333(f333(f247(x72741),f2(x72741)),f333(f333(f80(x72741),x72743),x72742))) % 183.90/184.45 [7275]~P122(x72751)+P1(f333(f333(f247(x72751),x72752),f2(x72751)))+P1(f333(f333(f247(x72751),f2(x72751)),x72752))+~P1(f333(f333(f247(x72751),f2(x72751)),f333(f333(f80(x72751),x72752),x72753))) % 183.90/184.45 [7276]~P60(x72761)+P1(f333(f333(f247(x72761),x72762),f2(x72761)))+P1(f333(f333(f247(x72761),f2(x72761)),x72762))+~P1(f333(f333(f247(x72761),f2(x72761)),f333(f333(f291(x72761),x72763),x72762))) % 183.90/184.45 [7277]~P60(x72771)+P1(f333(f333(f247(x72771),x72772),f2(x72771)))+P1(f333(f333(f247(x72771),f2(x72771)),x72772))+~P1(f333(f333(f247(x72771),f2(x72771)),f333(f333(f291(x72771),x72772),x72773))) % 183.90/184.45 [7367]~E(f333(f333(f104(f882(x73671,a870)),f333(f174(x73671),x73672)),f333(f174(x73671),x73673)),f196(f882(x73671,a870)))+~P1(f333(f138(x73671),x73673))+~P1(f333(f138(x73671),x73672))+P1(f333(f138(x73671),f333(f333(f135(x73671),x73672),x73673))) % 183.90/184.45 [7368]~P106(x73681)+~P1(f333(f61(x73681),x73683))+E(f11(x73681,f245(x73681),f333(f333(f311(x73681),x73682),x73683)),x73682)+~E(f333(f333(f22(f882(x73681,a870)),x73683),f333(f333(f311(x73681),x73682),f196(f882(x73681,a870)))),f196(f882(x73681,a870))) % 183.90/184.45 [7369]~P106(x73691)+~P1(f333(f61(x73691),x73693))+E(f12(x73691,f246(x73691),f333(f333(f311(x73691),x73692),x73693)),x73692)+~E(f333(f333(f22(f882(x73691,a870)),x73693),f333(f333(f311(x73691),x73692),f196(f882(x73691,a870)))),f196(f882(x73691,a870))) % 183.90/184.45 [7384]~P114(x73841)+~P1(f333(f333(f248(x73841),x73842),x73843))+~P1(f333(f333(f248(x73841),f333(f78(x73841),x73842)),x73843))+P1(f333(f333(f248(x73841),f333(f74(x73841),x73842)),x73843)) % 183.90/184.45 [7386]~P83(x73861)+~P1(f333(f333(f247(x73861),x73862),x73863))+~P1(f333(f333(f247(x73861),f333(f78(x73861),x73862)),x73863))+P1(f333(f333(f247(x73861),f333(f74(x73861),x73862)),x73863)) % 183.90/184.45 [7457]~P125(x74571)+P1(f333(f333(f248(x74571),f2(x74571)),x74572))+~P1(f333(f333(f248(x74571),f2(x74571)),x74573))+~P1(f333(f333(f248(x74571),f2(x74571)),f333(f333(f80(x74571),x74573),x74572))) % 183.90/184.45 [7458]~P125(x74581)+P1(f333(f333(f248(x74581),f2(x74581)),x74582))+~P1(f333(f333(f248(x74581),f2(x74581)),x74583))+~P1(f333(f333(f248(x74581),f2(x74581)),f333(f333(f80(x74581),x74582),x74583))) % 183.90/184.45 [7765]E(x77651,x77652)+~P1(f333(f61(x77653),x77651))+~P1(f333(f333(f247(a875),f333(f37(x77653),x77651)),f333(f37(x77653),x77652)))+~P1(f333(f333(f247(f882(x77653,a870)),x77652),x77651)) % 183.90/184.45 [7909]~P1(f333(f333(f248(a1),x79091),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x79092))+~P1(f333(f333(f247(a1),x79092),x79093))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x79091),x79092)),f333(f333(f38(a1),x79091),x79093))) % 183.90/184.45 [7921]~P1(f333(f333(f248(a1),f2(a1)),x79213))+~P1(f333(f333(f247(a1),f2(a1)),x79211))+~P1(f333(f333(f247(a1),x79213),x79212))+P1(f333(f333(f247(a1),f333(f333(f38(a1),x79211),x79212)),f333(f333(f38(a1),x79211),x79213))) % 183.90/184.45 [8062]E(f333(x80621,f472(x80622,x80621,x80623)),x80622)+~P1(f333(f333(f247(a1),x80622),f333(x80621,x80623)))+P1(f333(f333(f248(a875),f473(x80622,x80621,x80623)),x80623))+~P1(f333(f333(f247(a1),f333(x80621,f2(a875))),x80622)) % 183.90/184.45 [8063]E(f333(x80631,f474(x80632,x80631,x80633)),x80632)+~P1(f333(f333(f247(a1),x80632),f333(x80631,x80633)))+P1(f333(f333(f248(a875),f475(x80632,x80631,x80633)),x80633))+~P1(f333(f333(f247(a1),f333(x80631,f2(a875))),x80632)) % 183.90/184.45 [8167]~P1(f333(f61(x81671),x81673))+~P1(f333(f333(f248(a875),f333(f37(x81671),x81672)),f333(f37(x81671),x81673)))+~P1(f333(f333(f247(f882(x81671,a870)),x81672),x81673))+P1(f333(f333(f248(f882(x81671,a870)),x81672),x81673)) % 183.90/184.45 [8196]E(f333(f333(f79(a1),f419(x81963,x81961,x81962)),f420(x81963,x81961,x81962)),x81961)+E(f333(f333(f22(a1),x81961),x81962),x81961)+~P1(f333(f333(f248(a1),f2(a1)),x81962))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x81961),f77(a1))),x81963)) % 183.90/184.45 [8197]E(f333(f333(f22(a1),f432(x81973,x81971,x81972)),f433(x81973,x81971,x81972)),x81971)+E(f333(f333(f79(a1),x81971),x81972),x81971)+~P1(f333(f333(f248(a1),f2(a1)),x81972))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x81971),f77(a1))),x81973)) % 183.90/184.45 [8250]~P1(f333(f333(f247(a875),x82503),x82501))+P1(f333(f333(f248(a875),x82501),x82502))+~P1(f333(f333(f247(a875),x82503),x82502))+~P1(f333(f333(f248(a875),f333(f333(f22(a875),x82501),x82503)),f333(f333(f22(a875),x82502),x82503))) % 183.90/184.45 [8251]~P1(f333(f333(f247(a875),x82513),x82511))+P1(f333(f333(f247(a875),x82511),x82512))+~P1(f333(f333(f247(a875),x82513),x82512))+~P1(f333(f333(f247(a875),f333(f333(f22(a875),x82511),x82513)),f333(f333(f22(a875),x82512),x82513))) % 183.90/184.45 [8267]~P106(x82672)+E(x82671,f116(x82672))+~P14(x82672,f333(f170(x82672),x82671))+E(f333(f143(x82672,x82672,f333(f7(x82672,x82672,x82672),f246(x82672)),x82673),f333(f170(x82672),x82671)),f333(f333(f246(x82672),f333(f333(f166(x82672),x82671),f2(a875))),x82673)) % 183.90/184.45 [8333]E(f333(f333(f22(a1),x83331),x83332),x83331)+~P1(f333(f333(f248(a1),f2(a1)),x83332))+P1(f333(f333(f335(a1),f419(x83333,x83331,x83332)),x83333))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x83331),f77(a1))),x83333)) % 183.90/184.45 [8334]E(f333(f333(f79(a1),x83341),x83342),x83341)+~P1(f333(f333(f248(a1),f2(a1)),x83342))+P1(f333(f333(f335(a1),f432(x83343,x83341,x83342)),x83343))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x83341),f77(a1))),x83343)) % 183.90/184.45 [8410]~P1(f333(f333(f247(a1),x84101),f333(x84102,x84103)))+P1(f333(f333(f247(a875),f472(x84101,x84102,x84103)),x84103))+P1(f333(f333(f248(a875),f473(x84101,x84102,x84103)),x84103))+~P1(f333(f333(f247(a1),f333(x84102,f2(a875))),x84101)) % 183.90/184.45 [8411]~P1(f333(f333(f247(a1),x84111),f333(x84112,x84113)))+P1(f333(f333(f247(a875),f474(x84111,x84112,x84113)),x84113))+P1(f333(f333(f248(a875),f475(x84111,x84112,x84113)),x84113))+~P1(f333(f333(f247(a1),f333(x84112,f2(a875))),x84111)) % 183.90/184.45 [8489]E(f333(f333(f22(a1),x84891),x84892),x84891)+~P1(f333(f333(f248(a1),f2(a1)),x84892))+P1(f333(f333(f335(a1),f420(x84893,x84891,x84892)),f304(a1,f77(a1),x84892)))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x84891),f77(a1))),x84893)) % 183.90/184.45 [8490]E(f333(f333(f79(a1),x84901),x84902),x84901)+~P1(f333(f333(f248(a1),f2(a1)),x84902))+P1(f333(f333(f335(a1),f433(x84903,x84901,x84902)),f304(a1,f77(a1),x84902)))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x84901),f77(a1))),x84903)) % 183.90/184.45 [8618]~P120(x86181)+~P1(f333(f333(f248(x86181),x86182),f77(x86181)))+~P1(f333(f333(f248(x86181),f2(x86181)),x86182))+P1(f333(f333(f248(x86181),f333(f333(f80(x86181),x86182),f333(f333(f258(x86181),x86182),x86183))),f333(f333(f258(x86181),x86182),x86183))) % 183.90/184.45 [8701]~P1(f333(x87011,x87012))+P1(f333(x87011,f2(a875)))+~P1(f333(f333(f248(a875),x87012),x87013))+~P1(f333(x87011,f44(a875,f333(a115,f522(x87012,x87011,x87013)),x87013))) % 183.90/184.45 [8840]E(f551(x88401,x88402,x88403),f2(a875))+P1(f333(f333(x88401,x88403),x88402))+P1(f333(f333(x88401,f551(x88401,x88402,x88403)),f44(a875,f550(x88401,x88402,x88403),f551(x88401,x88402,x88403))))+~P1(f333(f321(f881(a875,a875),a231),f333(f333(f268(a875,a875),x88403),x88402))) % 183.90/184.45 [8878]~P25(x88781,x88781,x88782,x88783)+E(f333(f312(x88781,x88781,x88782),x88783),x88783)+~P1(f333(f61(x88781),x88783))+~P1(f333(f333(f247(f882(x88781,a870)),f333(f312(x88781,x88781,x88782),x88783)),x88783)) % 183.90/184.45 [9120]P1(f333(f333(x91201,x91202),x91203))+~P1(f333(f333(f248(a1),f548(x91201,x91203,x91202)),f2(a1)))+P1(f333(f333(x91201,f333(f78(a1),f547(x91201,x91203,x91202))),f333(f78(a1),f548(x91201,x91203,x91202))))+~P1(f333(f321(f881(a1,a1),a236),f333(f333(f268(a1,a1),x91202),x91203))) % 183.90/184.45 [9307]P1(f333(f333(x93071,x93072),x93073))+P1(f333(f333(x93071,f333(f333(f79(a1),f694(x93071,x93073,x93072)),f77(a1))),f696(x93071,x93073,x93072)))+~P1(f333(f333(f247(a1),f694(x93071,x93073,x93072)),f696(x93071,x93073,x93072)))+~P1(f333(f321(f881(a1,a1),a185),f333(f333(f268(a1,a1),x93072),x93073))) % 183.90/184.45 [9731]~P57(x97312)+~P57(x97311)+~P1(f333(f58(f881(x97311,x97312)),x97313))+P1(f333(f58(x97311),f333(f333(f8(f882(x97312,a870),a870,x97311),f58(x97312)),f333(f333(f8(f882(x97312,f881(x97311,x97312)),f882(x97312,a870),x97311),f333(f8(f881(x97311,x97312),a870,x97312),x97313)),f268(x97311,x97312))))) % 183.90/184.45 [9732]~P57(x97322)+~P57(x97321)+~P1(f333(f57(f881(x97321,x97322)),x97323))+P1(f333(f57(x97321),f333(f333(f8(f882(x97322,a870),a870,x97321),f57(x97322)),f333(f333(f8(f882(x97322,f881(x97321,x97322)),f882(x97322,a870),x97321),f333(f8(f881(x97321,x97322),a870,x97322),x97323)),f268(x97321,x97322))))) % 183.90/184.45 [9834]~P57(x98342)+~P57(x98341)+P1(f333(f58(f881(x98341,x98342)),x98343))+~P1(f333(f58(x98341),f333(f333(f8(f882(x98342,a870),a870,x98341),f58(x98342)),f333(f333(f8(f882(x98342,f881(x98341,x98342)),f882(x98342,a870),x98341),f333(f8(f881(x98341,x98342),a870,x98342),x98343)),f268(x98341,x98342))))) % 183.90/184.45 [9835]~P57(x98352)+~P57(x98351)+P1(f333(f57(f881(x98351,x98352)),x98353))+~P1(f333(f57(x98351),f333(f333(f8(f882(x98352,a870),a870,x98351),f57(x98352)),f333(f333(f8(f882(x98352,f881(x98351,x98352)),f882(x98352,a870),x98351),f333(f8(f881(x98351,x98352),a870,x98352),x98353)),f268(x98351,x98352))))) % 183.90/184.45 [10004]E(f333(x100041,f472(x100042,x100041,x100043)),x100042)+~P1(f333(f333(f247(a1),x100042),f333(x100041,x100043)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x100041,f333(f333(f79(a875),f473(x100042,x100041,x100043)),f77(a875)))),f333(x100041,f473(x100042,x100041,x100043))))),f77(a1)))+~P1(f333(f333(f247(a1),f333(x100041,f2(a875))),x100042)) % 183.90/184.45 [10005]E(f333(x100051,f474(x100052,x100051,x100053)),x100052)+~P1(f333(f333(f247(a1),x100052),f333(x100051,x100053)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x100051,f333(f333(f79(a875),f475(x100052,x100051,x100053)),f77(a875)))),f333(x100051,f475(x100052,x100051,x100053))))),f77(a1)))+~P1(f333(f333(f247(a1),f333(x100051,f2(a875))),x100052)) % 183.90/184.45 [10009]~P1(f333(f333(f247(a1),x100091),f333(x100092,x100093)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x100092,f333(f333(f79(a875),f473(x100091,x100092,x100093)),f77(a875)))),f333(x100092,f473(x100091,x100092,x100093))))),f77(a1)))+P1(f333(f333(f247(a875),f472(x100091,x100092,x100093)),x100093))+~P1(f333(f333(f247(a1),f333(x100092,f2(a875))),x100091)) % 183.90/184.45 [10010]~P1(f333(f333(f247(a1),x100101),f333(x100102,x100103)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x100102,f333(f333(f79(a875),f475(x100101,x100102,x100103)),f77(a875)))),f333(x100102,f475(x100101,x100102,x100103))))),f77(a1)))+P1(f333(f333(f247(a875),f474(x100101,x100102,x100103)),x100103))+~P1(f333(f333(f247(a1),f333(x100102,f2(a875))),x100101)) % 183.90/184.45 [10066]E(x100661,x100662)+~E(f333(f143(f876(x100663),f876(x100663),f135(x100663),f116(x100663)),x100661),f333(f143(f876(x100663),f876(x100663),f135(x100663),f116(x100663)),x100662))+~E(f333(f197(f876(f876(x100663))),x100661),f333(f197(f876(f876(x100663))),x100662))+~P1(f333(f333(f272(f876(x100663),f876(x100663),a870),f333(f333(f7(f876(x100663),f882(f876(x100663),a875),f882(f876(x100663),a870)),f333(f333(f8(f882(a875,a870),f882(f882(f876(x100663),a875),f882(f876(x100663),a870)),f876(x100663)),f8(a875,a870,f876(x100663))),f333(f333(f8(a875,f882(a875,a870),f876(x100663)),a330),f197(f876(x100663))))),f197(f876(x100663)))),f740(x100662,x100661,x100663))) % 183.90/184.45 [10067]E(x100671,x100672)+~E(f333(f143(f876(x100673),f876(x100673),f135(x100673),f116(x100673)),x100671),f333(f143(f876(x100673),f876(x100673),f135(x100673),f116(x100673)),x100672))+~E(f333(f197(f876(f876(x100673))),x100671),f333(f197(f876(f876(x100673))),x100672))+~P1(f333(f333(f272(f876(x100673),f876(x100673),a870),f333(f333(f7(f876(x100673),f882(f876(x100673),a875),f882(f876(x100673),a870)),f333(f333(f8(f882(a875,a870),f882(f882(f876(x100673),a875),f882(f876(x100673),a870)),f876(x100673)),f8(a875,a870,f876(x100673))),f333(f333(f8(a875,f882(a875,a870),f876(x100673)),a330),f197(f876(x100673))))),f197(f876(x100673)))),f741(x100671,x100672,x100673))) % 183.90/184.45 [6783]~E(f77(a875),f2(a875))+~P1(f333(f61(x67831),x67833))+~P1(f333(f61(x67831),x67832))+E(f333(f333(f79(a875),f333(f37(x67831),x67832)),f333(f37(x67831),x67833)),f333(f37(x67831),f333(f333(f113(f882(x67831,a870)),x67832),x67833))) % 183.90/184.45 [7198]~P99(x71981)+~P1(f333(f61(x71981),x71982))+~P1(f333(f333(f335(x71981),x71983),x71982))+P1(f333(f333(f247(x71981),f333(f63(x71981,f104(x71981)),x71982)),x71983)) % 183.90/184.45 [7199]~P106(x71991)+~P1(f333(f61(x71991),x71992))+~P1(f333(f333(f335(x71991),x71993),x71992))+P1(f333(f333(f247(x71991),f333(f63(x71991,f245(x71991)),x71992)),x71993)) % 183.90/184.45 [7451]~P1(f333(f61(x74511),x74513))+~P1(f333(f61(x74511),x74512))+~E(f333(f333(f104(f882(x74511,a870)),x74512),x74513),f196(f882(x74511,a870)))+E(f333(f333(f79(a875),f333(f37(x74511),x74512)),f333(f37(x74511),x74513)),f333(f37(x74511),f333(f333(f113(f882(x74511,a870)),x74512),x74513))) % 183.90/184.45 [8256]~P37(x82561,x82563)+~P37(x82561,x82562)+~E(f333(f333(f104(f882(x82561,a870)),f333(f266(x82561,x82561),x82562)),f333(f264(x82561,x82561),x82563)),f196(f882(x82561,a870)))+P37(x82561,f333(f333(f113(f882(f881(x82561,x82561),a870)),x82562),x82563)) % 183.90/184.45 [8348]E(x83481,f333(f333(f38(a875),x83482),x83483))+~P1(f333(f333(f248(a875),f2(a875)),x83483))+~P1(f333(f333(f248(a875),x83482),f333(f333(f80(a875),x83483),f333(a115,x83481))))+~P1(f333(f333(f247(a875),f333(f333(f80(a875),x83483),x83481)),x83482)) % 183.90/184.45 [8487]~P1(f333(f61(x84871),x84872))+~P1(f333(f61(x84871),x84873))+E(f333(f333(f79(a875),f333(f37(x84871),x84872)),f333(f37(x84871),x84873)),f333(f37(x84871),f333(f333(f113(f882(x84871,a870)),x84872),x84873)))+P1(f333(f333(f335(x84871),f369(x84873,x84872,x84871)),f333(f333(f104(f882(x84871,a870)),x84872),x84873))) % 183.90/184.45 [8852]~P122(x88522)+~E(x88521,f2(x88522))+~E(x88523,f2(x88522))+~P1(f333(f333(f248(x88522),f2(x88522)),f333(f333(f79(x88522),f333(f333(f80(x88522),x88523),x88523)),f333(f333(f80(x88522),x88521),x88521)))) % 183.90/184.45 [9387]~P37(x93871,x93873)+~P37(x93871,x93872)+P37(x93871,f333(f333(f113(f882(f881(x93871,x93871),a870)),x93872),x93873))+~P1(f333(f333(f247(f882(f881(x93871,x93871),a870)),f333(f333(f290(x93871,x93871,x93871),x93872),x93873)),x93872)) % 183.90/184.45 [9512]~P1(f333(x95121,x95123))+~P1(f333(f61(x95122),x95123))+P1(f333(x95121,f196(f882(x95122,a870))))+~P1(f333(x95121,f333(f333(f22(f882(x95122,a870)),f615(x95121,x95123,x95122)),f333(f333(f311(x95122),f616(x95121,x95123,x95122)),f196(f882(x95122,a870)))))) % 183.90/184.45 [9761]~P57(x97611)+~P57(x97612)+P10(x97611,f333(f333(f8(f882(x97612,x97611),a870,f876(x97611)),x97613),f333(f333(f8(f882(x97612,f879(x97611)),f882(x97612,x97611),f876(x97611)),f72(f879(x97611),x97611,x97612,f244(x97611))),f333(f333(f8(f876(f881(x97612,x97611)),f882(x97612,f879(x97611)),f876(x97611)),f180(x97612,x97611)),f333(f184(x97612,x97611),f55(x97612))))),f333(f197(f876(x97612)),f55(x97612)))+~P1(f333(f57(f882(x97612,x97611)),x97613)) % 183.90/184.45 [9762]~P57(x97621)+~P57(x97622)+P11(x97621,f333(f333(f8(f882(x97622,x97621),a870,f876(x97621)),x97623),f333(f333(f8(f882(x97622,f879(x97621)),f882(x97622,x97621),f876(x97621)),f72(f879(x97621),x97621,x97622,f244(x97621))),f333(f333(f8(f876(f881(x97622,x97621)),f882(x97622,f879(x97621)),f876(x97621)),f180(x97622,x97621)),f333(f184(x97622,x97621),f55(x97622))))),f333(f197(f876(x97622)),f55(x97622)))+~P1(f333(f58(f882(x97622,x97621)),x97623)) % 183.90/184.45 [9858]~P57(x98581)+~P57(x98582)+~P11(x98582,f333(f333(f8(f882(x98581,x98582),a870,f876(x98582)),x98583),f333(f333(f8(f882(x98581,f879(x98582)),f882(x98581,x98582),f876(x98582)),f72(f879(x98582),x98582,x98581,f244(x98582))),f333(f333(f8(f876(f881(x98581,x98582)),f882(x98581,f879(x98582)),f876(x98582)),f180(x98581,x98582)),f333(f184(x98581,x98582),f55(x98581))))),f333(f197(f876(x98581)),f55(x98581)))+P1(f333(f58(f882(x98581,x98582)),x98583)) % 183.90/184.45 [9859]~P57(x98591)+~P57(x98592)+~P10(x98592,f333(f333(f8(f882(x98591,x98592),a870,f876(x98592)),x98593),f333(f333(f8(f882(x98591,f879(x98592)),f882(x98591,x98592),f876(x98592)),f72(f879(x98592),x98592,x98591,f244(x98592))),f333(f333(f8(f876(f881(x98591,x98592)),f882(x98591,f879(x98592)),f876(x98592)),f180(x98591,x98592)),f333(f184(x98591,x98592),f55(x98591))))),f333(f197(f876(x98591)),f55(x98591)))+P1(f333(f57(f882(x98591,x98592)),x98593)) % 183.90/184.45 [8653]~P1(f333(f333(f248(a1),f2(a1)),x86533))+P1(f333(f333(f247(a1),f2(a1)),x86531))+~P1(f333(f333(f248(a1),x86532),x86533))+~P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),f333(f333(f80(a1),x86533),x86531)),x86532))) % 183.90/184.45 [8675]~P62(x86751)+~P1(f333(f61(x86751),x86752))+E(f333(f333(f22(f882(x86751,a870)),x86752),f333(f333(f311(x86751),x86753),f196(f882(x86751,a870)))),f196(f882(x86751,a870)))+E(f333(f333(f113(x86751),x86753),f13(x86751,f333(f333(f22(f882(x86751,a870)),x86752),f333(f333(f311(x86751),x86753),f196(f882(x86751,a870)))))),f13(x86751,f333(f333(f311(x86751),x86753),x86752))) % 183.90/184.45 [8676]~P62(x86761)+~P1(f333(f61(x86761),x86762))+E(f333(f333(f22(f882(x86761,a870)),x86762),f333(f333(f311(x86761),x86763),f196(f882(x86761,a870)))),f196(f882(x86761,a870)))+E(f333(f333(f104(x86761),x86763),f10(x86761,f333(f333(f22(f882(x86761,a870)),x86762),f333(f333(f311(x86761),x86763),f196(f882(x86761,a870)))))),f10(x86761,f333(f333(f311(x86761),x86763),x86762))) % 183.90/184.45 [8677]~P106(x86771)+~P1(f333(f61(x86771),x86772))+E(f333(f333(f22(f882(x86771,a870)),x86772),f333(f333(f311(x86771),x86773),f196(f882(x86771,a870)))),f196(f882(x86771,a870)))+E(f333(f333(f245(x86771),x86773),f14(x86771,f333(f333(f22(f882(x86771,a870)),x86772),f333(f333(f311(x86771),x86773),f196(f882(x86771,a870)))))),f14(x86771,f333(f333(f311(x86771),x86773),x86772))) % 183.90/184.45 [8678]~P106(x86781)+~P1(f333(f61(x86781),x86782))+E(f333(f333(f22(f882(x86781,a870)),x86782),f333(f333(f311(x86781),x86783),f196(f882(x86781,a870)))),f196(f882(x86781,a870)))+E(f333(f333(f246(x86781),x86783),f15(x86781,f333(f333(f22(f882(x86781,a870)),x86782),f333(f333(f311(x86781),x86783),f196(f882(x86781,a870)))))),f15(x86781,f333(f333(f311(x86781),x86783),x86782))) % 183.90/184.45 [8742]~P106(x87421)+~P1(f333(f61(x87421),x87422))+E(f333(f333(f22(f882(x87421,a870)),x87422),f333(f333(f311(x87421),x87423),f196(f882(x87421,a870)))),f196(f882(x87421,a870)))+E(f333(f333(f245(x87421),x87423),f11(x87421,f245(x87421),f333(f333(f22(f882(x87421,a870)),x87422),f333(f333(f311(x87421),x87423),f196(f882(x87421,a870)))))),f11(x87421,f245(x87421),f333(f333(f311(x87421),x87423),x87422))) % 183.90/184.45 [8743]~P106(x87431)+~P1(f333(f61(x87431),x87432))+E(f333(f333(f22(f882(x87431,a870)),x87432),f333(f333(f311(x87431),x87433),f196(f882(x87431,a870)))),f196(f882(x87431,a870)))+E(f333(f333(f246(x87431),x87433),f12(x87431,f246(x87431),f333(f333(f22(f882(x87431,a870)),x87432),f333(f333(f311(x87431),x87433),f196(f882(x87431,a870)))))),f12(x87431,f246(x87431),f333(f333(f311(x87431),x87433),x87432))) % 183.90/184.45 [9327]E(x93271,x93272)+~E(f333(f143(f876(x93273),f876(x93273),f135(x93273),f116(x93273)),x93271),f333(f143(f876(x93273),f876(x93273),f135(x93273),f116(x93273)),x93272))+~E(f333(f197(f876(f876(x93273))),x93271),f333(f197(f876(f876(x93273))),x93272))+P1(f333(f333(f335(f881(f876(x93273),f876(x93273))),f740(x93272,x93271,x93273)),f333(f174(f881(f876(x93273),f876(x93273))),f333(f333(f184(f876(x93273),f876(x93273)),x93271),x93272)))) % 183.90/184.45 [9328]E(x93281,x93282)+~E(f333(f143(f876(x93283),f876(x93283),f135(x93283),f116(x93283)),x93281),f333(f143(f876(x93283),f876(x93283),f135(x93283),f116(x93283)),x93282))+~E(f333(f197(f876(f876(x93283))),x93281),f333(f197(f876(f876(x93283))),x93282))+P1(f333(f333(f335(f881(f876(x93283),f876(x93283))),f741(x93281,x93282,x93283)),f333(f174(f881(f876(x93283),f876(x93283))),f333(f333(f184(f876(x93283),f876(x93283)),x93282),x93281)))) % 183.90/184.45 [10151]~P96(x101512)+E(x101511,f196(f882(x101512,a870)))+~P1(f333(f61(x101512),x101511))+E(f10(x101512,f333(f253(x101512),f333(f333(f8(f882(x101512,a870),a870,x101512),f86(x101512)),f333(f333(f7(x101512,f882(x101512,a870),f882(x101512,a870)),f333(f333(f8(f882(x101512,f882(a870,a870)),f882(f882(x101512,a870),f882(x101512,a870)),x101512),f18(x101512,a870,a870)),f333(f333(f8(f882(x101512,a870),f882(x101512,f882(a870,a870)),x101512),f333(f8(a870,f882(a870,a870),x101512),a331)),f333(f333(f7(x101512,f882(x101512,x101512),f882(x101512,a870)),f333(f333(f8(f882(x101512,a870),f882(f882(x101512,x101512),f882(x101512,a870)),x101512),f8(x101512,a870,x101512)),a330)),f333(f113(x101512),x101513))))),f333(f333(f7(x101512,f882(x101512,a870),a870),f335(x101512)),x101511))))),f333(f333(f113(x101512),x101513),f10(x101512,x101511))) % 183.90/184.45 [10152]~P96(x101522)+E(x101521,f196(f882(x101522,a870)))+~P1(f333(f61(x101522),x101521))+E(f13(x101522,f333(f253(x101522),f333(f333(f8(f882(x101522,a870),a870,x101522),f86(x101522)),f333(f333(f7(x101522,f882(x101522,a870),f882(x101522,a870)),f333(f333(f8(f882(x101522,f882(a870,a870)),f882(f882(x101522,a870),f882(x101522,a870)),x101522),f18(x101522,a870,a870)),f333(f333(f8(f882(x101522,a870),f882(x101522,f882(a870,a870)),x101522),f333(f8(a870,f882(a870,a870),x101522),a331)),f333(f333(f7(x101522,f882(x101522,x101522),f882(x101522,a870)),f333(f333(f8(f882(x101522,a870),f882(f882(x101522,x101522),f882(x101522,a870)),x101522),f8(x101522,a870,x101522)),a330)),f333(f104(x101522),x101523))))),f333(f333(f7(x101522,f882(x101522,a870),a870),f335(x101522)),x101521))))),f333(f333(f104(x101522),x101523),f13(x101522,x101521))) % 183.90/184.45 [10153]~P75(x101532)+E(x101531,f196(f882(x101532,a870)))+~P1(f333(f61(x101532),x101531))+E(f14(x101532,f333(f253(x101532),f333(f333(f8(f882(x101532,a870),a870,x101532),f86(x101532)),f333(f333(f7(x101532,f882(x101532,a870),f882(x101532,a870)),f333(f333(f8(f882(x101532,f882(a870,a870)),f882(f882(x101532,a870),f882(x101532,a870)),x101532),f18(x101532,a870,a870)),f333(f333(f8(f882(x101532,a870),f882(x101532,f882(a870,a870)),x101532),f333(f8(a870,f882(a870,a870),x101532),a331)),f333(f333(f7(x101532,f882(x101532,x101532),f882(x101532,a870)),f333(f333(f8(f882(x101532,a870),f882(f882(x101532,x101532),f882(x101532,a870)),x101532),f8(x101532,a870,x101532)),a330)),f333(f79(x101532),x101533))))),f333(f333(f7(x101532,f882(x101532,a870),a870),f335(x101532)),x101531))))),f333(f333(f79(x101532),x101533),f14(x101532,x101531))) % 183.90/184.45 [10154]~P75(x101542)+E(x101541,f196(f882(x101542,a870)))+~P1(f333(f61(x101542),x101541))+E(f15(x101542,f333(f253(x101542),f333(f333(f8(f882(x101542,a870),a870,x101542),f86(x101542)),f333(f333(f7(x101542,f882(x101542,a870),f882(x101542,a870)),f333(f333(f8(f882(x101542,f882(a870,a870)),f882(f882(x101542,a870),f882(x101542,a870)),x101542),f18(x101542,a870,a870)),f333(f333(f8(f882(x101542,a870),f882(x101542,f882(a870,a870)),x101542),f333(f8(a870,f882(a870,a870),x101542),a331)),f333(f333(f7(x101542,f882(x101542,x101542),f882(x101542,a870)),f333(f333(f8(f882(x101542,a870),f882(f882(x101542,x101542),f882(x101542,a870)),x101542),f8(x101542,a870,x101542)),a330)),f333(f79(x101542),x101543))))),f333(f333(f7(x101542,f882(x101542,a870),a870),f335(x101542)),x101541))))),f333(f333(f79(x101542),x101543),f15(x101542,x101541))) % 183.90/184.45 [10155]~P106(x101552)+E(x101551,f196(f882(x101552,a870)))+~P1(f333(f61(x101552),x101551))+E(f12(x101552,f246(x101552),f333(f253(x101552),f333(f333(f8(f882(x101552,a870),a870,x101552),f86(x101552)),f333(f333(f7(x101552,f882(x101552,a870),f882(x101552,a870)),f333(f333(f8(f882(x101552,f882(a870,a870)),f882(f882(x101552,a870),f882(x101552,a870)),x101552),f18(x101552,a870,a870)),f333(f333(f8(f882(x101552,a870),f882(x101552,f882(a870,a870)),x101552),f333(f8(a870,f882(a870,a870),x101552),a331)),f333(f333(f7(x101552,f882(x101552,x101552),f882(x101552,a870)),f333(f333(f8(f882(x101552,a870),f882(f882(x101552,x101552),f882(x101552,a870)),x101552),f8(x101552,a870,x101552)),a330)),f333(f245(x101552),x101553))))),f333(f333(f7(x101552,f882(x101552,a870),a870),f335(x101552)),x101551))))),f333(f333(f245(x101552),x101553),f12(x101552,f246(x101552),x101551))) % 183.90/184.45 [10156]~P106(x101562)+E(x101561,f196(f882(x101562,a870)))+~P1(f333(f61(x101562),x101561))+E(f11(x101562,f245(x101562),f333(f253(x101562),f333(f333(f8(f882(x101562,a870),a870,x101562),f86(x101562)),f333(f333(f7(x101562,f882(x101562,a870),f882(x101562,a870)),f333(f333(f8(f882(x101562,f882(a870,a870)),f882(f882(x101562,a870),f882(x101562,a870)),x101562),f18(x101562,a870,a870)),f333(f333(f8(f882(x101562,a870),f882(x101562,f882(a870,a870)),x101562),f333(f8(a870,f882(a870,a870),x101562),a331)),f333(f333(f7(x101562,f882(x101562,x101562),f882(x101562,a870)),f333(f333(f8(f882(x101562,a870),f882(f882(x101562,x101562),f882(x101562,a870)),x101562),f8(x101562,a870,x101562)),a330)),f333(f246(x101562),x101563))))),f333(f333(f7(x101562,f882(x101562,a870),a870),f335(x101562)),x101561))))),f333(f333(f246(x101562),x101563),f11(x101562,f245(x101562),x101561))) % 183.90/184.45 [9908]~P114(x99081)+~E(x99083,f2(x99081))+~E(x99082,f2(x99081))+E(f333(f333(f79(x99081),f333(f333(f258(x99081),x99082),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x99081),x99083),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f2(x99081)) % 183.90/184.45 [10051]~P120(x100511)+~P1(f333(f333(f247(x100511),f2(x100511)),x100513))+P1(f333(f333(f247(x100511),x100512),x100513))+~P1(f333(f333(f247(x100511),f333(f333(f258(x100511),x100512),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x100511),x100513),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))))) % 183.90/184.45 [10097]~P114(x100972)+~E(x100971,f2(x100972))+~E(x100973,f2(x100972))+~P1(f333(f333(f248(x100972),f2(x100972)),f333(f333(f79(x100972),f333(f333(f258(x100972),x100973),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))),f333(f333(f258(x100972),x100971),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))))) % 183.90/184.45 [9289]E(x92891,x92892)+~E(f676(x92891,x92892,x92894,x92893),f677(x92891,x92892,x92894,x92893))+P1(f333(f333(f335(f881(f876(x92893),f876(x92893))),f333(f333(f268(f876(x92893),f876(x92893)),x92892),x92891)),f148(x92893,x92894)))+P1(f333(f333(f335(f881(f876(x92893),f876(x92893))),f333(f333(f268(f876(x92893),f876(x92893)),x92891),x92892)),f148(x92893,x92894))) % 183.90/184.45 [4856]~P58(x48562)+~E(x48564,f2(x48562))+~E(x48561,f2(x48562))+E(x48561,f333(f333(f291(x48562),x48563),x48564)) % 183.90/184.45 [4857]~P58(x48571)+~E(x48573,f2(x48571))+~E(x48574,f2(x48571))+E(f333(f333(f291(x48571),x48572),x48573),x48574) % 183.90/184.45 [4967]~P58(x49672)+E(x49671,f2(x49672))+~E(x49673,f2(x49672))+~E(x49671,f333(f333(f291(x49672),x49674),x49673)) % 183.90/184.45 [4968]~P58(x49682)+E(x49681,f2(x49682))+~E(x49683,f2(x49682))+~E(f333(f333(f291(x49682),x49684),x49683),x49681) % 183.90/184.45 [5143]~P117(x51432)+E(x51431,f2(x51432))+~E(f333(f333(f291(x51432),x51433),x51431),x51434)+E(x51433,f333(f333(f80(x51432),x51434),x51431)) % 183.90/184.45 [5145]~P117(x51452)+E(x51451,f2(x51452))+~E(f333(f333(f80(x51452),x51453),x51451),x51454)+E(x51453,f333(f333(f291(x51452),x51454),x51451)) % 183.90/184.45 [5146]~P58(x51462)+E(x51461,f2(x51462))+~E(f333(f333(f291(x51462),x51463),x51461),x51464)+E(x51463,f333(f333(f80(x51462),x51464),x51461)) % 183.90/184.45 [5147]~P58(x51472)+E(x51471,f2(x51472))+~E(f333(f333(f80(x51472),x51473),x51471),x51474)+E(x51473,f333(f333(f291(x51472),x51474),x51471)) % 183.90/184.45 [5148]~P117(x51482)+E(x51481,f2(x51482))+~E(x51483,f333(f333(f291(x51482),x51484),x51481))+E(f333(f333(f80(x51482),x51483),x51481),x51484) % 183.90/184.45 [5150]~P117(x51502)+E(x51501,f2(x51502))+~E(x51503,f333(f333(f80(x51502),x51504),x51501))+E(f333(f333(f291(x51502),x51503),x51501),x51504) % 183.90/184.45 [5151]~P58(x51512)+E(x51511,f2(x51512))+~E(x51513,f333(f333(f291(x51512),x51514),x51511))+E(f333(f333(f80(x51512),x51513),x51511),x51514) % 183.90/184.45 [5152]~P58(x51522)+E(x51521,f2(x51522))+~E(x51523,f333(f333(f80(x51522),x51524),x51521))+E(f333(f333(f291(x51522),x51523),x51521),x51524) % 183.90/184.45 [5177]~P58(x51772)+~E(x51771,f2(x51772))+~E(f333(f333(f80(x51772),x51771),x51774),x51773)+E(x51771,f333(f333(f291(x51772),x51773),x51774)) % 183.90/184.45 [5178]~P58(x51781)+~E(x51784,f2(x51781))+~E(x51782,f333(f333(f80(x51781),x51784),x51783))+E(f333(f333(f291(x51781),x51782),x51783),x51784) % 183.90/184.45 [5251]~E(x52513,x52514)+~E(x52512,x52513)+~P108(x52511)+E(f304(x52511,x52512,x52513),f333(f333(f311(x52511),x52514),f196(f882(x52511,a870)))) % 183.90/184.45 [5457]~E(f117(x54572,x54571),x54573)+~E(f145(x54572,x54571),x54574)+E(x54571,f116(x54572))+E(f333(f333(f135(x54572),x54573),f333(f333(f152(x54572),x54574),f116(x54572))),x54571) % 183.90/184.45 [6071]~P120(x60713)+E(x60711,x60712)+~E(f333(f333(f258(x60713),x60714),x60711),f333(f333(f258(x60713),x60714),x60712))+~P1(f333(f333(f248(x60713),f77(x60713)),x60714)) % 183.90/184.45 [6072]E(x60721,x60722)+~E(f333(f333(f311(x60723),x60724),x60721),f333(f333(f311(x60723),x60724),x60722))+P1(f333(f333(f335(x60723),x60724),x60722))+P1(f333(f333(f335(x60723),x60724),x60721)) % 183.90/184.45 [6110]E(f333(x61101,x61102),f77(a875))+~E(f333(f333(f9(x61103,a875),x61101),x61104),f77(a875))+~P1(f333(f61(x61103),x61104))+~P1(f333(f333(f335(x61103),x61102),x61104)) % 183.90/184.45 [6111]E(f333(x61111,x61112),f2(a875))+~E(f333(f333(f6(x61113,a875),x61111),x61114),f2(a875))+~P1(f333(f61(x61113),x61114))+~P1(f333(f333(f335(x61113),x61112),x61114)) % 183.90/184.45 [6326]~P108(x63261)+~P1(f333(f333(f248(x63261),x63264),x63263))+P1(f333(f333(f248(x63261),x63262),x63263))+~P1(f333(f333(f248(x63261),x63262),x63264)) % 183.90/184.45 [6327]~P108(x63271)+~P1(f333(f333(f247(x63271),x63274),x63273))+P1(f333(f333(f248(x63271),x63272),x63273))+~P1(f333(f333(f248(x63271),x63272),x63274)) % 183.90/184.45 [6328]~P108(x63281)+~P1(f333(f333(f247(x63281),x63282),x63284))+P1(f333(f333(f248(x63281),x63282),x63283))+~P1(f333(f333(f248(x63281),x63284),x63283)) % 183.90/184.45 [6329]~P105(x63291)+~P1(f333(f333(f248(x63291),x63292),x63294))+P1(f333(f333(f248(x63291),x63292),x63293))+~P1(f333(f333(f248(x63291),x63294),x63293)) % 183.90/184.45 [6330]~P105(x63301)+~P1(f333(f333(f247(x63301),x63302),x63304))+P1(f333(f333(f248(x63301),x63302),x63303))+~P1(f333(f333(f248(x63301),x63304),x63303)) % 183.90/184.45 [6331]~P105(x63311)+~P1(f333(f333(f247(x63311),x63314),x63313))+P1(f333(f333(f248(x63311),x63312),x63313))+~P1(f333(f333(f248(x63311),x63312),x63314)) % 183.90/184.45 [6332]~P108(x63321)+~P1(f333(f333(f247(x63321),x63324),x63323))+P1(f333(f333(f247(x63321),x63322),x63323))+~P1(f333(f333(f247(x63321),x63322),x63324)) % 183.90/184.45 [6333]~P105(x63331)+~P1(f333(f333(f247(x63331),x63332),x63334))+P1(f333(f333(f247(x63331),x63332),x63333))+~P1(f333(f333(f247(x63331),x63334),x63333)) % 183.90/184.45 [6414]~P35(x64144,x64143,x64142)+E(x64141,f806(x64142,x64143,x64144))+~P1(f333(x64143,x64141))+~P1(f333(f333(f335(x64144),x64141),f333(f174(x64144),x64142))) % 183.90/184.45 [6558]~P4(x65581)+~P1(f333(f333(f247(x65581),x65582),f40(x65581,x65584)))+P1(f333(f333(f247(x65581),x65582),x65583))+~P1(f333(f333(f335(x65581),x65583),x65584)) % 183.90/184.45 [6704]~P106(x67041)+~P14(x67041,f333(f333(f152(x67041),x67042),x67044))+~P1(f333(f333(f335(x67041),x67043),f333(f174(x67041),x67044)))+P1(f333(f333(f247(x67041),x67042),x67043)) % 183.90/184.45 [6794]~P4(x67941)+~P1(f333(f333(f247(x67941),f39(x67941,x67944)),x67943))+P1(f333(f333(f247(x67941),x67942),x67943))+~P1(f333(f333(f335(x67941),x67942),x67944)) % 183.90/184.45 [7201]~P106(x72011)+E(f333(f333(f113(f882(x72011,a870)),f333(f303(x72011,x72012),x72013)),f333(f303(x72011,x72013),x72014)),f333(f303(x72011,x72012),x72014))+~P1(f333(f333(f247(x72011),x72013),x72014))+~P1(f333(f333(f247(x72011),x72012),x72013)) % 183.90/184.45 [7238]P35(x72381,x72382,x72383)+~E(f809(x72383,x72382,x72381,x72384),x72384)+~P1(f333(x72382,x72384))+~P1(f333(f333(f335(x72381),x72384),f333(f174(x72381),x72383))) % 183.90/184.45 [7312]~P106(x73121)+E(f333(f333(f113(f882(x73121,a870)),f333(f303(x73121,x73122),x73123)),f304(x73121,x73123,x73124)),f304(x73121,x73122,x73124))+~P1(f333(f333(f247(x73121),x73123),x73124))+~P1(f333(f333(f247(x73121),x73122),x73123)) % 183.90/184.45 [7378]~P106(x73781)+E(f333(f333(f113(f882(x73781,a870)),f307(x73781,x73782,x73783)),f333(f303(x73781,x73783),x73784)),f307(x73781,x73782,x73784))+~P1(f333(f333(f248(x73781),x73782),x73783))+~P1(f333(f333(f247(x73781),x73783),x73784)) % 183.90/184.45 [7398]~P106(x73981)+E(f333(f333(f113(f882(x73981,a870)),f304(x73981,x73982,x73983)),f307(x73981,x73983,x73984)),f333(f303(x73981,x73982),x73984))+~P1(f333(f333(f248(x73981),x73983),x73984))+~P1(f333(f333(f247(x73981),x73982),x73983)) % 183.90/184.45 [7430]~P106(x74301)+E(f333(f333(f113(f882(x74301,a870)),f307(x74301,x74302,x74303)),f304(x74301,x74303,x74304)),f306(x74301,x74302,x74304))+~P1(f333(f333(f248(x74301),x74302),x74303))+~P1(f333(f333(f247(x74301),x74303),x74304)) % 183.90/184.45 [7431]~P106(x74311)+E(f333(f333(f113(f882(x74311,a870)),f306(x74311,x74312,x74313)),f307(x74311,x74313,x74314)),f307(x74311,x74312,x74314))+~P1(f333(f333(f248(x74311),x74313),x74314))+~P1(f333(f333(f247(x74311),x74312),x74313)) % 183.90/184.45 [7432]~P106(x74321)+E(f333(f333(f113(f882(x74321,a870)),f306(x74321,x74322,x74323)),f306(x74321,x74323,x74324)),f306(x74321,x74322,x74324))+~P1(f333(f333(f247(x74321),x74323),x74324))+~P1(f333(f333(f247(x74321),x74322),x74323)) % 183.90/184.45 [7433]~P106(x74331)+E(f333(f333(f113(f882(x74331,a870)),f304(x74331,x74332,x74333)),f306(x74331,x74333,x74334)),f304(x74331,x74332,x74334))+~P1(f333(f333(f247(x74331),x74333),x74334))+~P1(f333(f333(f247(x74331),x74332),x74333)) % 183.90/184.45 [8240]P25(x82401,x82402,f349(x82403,x82402,x82404,x82401),x82404)+~P1(f333(f61(x82402),x82403))+~P1(f333(f61(x82401),x82404))+~P1(f333(f333(f247(a875),f333(f37(x82401),x82404)),f333(f37(x82402),x82403))) % 183.90/184.45 [8261]P35(x82611,x82612,x82613)+~P1(f333(x82612,x82614))+P1(f333(x82612,f809(x82613,x82612,x82611,x82614)))+~P1(f333(f333(f335(x82611),x82614),f333(f174(x82611),x82613))) % 183.90/184.45 [8312]~P73(x83121)+~E(f333(x83123,f860(x83123,x83124,x83122,x83121)),f77(x83121))+E(f333(f333(f333(f65(x83121,x83122,f80(x83121)),x83123),f77(x83121)),x83124),f77(x83121))+~P1(f333(f61(x83122),x83124)) % 183.90/184.45 [8585]~P120(x85851)+~P1(f333(f333(f247(x85851),f2(x85851)),x85853))+P1(f333(f333(f247(x85851),x85852),x85853))+~P1(f333(f333(f247(x85851),f333(f333(f258(x85851),x85852),f333(a115,x85854))),f333(f333(f258(x85851),x85853),f333(a115,x85854)))) % 183.90/184.45 [8879]P35(x88791,x88792,x88793)+~P1(f333(x88792,x88794))+~P1(f333(f333(f335(x88791),x88794),f333(f174(x88791),x88793)))+P1(f333(f333(f335(x88791),f809(x88793,x88792,x88791,x88794)),f333(f174(x88791),x88793))) % 183.90/184.45 [8967]~P73(x89671)+E(f333(f333(f333(f65(x89671,x89672,f80(x89671)),x89673),f77(x89671)),x89674),f77(x89671))+~P1(f333(f61(x89672),x89674))+P1(f333(f333(f335(x89672),f860(x89673,x89674,x89672,x89671)),x89674)) % 183.90/184.45 [9453]~P1(f333(f333(f247(a1),x94534),f2(a1)))+P1(f333(f333(f247(a1),f333(f333(f79(a1),f333(f333(f80(a1),x94531),f44(a1,x94532,x94533))),x94534)),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x94533))+~P1(f333(f333(f248(a1),x94531),x94534)) % 183.90/184.45 [9901]~P1(f333(f61(x99011),x99012))+~P1(f333(f333(f335(x99011),x99014),x99012))+~P1(f333(f333(f335(x99011),x99013),x99012))+P1(f333(f333(f248(a875),f333(f37(x99011),f333(f333(f22(f882(x99011,a870)),f333(f333(f22(f882(x99011,a870)),x99012),f333(f333(f311(x99011),x99013),f196(f882(x99011,a870))))),f333(f333(f311(x99011),x99014),f196(f882(x99011,a870)))))),f333(f37(x99011),x99012))) % 183.90/184.45 [6909]~P106(x69091)+~P1(f333(f333(f248(x69091),x69092),x69094))+~P1(f333(f333(f248(x69091),x69092),x69093))+P1(f333(f333(f248(x69091),x69092),f333(f333(f245(x69091),x69093),x69094))) % 183.90/184.45 [6912]~P99(x69121)+~P1(f333(f333(f247(x69121),x69122),x69124))+~P1(f333(f333(f247(x69121),x69122),x69123))+P1(f333(f333(f247(x69121),x69122),f333(f333(f104(x69121),x69123),x69124))) % 183.90/184.45 [6915]~P106(x69151)+~P1(f333(f333(f247(x69151),x69152),x69154))+~P1(f333(f333(f247(x69151),x69152),x69153))+P1(f333(f333(f247(x69151),x69152),f333(f333(f245(x69151),x69153),x69154))) % 183.90/184.45 [6934]~P59(x69342)+E(x69341,f2(x69342))+E(f333(f333(f291(x69342),f333(f333(f258(x69342),x69341),x69343)),f333(f333(f258(x69342),x69341),x69344)),f333(f333(f258(x69342),x69341),f333(f333(f22(a875),x69343),x69344)))+~P1(f333(f333(f247(a875),x69344),x69343)) % 183.90/184.45 [6979]~P106(x69791)+~P14(x69791,f333(f333(f152(x69791),x69793),x69794))+P14(x69791,f333(f333(f152(x69791),x69792),f333(f333(f152(x69791),x69793),x69794)))+~P1(f333(f333(f247(x69791),x69792),x69793)) % 183.90/184.45 [7020]~P120(x70201)+~P1(f333(f333(f248(x70201),f2(x70201)),x70203))+~P1(f333(f333(f248(x70201),x70202),x70204))+P1(f333(f333(f248(x70201),x70202),f333(f333(f79(x70201),x70203),x70204))) % 183.90/184.45 [7021]~P85(x70211)+~P1(f333(f333(f247(x70211),f2(x70211)),x70213))+~P1(f333(f333(f248(x70211),x70212),x70214))+P1(f333(f333(f248(x70211),x70212),f333(f333(f79(x70211),x70213),x70214))) % 183.90/184.45 [7022]~P85(x70221)+~P1(f333(f333(f247(x70221),x70222),x70224))+~P1(f333(f333(f248(x70221),f2(x70221)),x70223))+P1(f333(f333(f248(x70221),x70222),f333(f333(f79(x70221),x70223),x70224))) % 183.90/184.45 [7023]~P85(x70231)+~P1(f333(f333(f247(x70231),f2(x70231)),x70234))+~P1(f333(f333(f247(x70231),x70232),x70233))+P1(f333(f333(f247(x70231),x70232),f333(f333(f79(x70231),x70233),x70234))) % 183.90/184.45 [7024]~P85(x70241)+~P1(f333(f333(f247(x70241),f2(x70241)),x70243))+~P1(f333(f333(f247(x70241),x70242),x70244))+P1(f333(f333(f247(x70241),x70242),f333(f333(f79(x70241),x70243),x70244))) % 183.90/184.45 [7063]~P106(x70631)+P1(f333(f333(f248(x70631),x70632),x70633))+P1(f333(f333(f248(x70631),x70632),x70634))+~P1(f333(f333(f248(x70631),x70632),f333(f333(f246(x70631),x70634),x70633))) % 183.90/184.45 [7064]~P106(x70641)+P1(f333(f333(f247(x70641),x70642),x70643))+P1(f333(f333(f247(x70641),x70642),x70644))+~P1(f333(f333(f247(x70641),x70642),f333(f333(f246(x70641),x70644),x70643))) % 183.90/184.45 [7351]~P108(x73512)+~P57(x73511)+~P1(f333(f333(f248(f882(x73511,x73512)),x73513),x73514))+P1(f333(f333(f247(f882(x73511,x73512)),x73513),x73514)) % 183.90/184.45 [7723]~P61(x77231)+~P1(f333(f333(f248(x77231),x77234),f2(x77231)))+~P1(f333(f333(f248(x77231),x77233),f333(f333(f291(x77231),x77232),x77234)))+P1(f333(f333(f248(x77231),x77232),f333(f333(f80(x77231),x77233),x77234))) % 183.90/184.45 [7724]~P61(x77241)+~P1(f333(f333(f248(x77241),x77244),f2(x77241)))+~P1(f333(f333(f248(x77241),x77243),f333(f333(f80(x77241),x77242),x77244)))+P1(f333(f333(f248(x77241),x77242),f333(f333(f291(x77241),x77243),x77244))) % 183.90/184.45 [7725]~P61(x77251)+~P1(f333(f333(f248(x77251),x77254),f2(x77251)))+~P1(f333(f333(f247(x77251),x77253),f333(f333(f291(x77251),x77252),x77254)))+P1(f333(f333(f247(x77251),x77252),f333(f333(f80(x77251),x77253),x77254))) % 183.90/184.45 [7726]~P61(x77261)+~P1(f333(f333(f248(x77261),x77264),f2(x77261)))+~P1(f333(f333(f247(x77261),x77263),f333(f333(f80(x77261),x77262),x77264)))+P1(f333(f333(f247(x77261),x77262),f333(f333(f291(x77261),x77263),x77264))) % 183.90/184.45 [7839]~P122(x78391)+~P1(f333(f333(f248(x78391),x78393),f2(x78391)))+~P1(f333(f333(f248(x78391),x78394),x78392))+P1(f333(f333(f248(x78391),f333(f333(f80(x78391),x78392),x78393)),f333(f333(f80(x78391),x78394),x78393))) % 183.90/184.45 [7840]~P122(x78401)+~P1(f333(f333(f248(x78401),x78402),f2(x78401)))+~P1(f333(f333(f248(x78401),x78404),x78403))+P1(f333(f333(f248(x78401),f333(f333(f80(x78401),x78402),x78403)),f333(f333(f80(x78401),x78402),x78404))) % 183.90/184.45 [7841]~P61(x78411)+~P1(f333(f333(f248(x78411),x78413),f2(x78411)))+~P1(f333(f333(f248(x78411),x78414),x78412))+P1(f333(f333(f248(x78411),f333(f333(f291(x78411),x78412),x78413)),f333(f333(f291(x78411),x78414),x78413))) % 183.90/184.45 [7842]~P123(x78421)+~P1(f333(f333(f247(x78421),x78422),f2(x78421)))+~P1(f333(f333(f247(x78421),x78424),x78423))+P1(f333(f333(f247(x78421),f333(f333(f80(x78421),x78422),x78423)),f333(f333(f80(x78421),x78422),x78424))) % 183.90/184.45 [7843]~P122(x78431)+~P1(f333(f333(f248(x78431),x78432),f2(x78431)))+~P1(f333(f333(f247(x78431),x78434),x78433))+P1(f333(f333(f247(x78431),f333(f333(f80(x78431),x78432),x78433)),f333(f333(f80(x78431),x78432),x78434))) % 183.90/184.45 [7844]~P123(x78441)+~P1(f333(f333(f247(x78441),x78443),f2(x78441)))+~P1(f333(f333(f247(x78441),x78444),x78442))+P1(f333(f333(f247(x78441),f333(f333(f80(x78441),x78442),x78443)),f333(f333(f80(x78441),x78444),x78443))) % 183.90/184.45 [7845]~P60(x78451)+~P1(f333(f333(f247(x78451),x78453),f2(x78451)))+~P1(f333(f333(f247(x78451),x78454),x78452))+P1(f333(f333(f247(x78451),f333(f333(f291(x78451),x78452),x78453)),f333(f333(f291(x78451),x78454),x78453))) % 183.90/184.45 [7847]~P120(x78471)+~P1(f333(f333(f248(x78471),f77(x78471)),x78472))+~P1(f333(f333(f248(a875),x78473),x78474))+P1(f333(f333(f248(x78471),f333(f333(f258(x78471),x78472),x78473)),f333(f333(f258(x78471),x78472),x78474))) % 183.90/184.45 [7848]~P120(x78481)+~P1(f333(f333(f248(x78481),f77(x78481)),x78482))+~P1(f333(f333(f247(a875),x78483),x78484))+P1(f333(f333(f247(x78481),f333(f333(f258(x78481),x78482),x78483)),f333(f333(f258(x78481),x78482),x78484))) % 183.90/184.45 [7849]~P120(x78491)+~P1(f333(f333(f247(x78491),f77(x78491)),x78492))+~P1(f333(f333(f247(a875),x78493),x78494))+P1(f333(f333(f247(x78491),f333(f333(f258(x78491),x78492),x78493)),f333(f333(f258(x78491),x78492),x78494))) % 183.90/184.45 [7876]P1(f333(f333(f248(a875),f2(a875)),f333(x78761,x78762)))+~P1(f333(f61(x78763),x78764))+~P1(f333(f333(f335(x78763),x78762),x78764))+~P1(f333(f333(f248(a875),f2(a875)),f333(f333(f9(x78763,a875),x78761),x78764))) % 183.90/184.45 [7886]~P125(x78861)+~P1(f333(f333(f248(x78861),x78863),x78864))+~P1(f333(f333(f248(x78861),f2(x78861)),x78862))+P1(f333(f333(f248(x78861),f333(f333(f80(x78861),x78862),x78863)),f333(f333(f80(x78861),x78862),x78864))) % 183.90/184.45 [7887]~P115(x78871)+~P1(f333(f333(f248(x78871),x78873),x78874))+~P1(f333(f333(f248(x78871),f2(x78871)),x78872))+P1(f333(f333(f248(x78871),f333(f333(f80(x78871),x78872),x78873)),f333(f333(f80(x78871),x78872),x78874))) % 183.90/184.45 [7888]~P122(x78881)+~P1(f333(f333(f248(x78881),x78882),x78884))+~P1(f333(f333(f248(x78881),f2(x78881)),x78883))+P1(f333(f333(f248(x78881),f333(f333(f80(x78881),x78882),x78883)),f333(f333(f80(x78881),x78884),x78883))) % 183.90/184.45 [7889]~P125(x78891)+~P1(f333(f333(f248(x78891),x78892),x78894))+~P1(f333(f333(f248(x78891),f2(x78891)),x78893))+P1(f333(f333(f248(x78891),f333(f333(f80(x78891),x78892),x78893)),f333(f333(f80(x78891),x78894),x78893))) % 183.90/184.45 [7890]~P122(x78901)+~P1(f333(f333(f248(x78901),x78903),x78904))+~P1(f333(f333(f248(x78901),f2(x78901)),x78902))+P1(f333(f333(f248(x78901),f333(f333(f80(x78901),x78902),x78903)),f333(f333(f80(x78901),x78902),x78904))) % 183.90/184.45 [7891]~P61(x78911)+~P1(f333(f333(f248(x78911),x78912),x78914))+~P1(f333(f333(f248(x78911),f2(x78911)),x78913))+P1(f333(f333(f248(x78911),f333(f333(f291(x78911),x78912),x78913)),f333(f333(f291(x78911),x78914),x78913))) % 183.90/184.45 [7892]~P122(x78921)+~P1(f333(f333(f248(x78921),f2(x78921)),x78922))+~P1(f333(f333(f247(x78921),x78923),x78924))+P1(f333(f333(f247(x78921),f333(f333(f80(x78921),x78922),x78923)),f333(f333(f80(x78921),x78922),x78924))) % 183.90/184.45 [7893]~P132(x78931)+~P1(f333(f333(f247(x78931),x78933),x78934))+~P1(f333(f333(f247(x78931),f2(x78931)),x78932))+P1(f333(f333(f247(x78931),f333(f333(f80(x78931),x78932),x78933)),f333(f333(f80(x78931),x78932),x78934))) % 183.90/184.45 [7894]~P131(x78941)+~P1(f333(f333(f247(x78941),x78943),x78944))+~P1(f333(f333(f247(x78941),f2(x78941)),x78942))+P1(f333(f333(f247(x78941),f333(f333(f80(x78941),x78942),x78943)),f333(f333(f80(x78941),x78942),x78944))) % 183.90/184.45 [7895]~P132(x78951)+~P1(f333(f333(f247(x78951),x78952),x78954))+~P1(f333(f333(f247(x78951),f2(x78951)),x78953))+P1(f333(f333(f247(x78951),f333(f333(f80(x78951),x78952),x78953)),f333(f333(f80(x78951),x78954),x78953))) % 183.90/184.45 [7896]~P120(x78961)+~P1(f333(f333(f247(x78961),x78962),x78964))+~P1(f333(f333(f247(x78961),f2(x78961)),x78962))+P1(f333(f333(f247(x78961),f333(f333(f258(x78961),x78962),x78963)),f333(f333(f258(x78961),x78964),x78963))) % 183.90/184.45 [7897]~P60(x78971)+~P1(f333(f333(f247(x78971),x78972),x78974))+~P1(f333(f333(f247(x78971),f2(x78971)),x78973))+P1(f333(f333(f247(x78971),f333(f333(f291(x78971),x78972),x78973)),f333(f333(f291(x78971),x78974),x78973))) % 183.90/184.45 [7940]~P107(x79402)+P1(f333(f333(f247(f882(x79401,x79402)),x79404),x79403))+~P1(f333(f333(f247(f882(x79401,x79402)),x79403),x79404))+P1(f333(f333(f248(f882(x79401,x79402)),x79403),x79404)) % 183.90/184.45 [7983]P1(f333(f333(f335(x79831),x79832),x79833))+P1(f333(f333(f335(x79831),x79832),x79834))+~P1(f333(f333(f247(f882(x79831,a870)),x79834),x79833))+P1(f333(f333(f248(f882(x79831,a870)),x79834),f333(f333(f311(x79831),x79832),x79833))) % 183.90/184.45 [8145]P1(f333(f333(f335(x81451),x81452),x81453))+P1(f333(f333(f335(x81451),x81452),x81454))+~P1(f333(f333(f248(f882(x81451,a870)),x81454),f333(f333(f311(x81451),x81452),x81453)))+P1(f333(f333(f247(f882(x81451,a870)),x81454),x81453)) % 183.90/184.45 [8154]~P57(x81541)+P10(x81541,x81542,x81543)+~P1(f333(x81542,x81544))+~P1(f333(f333(f335(f876(x81541)),x81544),f333(f174(f876(x81541)),f54(x81541,x81543,f55(x81541))))) % 183.90/184.45 [8164]~P11(x81643,x81641,x81644)+~P57(x81643)+P1(f333(x81641,x81642))+~P1(f333(f333(f335(f876(x81643)),x81642),f333(f174(f876(x81643)),f54(x81643,x81644,f55(x81643))))) % 183.90/184.45 [8217]~P122(x82171)+P1(f333(f333(f248(x82171),x82173),x82172))+P1(f333(f333(f248(x82171),x82172),x82173))+~P1(f333(f333(f248(x82171),f333(f333(f80(x82171),x82174),x82172)),f333(f333(f80(x82171),x82174),x82173))) % 183.90/184.45 [8218]~P122(x82181)+P1(f333(f333(f248(x82181),x82183),x82182))+P1(f333(f333(f248(x82181),x82182),x82183))+~P1(f333(f333(f248(x82181),f333(f333(f80(x82181),x82182),x82184)),f333(f333(f80(x82181),x82183),x82184))) % 183.90/184.45 [8229]~P122(x82291)+P1(f333(f333(f248(x82291),x82294),f2(x82291)))+P1(f333(f333(f248(x82291),x82292),x82293))+~P1(f333(f333(f248(x82291),f333(f333(f80(x82291),x82292),x82294)),f333(f333(f80(x82291),x82293),x82294))) % 183.90/184.45 [8230]~P122(x82301)+P1(f333(f333(f248(x82301),x82304),f2(x82301)))+P1(f333(f333(f248(x82301),x82302),x82303))+~P1(f333(f333(f248(x82301),f333(f333(f80(x82301),x82304),x82302)),f333(f333(f80(x82301),x82304),x82303))) % 183.90/184.45 [8234]~P122(x82341)+P1(f333(f333(f248(x82341),x82342),x82343))+P1(f333(f333(f248(x82341),f2(x82341)),x82344))+~P1(f333(f333(f248(x82341),f333(f333(f80(x82341),x82344),x82343)),f333(f333(f80(x82341),x82344),x82342))) % 183.90/184.45 [8235]~P122(x82351)+P1(f333(f333(f248(x82351),x82352),x82353))+P1(f333(f333(f248(x82351),f2(x82351)),x82354))+~P1(f333(f333(f248(x82351),f333(f333(f80(x82351),x82353),x82354)),f333(f333(f80(x82351),x82352),x82354))) % 183.90/184.45 [8248]~P122(x82481)+P1(f333(f333(f248(x82481),x82482),f2(x82481)))+P1(f333(f333(f248(x82481),f2(x82481)),x82482))+~P1(f333(f333(f248(x82481),f333(f333(f80(x82481),x82483),x82482)),f333(f333(f80(x82481),x82484),x82482))) % 183.90/184.45 [8249]~P122(x82491)+P1(f333(f333(f248(x82491),x82492),f2(x82491)))+P1(f333(f333(f248(x82491),f2(x82491)),x82492))+~P1(f333(f333(f248(x82491),f333(f333(f80(x82491),x82492),x82493)),f333(f333(f80(x82491),x82492),x82494))) % 183.90/184.45 [8275]~P122(x82751)+~P1(f333(f333(f248(x82751),x82754),f2(x82751)))+P1(f333(f333(f248(x82751),x82752),x82753))+~P1(f333(f333(f248(x82751),f333(f333(f80(x82751),x82754),x82753)),f333(f333(f80(x82751),x82754),x82752))) % 183.90/184.45 [8276]~P122(x82761)+~P1(f333(f333(f248(x82761),x82764),f2(x82761)))+P1(f333(f333(f247(x82761),x82762),x82763))+~P1(f333(f333(f247(x82761),f333(f333(f80(x82761),x82764),x82763)),f333(f333(f80(x82761),x82764),x82762))) % 183.90/184.45 [8288]~P120(x82883)+~P1(f333(f333(f248(x82883),f77(x82883)),x82884))+P1(f333(f333(f248(a875),x82881),x82882))+~P1(f333(f333(f248(x82883),f333(f333(f258(x82883),x82884),x82881)),f333(f333(f258(x82883),x82884),x82882))) % 183.90/184.45 [8290]~P120(x82903)+~P1(f333(f333(f248(x82903),f77(x82903)),x82904))+P1(f333(f333(f247(a875),x82901),x82902))+~P1(f333(f333(f247(x82903),f333(f333(f258(x82903),x82904),x82901)),f333(f333(f258(x82903),x82904),x82902))) % 183.90/184.45 [8300]~P122(x83001)+P1(f333(f333(f248(x83001),x83002),x83003))+~P1(f333(f333(f248(x83001),f2(x83001)),x83004))+~P1(f333(f333(f248(x83001),f333(f333(f80(x83001),x83004),x83002)),f333(f333(f80(x83001),x83004),x83003))) % 183.90/184.45 [8301]~P125(x83011)+P1(f333(f333(f248(x83011),x83012),x83013))+~P1(f333(f333(f247(x83011),f2(x83011)),x83014))+~P1(f333(f333(f248(x83011),f333(f333(f80(x83011),x83014),x83012)),f333(f333(f80(x83011),x83014),x83013))) % 183.90/184.45 [8302]~P126(x83021)+P1(f333(f333(f248(x83021),x83022),x83023))+~P1(f333(f333(f247(x83021),f2(x83021)),x83024))+~P1(f333(f333(f248(x83021),f333(f333(f80(x83021),x83024),x83022)),f333(f333(f80(x83021),x83024),x83023))) % 183.90/184.45 [8303]~P120(x83031)+~P1(f333(f333(f247(x83031),f2(x83031)),x83033))+P1(f333(f333(f248(x83031),x83032),x83033))+~P1(f333(f333(f248(x83031),f333(f333(f258(x83031),x83032),x83034)),f333(f333(f258(x83031),x83033),x83034))) % 183.90/184.45 [8304]~P125(x83041)+P1(f333(f333(f248(x83041),x83042),x83043))+~P1(f333(f333(f247(x83041),f2(x83041)),x83044))+~P1(f333(f333(f248(x83041),f333(f333(f80(x83041),x83042),x83044)),f333(f333(f80(x83041),x83043),x83044))) % 183.90/184.45 [8305]~P126(x83051)+P1(f333(f333(f248(x83051),x83052),x83053))+~P1(f333(f333(f247(x83051),f2(x83051)),x83054))+~P1(f333(f333(f248(x83051),f333(f333(f80(x83051),x83052),x83054)),f333(f333(f80(x83051),x83053),x83054))) % 183.90/184.45 [8306]~P122(x83061)+P1(f333(f333(f247(x83061),x83062),x83063))+~P1(f333(f333(f248(x83061),f2(x83061)),x83064))+~P1(f333(f333(f247(x83061),f333(f333(f80(x83061),x83064),x83062)),f333(f333(f80(x83061),x83064),x83063))) % 183.90/184.45 [8307]~P125(x83071)+P1(f333(f333(f247(x83071),x83072),x83073))+~P1(f333(f333(f248(x83071),f2(x83071)),x83074))+~P1(f333(f333(f247(x83071),f333(f333(f80(x83071),x83074),x83072)),f333(f333(f80(x83071),x83074),x83073))) % 183.90/184.45 [8308]~P125(x83081)+P1(f333(f333(f247(x83081),x83082),x83083))+~P1(f333(f333(f248(x83081),f2(x83081)),x83084))+~P1(f333(f333(f247(x83081),f333(f333(f80(x83081),x83082),x83084)),f333(f333(f80(x83081),x83083),x83084))) % 183.90/184.45 [8351]P1(f333(f333(f335(x83511),x83512),x83513))+~P1(f333(f333(f247(f882(x83511,a870)),x83513),x83514))+~P1(f333(f333(f248(f882(x83511,a870)),x83513),x83514))+P1(f333(f333(f248(f882(x83511,a870)),x83513),f333(f333(f311(x83511),x83512),x83514))) % 183.90/184.45 [8608]~P57(x86081)+~P92(x86082)+~E(f333(x86083,f802(x86084,x86083,x86081,x86082)),f333(x86084,f802(x86084,x86083,x86081,x86082)))+P1(f333(f333(f90(f882(x86081,x86082)),x86083),x86084)) % 183.90/184.45 [8722]E(f333(f333(f22(a1),f435(x87221,x87222,x87223,x87224)),f436(x87221,x87222,x87223,x87224)),x87224)+~P1(f333(f333(f248(a1),f2(a1)),x87223))+~P1(f333(f333(f247(a1),x87221),x87224))+P1(f333(f333(f247(a1),x87221),f333(f333(f79(a1),x87224),x87223))) % 183.90/184.45 [8723]E(f333(f333(f22(a1),f445(x87231,x87232,x87233,x87234)),f446(x87231,x87232,x87233,x87234)),x87234)+~P1(f333(f333(f248(a1),f2(a1)),x87233))+~P1(f333(f333(f248(a1),x87231),x87234))+P1(f333(f333(f248(a1),x87231),f333(f333(f79(a1),x87234),x87233))) % 183.90/184.45 [8859]~E(f333(f333(f166(x88591),x88593),f695(x88594,x88593,x88591,x88592)),f333(f333(f166(x88591),x88594),f695(x88594,x88593,x88591,x88592)))+E(f333(f333(f177(x88591),x88592),x88593),f333(f333(f177(x88591),x88592),x88594))+~P1(f333(f333(f247(a875),x88592),f333(f197(f876(x88591)),x88593)))+~P1(f333(f333(f247(a875),x88592),f333(f197(f876(x88591)),x88594))) % 183.90/184.45 [8933]~P1(f333(f333(f248(a1),f2(a1)),x89333))+~P1(f333(f333(f247(a1),x89331),x89334))+P1(f333(f333(f335(a1),f435(x89331,x89332,x89333,x89334)),x89332))+P1(f333(f333(f247(a1),x89331),f333(f333(f79(a1),x89334),x89333))) % 183.90/184.45 [8934]~P1(f333(f333(f248(a1),f2(a1)),x89343))+~P1(f333(f333(f248(a1),x89341),x89344))+P1(f333(f333(f335(a1),f445(x89341,x89342,x89343,x89344)),x89342))+P1(f333(f333(f248(a1),x89341),f333(f333(f79(a1),x89344),x89343))) % 183.90/184.45 [8976]~P99(x89761)+~P1(f333(f61(x89761),x89763))+~P1(f333(f333(f335(x89761),x89764),x89763))+P1(f333(f333(f247(x89761),f333(f333(f64(x89761,x89761,f104(x89761)),x89762),x89763)),f333(f333(f104(x89761),x89764),x89762))) % 183.90/184.45 [8977]~P106(x89771)+~P1(f333(f61(x89771),x89773))+~P1(f333(f333(f335(x89771),x89774),x89773))+P1(f333(f333(f247(x89771),f333(f333(f64(x89771,x89771,f245(x89771)),x89772),x89773)),f333(f333(f245(x89771),x89774),x89772))) % 183.90/184.45 [9023]E(f333(f333(f177(x90231),x90232),x90233),f333(f333(f177(x90231),x90232),x90234))+P1(f333(f333(f248(a875),f695(x90233,x90234,x90231,x90232)),x90232))+~P1(f333(f333(f247(a875),x90232),f333(f197(f876(x90231)),x90233)))+~P1(f333(f333(f247(a875),x90232),f333(f197(f876(x90231)),x90234))) % 183.90/184.45 [9028]~P1(f333(f333(f248(a1),f2(a1)),x90283))+~P1(f333(f333(f248(a1),x90281),x90282))+P1(f333(f333(f335(a1),f446(x90281,x90284,x90283,x90282)),f304(a1,f77(a1),x90283)))+P1(f333(f333(f248(a1),x90281),f333(f333(f79(a1),x90282),x90283))) % 183.90/184.45 [9029]~P1(f333(f333(f248(a1),f2(a1)),x90293))+~P1(f333(f333(f247(a1),x90291),x90292))+P1(f333(f333(f335(a1),f436(x90291,x90294,x90293,x90292)),f304(a1,f77(a1),x90293)))+P1(f333(f333(f247(a1),x90291),f333(f333(f79(a1),x90292),x90293))) % 183.90/184.45 [9192]~E(f333(f180(x91921,x91922),x91923),f333(f180(x91921,x91922),x91924))+E(f333(f174(f881(x91921,x91922)),x91923),f333(f174(f881(x91921,x91922)),x91924))+~P1(f333(f138(x91921),f333(f333(f155(f881(x91921,x91922),x91921),f267(x91921,x91922)),x91924)))+~P1(f333(f138(x91921),f333(f333(f155(f881(x91921,x91922),x91921),f267(x91921,x91922)),x91923))) % 183.90/184.45 [9204]E(f333(f180(x92041,x92042),x92043),f333(f180(x92041,x92042),x92044))+~E(f333(f174(f881(x92041,x92042)),x92043),f333(f174(f881(x92041,x92042)),x92044))+~P1(f333(f138(x92041),f333(f333(f155(f881(x92041,x92042),x92041),f267(x92041,x92042)),x92044)))+~P1(f333(f138(x92041),f333(f333(f155(f881(x92041,x92042),x92041),f267(x92041,x92042)),x92043))) % 183.90/184.45 [9347]~P106(x93471)+~P1(f333(f61(x93471),x93474))+P1(f333(f333(f335(x93471),f524(x93472,x93473,x93474,x93471)),x93474))+P1(f333(f333(f247(x93471),f333(f333(f64(x93471,x93471,f246(x93471)),x93472),x93474)),f333(f333(f246(x93471),x93473),x93472))) % 183.90/184.45 [9348]~P98(x93481)+~P1(f333(f61(x93481),x93484))+P1(f333(f333(f335(x93481),f530(x93482,x93483,x93484,x93481)),x93484))+P1(f333(f333(f247(x93481),f333(f333(f64(x93481,x93481,f113(x93481)),x93482),x93484)),f333(f333(f113(x93481),x93483),x93482))) % 183.90/184.45 [9471]~P98(x94711)+~P1(f333(f61(x94711),x94713))+~P1(f333(f333(f247(x94711),f530(x94712,x94714,x94713,x94711)),x94714))+P1(f333(f333(f247(x94711),f333(f333(f64(x94711,x94711,f113(x94711)),x94712),x94713)),f333(f333(f113(x94711),x94714),x94712))) % 183.90/184.45 [9472]~P106(x94721)+~P1(f333(f61(x94721),x94723))+~P1(f333(f333(f247(x94721),f524(x94722,x94724,x94723,x94721)),x94724))+P1(f333(f333(f247(x94721),f333(f333(f64(x94721,x94721,f246(x94721)),x94722),x94723)),f333(f333(f246(x94721),x94724),x94722))) % 183.90/184.45 [9475]~P1(f333(f333(f248(a1),f2(a1)),x94753))+~P1(f333(f333(f247(a1),f2(a1)),x94754))+~P1(f333(f333(f248(a1),x94754),x94751))+P1(f333(f333(f248(a1),f333(f333(f79(a1),f333(f333(f80(a1),x94751),f44(a1,x94752,x94753))),x94754)),f333(f333(f80(a1),x94751),x94753))) % 183.90/184.45 [9870]E(x98701,x98702)+P1(f333(f333(f335(f881(f876(x98703),f876(x98703))),f333(f333(f268(f876(x98703),f876(x98703)),x98702),x98701)),f148(x98703,x98704)))+P1(f333(f333(f335(f881(f876(x98703),f876(x98703))),f333(f333(f268(f876(x98703),f876(x98703)),x98701),x98702)),f148(x98703,x98704)))+~P1(f333(f333(f335(f881(x98703,x98703)),f333(f333(f268(x98703,x98703),f676(x98701,x98702,x98704,x98703)),f677(x98701,x98702,x98704,x98703))),x98704)) % 183.90/184.45 [9871]E(x98711,x98712)+P1(f333(f333(f335(f881(f876(x98713),f876(x98713))),f333(f333(f268(f876(x98713),f876(x98713)),x98712),x98711)),f148(x98713,x98714)))+P1(f333(f333(f335(f881(f876(x98713),f876(x98713))),f333(f333(f268(f876(x98713),f876(x98713)),x98711),x98712)),f148(x98713,x98714)))+~P1(f333(f333(f335(f881(x98713,x98713)),f333(f333(f268(x98713,x98713),f677(x98711,x98712,x98714,x98713)),f676(x98711,x98712,x98714,x98713))),x98714)) % 183.90/184.45 [7418]~P106(x74181)+~P1(f333(f333(f248(x74181),x74183),x74184))+~P1(f333(f333(f248(x74181),x74182),x74184))+P1(f333(f333(f248(x74181),f333(f333(f246(x74181),x74182),x74183)),x74184)) % 183.90/184.45 [7421]~P98(x74211)+~P1(f333(f333(f247(x74211),x74213),x74214))+~P1(f333(f333(f247(x74211),x74212),x74214))+P1(f333(f333(f247(x74211),f333(f333(f113(x74211),x74212),x74213)),x74214)) % 183.90/184.45 [7424]~P106(x74241)+~P1(f333(f333(f247(x74241),x74243),x74244))+~P1(f333(f333(f247(x74241),x74242),x74244))+P1(f333(f333(f247(x74241),f333(f333(f246(x74241),x74242),x74243)),x74244)) % 183.90/184.45 [7748]~E(x77481,x77483)+E(f140(a875,f333(f303(a875,x77481),x77482)),f333(f333(f152(a875),x77483),x77484))+~E(f140(a875,f333(f303(a875,f333(f333(f79(a875),x77481),f77(a875))),x77482)),x77484)+~P1(f333(f333(f248(a875),x77481),x77482)) % 183.90/184.45 [7759]~P106(x77591)+P1(f333(f333(f248(x77591),x77592),x77593))+P1(f333(f333(f248(x77591),x77594),x77593))+~P1(f333(f333(f248(x77591),f333(f333(f245(x77591),x77594),x77592)),x77593)) % 183.90/184.45 [7760]~P106(x77601)+P1(f333(f333(f247(x77601),x77602),x77603))+P1(f333(f333(f247(x77601),x77604),x77603))+~P1(f333(f333(f247(x77601),f333(f333(f245(x77601),x77604),x77602)),x77603)) % 183.90/184.45 [8044]~P60(x80441)+~P1(f333(f333(f248(x80441),f2(x80441)),x80443))+~P1(f333(f333(f248(x80441),x80442),f333(f333(f291(x80441),x80444),x80443)))+P1(f333(f333(f248(x80441),f333(f333(f80(x80441),x80442),x80443)),x80444)) % 183.90/184.45 [8045]~P61(x80451)+~P1(f333(f333(f248(x80451),f2(x80451)),x80453))+~P1(f333(f333(f248(x80451),x80452),f333(f333(f291(x80451),x80454),x80453)))+P1(f333(f333(f248(x80451),f333(f333(f80(x80451),x80452),x80453)),x80454)) % 183.90/184.45 [8046]~P60(x80461)+~P1(f333(f333(f248(x80461),f2(x80461)),x80463))+~P1(f333(f333(f248(x80461),x80462),f333(f333(f80(x80461),x80464),x80463)))+P1(f333(f333(f248(x80461),f333(f333(f291(x80461),x80462),x80463)),x80464)) % 183.90/184.45 [8048]~P61(x80481)+~P1(f333(f333(f248(x80481),f2(x80481)),x80483))+~P1(f333(f333(f248(x80481),x80482),f333(f333(f80(x80481),x80484),x80483)))+P1(f333(f333(f248(x80481),f333(f333(f291(x80481),x80482),x80483)),x80484)) % 183.90/184.45 [8049]~P60(x80491)+~P1(f333(f333(f248(x80491),f2(x80491)),x80493))+~P1(f333(f333(f247(x80491),x80492),f333(f333(f291(x80491),x80494),x80493)))+P1(f333(f333(f247(x80491),f333(f333(f80(x80491),x80492),x80493)),x80494)) % 183.90/184.45 [8050]~P61(x80501)+~P1(f333(f333(f248(x80501),f2(x80501)),x80503))+~P1(f333(f333(f247(x80501),x80502),f333(f333(f291(x80501),x80504),x80503)))+P1(f333(f333(f247(x80501),f333(f333(f80(x80501),x80502),x80503)),x80504)) % 183.90/184.45 [8051]~P60(x80511)+~P1(f333(f333(f248(x80511),f2(x80511)),x80513))+~P1(f333(f333(f247(x80511),x80512),f333(f333(f80(x80511),x80514),x80513)))+P1(f333(f333(f247(x80511),f333(f333(f291(x80511),x80512),x80513)),x80514)) % 183.90/184.45 [8053]~P61(x80531)+~P1(f333(f333(f248(x80531),f2(x80531)),x80533))+~P1(f333(f333(f247(x80531),x80532),f333(f333(f80(x80531),x80534),x80533)))+P1(f333(f333(f247(x80531),f333(f333(f291(x80531),x80532),x80533)),x80534)) % 183.90/184.45 [8186]~P60(x81861)+~P1(f333(f333(f248(x81861),f2(x81861)),x81864))+P1(f333(f333(f248(x81861),x81862),f333(f333(f80(x81861),x81863),x81864)))+~P1(f333(f333(f248(x81861),f333(f333(f291(x81861),x81862),x81864)),x81863)) % 183.90/184.45 [8187]~P60(x81871)+~P1(f333(f333(f248(x81871),f2(x81871)),x81874))+P1(f333(f333(f248(x81871),x81872),f333(f333(f291(x81871),x81873),x81874)))+~P1(f333(f333(f248(x81871),f333(f333(f80(x81871),x81872),x81874)),x81873)) % 183.90/184.45 [8189]~P61(x81891)+~P1(f333(f333(f248(x81891),f2(x81891)),x81894))+P1(f333(f333(f248(x81891),x81892),f333(f333(f80(x81891),x81893),x81894)))+~P1(f333(f333(f248(x81891),f333(f333(f291(x81891),x81892),x81894)),x81893)) % 183.90/184.45 [8190]~P61(x81901)+~P1(f333(f333(f248(x81901),f2(x81901)),x81904))+P1(f333(f333(f248(x81901),x81902),f333(f333(f291(x81901),x81903),x81904)))+~P1(f333(f333(f248(x81901),f333(f333(f80(x81901),x81902),x81904)),x81903)) % 183.90/184.45 [8191]~P60(x81911)+~P1(f333(f333(f248(x81911),f2(x81911)),x81914))+P1(f333(f333(f247(x81911),x81912),f333(f333(f80(x81911),x81913),x81914)))+~P1(f333(f333(f247(x81911),f333(f333(f291(x81911),x81912),x81914)),x81913)) % 183.90/184.45 [8192]~P60(x81921)+~P1(f333(f333(f248(x81921),f2(x81921)),x81924))+P1(f333(f333(f247(x81921),x81922),f333(f333(f291(x81921),x81923),x81924)))+~P1(f333(f333(f247(x81921),f333(f333(f80(x81921),x81922),x81924)),x81923)) % 183.90/184.45 [8194]~P61(x81941)+~P1(f333(f333(f248(x81941),f2(x81941)),x81944))+P1(f333(f333(f247(x81941),x81942),f333(f333(f80(x81941),x81943),x81944)))+~P1(f333(f333(f247(x81941),f333(f333(f291(x81941),x81942),x81944)),x81943)) % 183.90/184.45 [8195]~P61(x81951)+~P1(f333(f333(f248(x81951),f2(x81951)),x81954))+P1(f333(f333(f247(x81951),x81952),f333(f333(f291(x81951),x81953),x81954)))+~P1(f333(f333(f247(x81951),f333(f333(f80(x81951),x81952),x81954)),x81953)) % 183.90/184.45 [8355]~P61(x83551)+~P1(f333(f333(f248(x83551),x83553),f2(x83551)))+~P1(f333(f333(f248(x83551),f333(f333(f291(x83551),x83554),x83553)),x83552))+P1(f333(f333(f248(x83551),f333(f333(f80(x83551),x83552),x83553)),x83554)) % 183.90/184.45 [8356]~P61(x83561)+~P1(f333(f333(f248(x83561),x83563),f2(x83561)))+~P1(f333(f333(f248(x83561),f333(f333(f80(x83561),x83564),x83563)),x83562))+P1(f333(f333(f248(x83561),f333(f333(f291(x83561),x83562),x83563)),x83564)) % 183.90/184.45 [8357]~P61(x83571)+~P1(f333(f333(f248(x83571),x83573),f2(x83571)))+~P1(f333(f333(f247(x83571),f333(f333(f291(x83571),x83574),x83573)),x83572))+P1(f333(f333(f247(x83571),f333(f333(f80(x83571),x83572),x83573)),x83574)) % 183.90/184.45 [8358]~P61(x83581)+~P1(f333(f333(f248(x83581),x83583),f2(x83581)))+~P1(f333(f333(f247(x83581),f333(f333(f80(x83581),x83584),x83583)),x83582))+P1(f333(f333(f247(x83581),f333(f333(f291(x83581),x83582),x83583)),x83584)) % 183.90/184.45 [8368]~P1(f333(x83681,x83684))+~P1(f333(f333(f248(a875),x83682),f333(f333(f80(a875),x83683),f333(a115,x83684))))+P1(f333(x83681,f333(f333(f38(a875),x83682),x83683)))+~P1(f333(f333(f247(a875),f333(f333(f80(a875),x83683),x83684)),x83682)) % 183.90/184.45 [8582]~P98(x85821)+~P1(f333(f61(x85821),x85824))+~P1(f333(f333(f335(x85821),x85822),x85824))+P1(f333(f333(f247(x85821),f333(f333(f113(x85821),x85822),x85823)),f333(f333(f64(x85821,x85821,f113(x85821)),x85823),x85824))) % 183.90/184.45 [8583]~P106(x85831)+~P1(f333(f61(x85831),x85834))+~P1(f333(f333(f335(x85831),x85832),x85834))+P1(f333(f333(f247(x85831),f333(f333(f246(x85831),x85832),x85833)),f333(f333(f64(x85831,x85831,f246(x85831)),x85833),x85834))) % 183.90/184.45 [8724]~P1(f333(f61(x87241),x87242))+E(f333(f37(x87241),f333(f333(f22(f882(x87241,a870)),x87242),f333(f333(f311(x87241),x87243),x87244))),f333(f333(f22(a875),f333(f37(x87241),f333(f333(f22(f882(x87241,a870)),x87242),x87244))),f77(a875)))+P1(f333(f333(f335(x87241),x87243),x87244))+~P1(f333(f333(f335(x87241),x87243),x87242)) % 183.90/184.45 [8794]E(f333(f333(f79(a1),f437(x87941,x87942,x87943,x87944)),f438(x87941,x87942,x87943,x87944)),x87944)+~P1(f333(f333(f248(a1),f2(a1)),x87943))+~P1(f333(f333(f247(a1),x87944),x87941))+P1(f333(f333(f247(a1),f333(f333(f22(a1),x87944),x87943)),x87941)) % 183.90/184.45 [8795]E(f333(f333(f79(a1),f447(x87951,x87952,x87953,x87954)),f448(x87951,x87952,x87953,x87954)),x87954)+~P1(f333(f333(f248(a1),f2(a1)),x87953))+~P1(f333(f333(f248(a1),x87954),x87951))+P1(f333(f333(f248(a1),f333(f333(f22(a1),x87954),x87953)),x87951)) % 183.90/184.45 [9008]~P1(f333(f333(f248(a1),f2(a1)),x90083))+~P1(f333(f333(f247(a1),x90084),x90081))+P1(f333(f333(f335(a1),f437(x90081,x90082,x90083,x90084)),x90082))+P1(f333(f333(f247(a1),f333(f333(f22(a1),x90084),x90083)),x90081)) % 183.90/184.45 [9009]~P1(f333(f333(f248(a1),f2(a1)),x90093))+~P1(f333(f333(f248(a1),x90094),x90091))+P1(f333(f333(f335(a1),f447(x90091,x90092,x90093,x90094)),x90092))+P1(f333(f333(f248(a1),f333(f333(f22(a1),x90094),x90093)),x90091)) % 183.90/184.45 [9094]~P1(f333(f333(f248(a1),f2(a1)),x90942))+~P1(f333(f333(f248(a1),x90941),x90943))+P1(f333(f333(f335(a1),f448(x90943,x90944,x90942,x90941)),f304(a1,f77(a1),x90942)))+P1(f333(f333(f248(a1),f333(f333(f22(a1),x90941),x90942)),x90943)) % 183.90/184.45 [9095]~P1(f333(f333(f248(a1),f2(a1)),x90952))+~P1(f333(f333(f247(a1),x90951),x90953))+P1(f333(f333(f335(a1),f438(x90953,x90954,x90952,x90951)),f304(a1,f77(a1),x90952)))+P1(f333(f333(f247(a1),f333(f333(f22(a1),x90951),x90952)),x90953)) % 183.90/184.45 [9111]~P1(f333(f333(f248(a1),f2(a1)),x91113))+~P1(f333(f333(f247(a1),f2(a1)),x91114))+~P1(f333(f333(f248(a1),x91114),x91111))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),f333(f333(f80(a1),x91111),f44(a1,x91112,x91113))),x91114))) % 183.90/184.45 [9175]~P99(x91751)+~P1(f333(f61(x91751),x91754))+~P1(f333(f333(f247(x91751),x91752),f529(x91753,x91752,x91754,x91751)))+P1(f333(f333(f247(x91751),f333(f333(f104(x91751),x91752),x91753)),f333(f333(f64(x91751,x91751,f104(x91751)),x91753),x91754))) % 183.90/184.45 [9176]~P106(x91761)+~P1(f333(f61(x91761),x91764))+~P1(f333(f333(f247(x91761),x91762),f523(x91763,x91762,x91764,x91761)))+P1(f333(f333(f247(x91761),f333(f333(f245(x91761),x91762),x91763)),f333(f333(f64(x91761,x91761,f245(x91761)),x91763),x91764))) % 183.90/184.45 [9191]~P1(f333(f333(f247(a1),x91914),f2(a1)))+~P1(f333(f333(f248(a1),f2(a1)),x91912))+~P1(f333(f333(f248(a1),x91911),x91914))+P1(f333(f333(f248(a1),f333(f333(f80(a1),x91911),x91912)),f333(f333(f79(a1),f333(f333(f80(a1),x91911),f44(a1,x91913,x91912))),x91914))) % 183.90/184.45 [9213]P1(f333(f61(x92131),x92132))+~P1(f333(f61(x92131),x92133))+~P1(f333(f333(f335(f882(x92131,a870)),x92132),f333(f333(f60(x92131),x92133),x92134)))+~P1(f333(f333(f247(f882(f881(x92131,x92131),a870)),x92134),f333(f333(f270(x92131,x92131),x92133),f333(f16(f882(x92131,a870),x92131),x92133)))) % 183.90/184.45 [9241]~P106(x92411)+~P1(f333(f61(x92411),x92414))+P1(f333(f333(f335(x92411),f523(x92412,x92413,x92414,x92411)),x92414))+P1(f333(f333(f247(x92411),f333(f333(f245(x92411),x92413),x92412)),f333(f333(f64(x92411,x92411,f245(x92411)),x92412),x92414))) % 183.90/184.45 [9242]~P99(x92421)+~P1(f333(f61(x92421),x92424))+P1(f333(f333(f335(x92421),f529(x92422,x92423,x92424,x92421)),x92424))+P1(f333(f333(f247(x92421),f333(f333(f104(x92421),x92423),x92422)),f333(f333(f64(x92421,x92421,f104(x92421)),x92422),x92424))) % 183.90/184.45 [9637]~P1(f333(f61(x96372),x96374))+~P1(f333(f61(x96371),x96373))+~P1(f333(f333(f247(a875),f333(f37(x96372),x96374)),f333(f37(x96371),x96373)))+P1(f333(f333(f247(f882(x96371,a870)),f333(f312(x96372,x96371,f349(x96373,x96371,x96374,x96372)),x96374)),x96373)) % 183.90/184.45 [9288]~P1(f333(f333(f335(x92881),x92882),x92884))+P1(f333(f333(f335(x92881),x92882),x92883))+~P1(f333(f333(f248(f882(x92881,a870)),x92884),f333(f333(f311(x92881),x92882),x92883)))+P1(f333(f333(f248(f882(x92881,a870)),f333(f333(f22(f882(x92881,a870)),x92884),f333(f333(f311(x92881),x92882),f196(f882(x92881,a870))))),x92883)) % 183.90/184.45 [9449]~P1(f333(f333(f335(x94491),x94492),x94494))+P1(f333(f333(f335(x94491),x94492),x94493))+P1(f333(f333(f248(f882(x94491,a870)),x94494),f333(f333(f311(x94491),x94492),x94493)))+~P1(f333(f333(f248(f882(x94491,a870)),f333(f333(f22(f882(x94491,a870)),x94494),f333(f333(f311(x94491),x94492),f196(f882(x94491,a870))))),x94493)) % 183.90/184.45 [9478]P1(f333(f333(f335(x94781),x94782),x94783))+~P1(f333(f333(f247(f882(x94781,a870)),x94784),x94783))+P1(f333(f333(f248(f882(x94781,a870)),x94784),f333(f333(f311(x94781),x94782),x94783)))+~P1(f333(f333(f248(f882(x94781,a870)),f333(f333(f22(f882(x94781,a870)),x94784),f333(f333(f311(x94781),x94782),f196(f882(x94781,a870))))),x94783)) % 183.90/184.45 [9483]~P1(f333(f333(f335(x94831),x94833),x94832))+~P1(f333(f333(f248(f882(x94831,a870)),x94832),x94834))+P1(f333(f333(f248(f882(x94831,a870)),x94832),f333(f333(f311(x94831),x94833),x94834)))+~P1(f333(f333(f248(f882(x94831,a870)),f333(f333(f22(f882(x94831,a870)),x94832),f333(f333(f311(x94831),x94833),f196(f882(x94831,a870))))),x94834)) % 183.90/184.45 [9496]~P1(f333(f333(f247(f882(x94961,a870)),x94962),x94964))+~P1(f333(f333(f248(f882(x94961,a870)),x94962),x94964))+P1(f333(f333(f248(f882(x94961,a870)),x94962),f333(f333(f311(x94961),x94963),x94964)))+~P1(f333(f333(f248(f882(x94961,a870)),f333(f333(f22(f882(x94961,a870)),x94962),f333(f333(f311(x94961),x94963),f196(f882(x94961,a870))))),x94964)) % 183.90/184.45 [9540]~P108(x95402)+~P57(x95401)+~P1(f333(f333(f247(f882(x95401,x95402)),x95403),x95404))+P1(f333(f58(x95401),f333(f333(f18(x95401,x95402,a870),f333(f333(f8(x95402,f882(x95402,a870),x95401),f247(x95402)),x95403)),x95404))) % 183.90/184.45 [9684]~P108(x96842)+~P57(x96841)+P1(f333(f333(f247(f882(x96841,x96842)),x96843),x96844))+~P1(f333(f58(x96841),f333(f333(f18(x96841,x96842,a870),f333(f333(f8(x96842,f882(x96842,a870),x96841),f247(x96842)),x96843)),x96844))) % 183.90/184.45 [9854]E(f333(f333(f166(x98541),f333(f333(f166(f876(x98541)),f182(x98541,x98542)),x98543)),x98544),f333(f333(f166(x98541),f333(f333(f166(f876(x98541)),x98542),x98544)),x98543))+~P1(f333(f333(f248(a875),x98543),f333(f197(f876(f876(x98541))),f182(x98541,x98542))))+~P14(a875,f333(f170(a875),f333(f333(f155(f876(x98541),a875),f197(f876(x98541))),x98542)))+~P1(f333(f333(f248(a875),x98544),f333(f197(f876(f876(x98541))),f333(f137(f876(x98541),f333(f333(f8(a875,a870,f876(x98541)),f333(f248(a875),x98543)),f197(f876(x98541)))),x98542)))) % 183.90/184.45 [9883]~P1(f333(f333(f335(f881(a875,a875)),x98834),x98831))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x98834),x98832)),a34))+~P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98831),x98833)),a35))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98831),f333(f333(f311(f881(a875,a875)),x98832),x98833))),a35)) % 183.90/184.45 [9884]~P1(f333(f333(f335(f881(a875,a875)),x98844),x98841))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x98844),x98842)),a69))+~P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98841),x98843)),a70))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98841),f333(f333(f311(f881(a875,a875)),x98842),x98843))),a70)) % 183.90/184.45 [9768]~P108(x97682)+~P57(x97681)+~P1(f333(f333(f248(f882(x97681,x97682)),x97683),x97684))+P1(f333(f57(x97681),f333(f333(f8(a870,a870,x97681),a328),f333(f333(f18(x97681,x97682,a870),f333(f333(f8(x97682,f882(x97682,a870),x97681),a330),x97683)),x97684)))) % 183.90/184.45 [9897]~P1(f333(f333(f335(f881(a875,a875)),x98974),x98973))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x98971),x98974)),a34))+~P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98972),x98973)),a36))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f333(f333(f311(f881(a875,a875)),x98971),x98972)),x98973)),a36)) % 183.90/184.45 [9898]~P1(f333(f333(f335(f881(a875,a875)),x98984),x98983))+~P1(f333(f333(f335(f881(f881(a875,a875),f881(a875,a875))),f333(f333(f268(f881(a875,a875),f881(a875,a875)),x98981),x98984)),a69))+~P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98982),x98983)),a68))+P1(f333(f333(f335(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f333(f333(f268(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f333(f333(f311(f881(a875,a875)),x98981),x98982)),x98983)),a68)) % 183.90/184.45 [6020]~P6(x60204,x60201)+~P1(f333(f333(x60201,x60202),x60205))+P1(f333(f333(x60201,x60202),x60203))+~P1(f333(f333(x60201,x60205),x60203)) % 183.90/184.45 [5283]~P65(x52835)+E(x52831,x52832)+~E(x52833,x52834)+~E(f333(f333(f22(x52835),x52833),x52834),f333(f333(f22(x52835),x52831),x52832)) % 183.90/184.45 [6128]~P17(x61285,x61281,x61283)+E(f333(f333(x61281,x61282),f333(x61283,x61284)),f333(x61283,x61284))+~P1(f333(f61(x61285),x61284))+~P1(f333(f333(f335(x61285),x61282),x61284)) % 183.90/184.45 [6317]~P82(x63171)+~E(f333(f333(f22(x63171),x63174),x63175),f333(f333(f22(x63171),x63172),x63173))+~P1(f333(f333(f248(x63171),x63174),x63175))+P1(f333(f333(f248(x63171),x63172),x63173)) % 183.90/184.45 [6319]~P82(x63191)+~E(f333(f333(f22(x63191),x63194),x63195),f333(f333(f22(x63191),x63192),x63193))+~P1(f333(f333(f247(x63191),x63194),x63195))+P1(f333(f333(f247(x63191),x63192),x63193)) % 183.90/184.45 [7279]~E(x72792,f333(f333(f152(x72791),x72794),x72795))+P1(f333(f333(f335(f876(x72791)),x72792),f162(x72791,x72793)))+~P1(f333(f333(f335(f876(x72791)),x72795),f162(x72791,x72793)))+~P1(f333(f333(f335(x72791),x72794),x72793)) % 183.90/184.45 [7699]~E(f333(f197(f876(x76991)),x76993),f333(f197(f876(x76992)),x76994))+~E(f333(f333(f155(f881(x76991,x76992),x76992),f271(x76991,x76992)),x76995),x76994)+~E(f333(f333(f155(f881(x76991,x76992),x76991),f267(x76991,x76992)),x76995),x76993)+E(f333(f333(f184(x76991,x76992),x76993),x76994),x76995) % 183.90/184.45 [8041]~P108(x80411)+P1(f333(f333(f248(f882(x80411,a870)),f304(x80411,x80412,x80413)),f304(x80411,x80414,x80415)))+~P1(f333(f333(f247(x80411),x80414),x80415))+P1(f333(f333(f247(x80411),x80412),x80413)) % 183.90/184.45 [8137]~P108(x81371)+P1(f333(f333(f247(f882(x81371,a870)),f304(x81371,x81372,x81373)),f304(x81371,x81374,x81375)))+~P1(f333(f333(f247(x81371),x81373),x81375))+~P1(f333(f333(f247(x81371),x81374),x81372)) % 183.90/184.45 [8263]~P106(x82631)+P1(f333(f333(f247(x82631),x82632),x82633))+P1(f333(f333(f247(x82631),x82634),x82633))+~P1(f333(f333(f247(f882(x82631,a870)),f333(f303(x82631,x82633),x82632)),f333(f303(x82631,x82634),x82635))) % 183.90/184.45 [8264]~P106(x82641)+P1(f333(f333(f247(x82641),x82642),x82643))+P1(f333(f333(f247(x82641),x82642),x82644))+~P1(f333(f333(f247(f882(x82641,a870)),f333(f303(x82641,x82643),x82642)),f333(f303(x82641,x82645),x82644))) % 183.90/184.45 [8504]~P108(x85041)+~P1(f333(f333(f248(f882(x85041,a870)),f304(x85041,x85044,x85042)),f304(x85041,x85045,x85043)))+P1(f333(f333(f247(x85041),x85042),x85043))+~P1(f333(f333(f247(x85041),x85044),x85042)) % 183.90/184.45 [8505]~P108(x85051)+~P1(f333(f333(f247(f882(x85051,a870)),f304(x85051,x85054,x85052)),f304(x85051,x85055,x85053)))+P1(f333(f333(f247(x85051),x85052),x85053))+~P1(f333(f333(f247(x85051),x85054),x85052)) % 183.90/184.45 [8506]~P108(x85061)+~P1(f333(f333(f248(f882(x85061,a870)),f304(x85061,x85063,x85064)),f304(x85061,x85062,x85065)))+P1(f333(f333(f247(x85061),x85062),x85063))+~P1(f333(f333(f247(x85061),x85063),x85064)) % 183.90/184.45 [8507]~P108(x85071)+~P1(f333(f333(f247(f882(x85071,a870)),f304(x85071,x85073,x85074)),f304(x85071,x85072,x85075)))+P1(f333(f333(f247(x85071),x85072),x85073))+~P1(f333(f333(f247(x85071),x85073),x85074)) % 183.90/184.45 [6019]~P17(x60192,x60195,x60193)+E(x60191,f196(f882(x60192,a870)))+~P1(f333(f61(x60192),x60191))+E(f333(x60193,f333(f333(f311(x60192),x60194),x60191)),f333(f333(x60195,x60194),f333(x60193,x60191))) % 183.90/184.45 [6781]~E(x67811,x67812)+~E(f333(f333(f104(f882(x67813,a870)),x67814),x67815),f196(f882(x67813,a870)))+~P1(f333(f333(f335(x67813),x67812),x67815))+~P1(f333(f333(f335(x67813),x67811),x67814)) % 183.90/184.45 [6863]~P18(x68632,x68635,x68631)+~P1(f333(f61(x68632),x68634))+E(f333(x68631,f333(f333(f311(x68632),x68633),x68634)),f333(f333(f64(x68632,x68632,x68635),x68633),x68634))+P1(f333(f333(f335(x68632),x68633),x68634)) % 183.90/184.45 [6930]~P66(x69302)+~P1(f333(f61(x69301),x69305))+E(f333(f333(f6(x69301,x69302),x69303),f333(f333(f311(x69301),x69304),x69305)),f333(f333(f79(x69302),f333(x69303,x69304)),f333(f333(f6(x69301,x69302),x69303),x69305)))+P1(f333(f333(f335(x69301),x69304),x69305)) % 183.90/184.45 [6932]~P73(x69322)+~P1(f333(f61(x69321),x69325))+E(f333(f333(f9(x69321,x69322),x69323),f333(f333(f311(x69321),x69324),x69325)),f333(f333(f80(x69322),f333(x69323,x69324)),f333(f333(f9(x69321,x69322),x69323),x69325)))+P1(f333(f333(f335(x69321),x69324),x69325)) % 183.90/184.45 [7436]~P18(x74362,x74365,x74361)+~P1(f333(f61(x74362),x74364))+E(f333(x74361,f333(f333(f311(x74362),x74363),x74364)),x74363)+~E(f333(f333(f22(f882(x74362,a870)),x74364),f333(f333(f311(x74362),x74363),f196(f882(x74362,a870)))),f196(f882(x74362,a870))) % 183.90/184.45 [7752]~P1(f333(x77521,x77523))+~P1(f333(f333(f202(x77522),x77523),x77525))+~P1(f333(f333(f202(f31(x77521,x77522)),x77525),x77524))+P1(f333(f333(f202(f31(x77521,x77522)),x77523),x77524)) % 183.90/184.45 [7806]~P79(x78061)+~P1(f333(f333(f248(x78061),x78063),x78065))+~P1(f333(f333(f248(x78061),x78062),x78064))+P1(f333(f333(f248(x78061),f333(f333(f79(x78061),x78062),x78063)),f333(f333(f79(x78061),x78064),x78065))) % 183.90/184.45 [7807]~P79(x78071)+~P1(f333(f333(f247(x78071),x78072),x78074))+~P1(f333(f333(f248(x78071),x78073),x78075))+P1(f333(f333(f248(x78071),f333(f333(f79(x78071),x78072),x78073)),f333(f333(f79(x78071),x78074),x78075))) % 183.90/184.45 [7808]~P79(x78081)+~P1(f333(f333(f247(x78081),x78083),x78085))+~P1(f333(f333(f248(x78081),x78082),x78084))+P1(f333(f333(f248(x78081),f333(f333(f79(x78081),x78082),x78083)),f333(f333(f79(x78081),x78084),x78085))) % 183.90/184.45 [7809]~P98(x78091)+~P1(f333(f333(f247(x78091),x78093),x78095))+~P1(f333(f333(f247(x78091),x78092),x78094))+P1(f333(f333(f247(x78091),f333(f333(f113(x78091),x78092),x78093)),f333(f333(f113(x78091),x78094),x78095))) % 183.90/184.45 [7810]~P99(x78101)+~P1(f333(f333(f247(x78101),x78103),x78105))+~P1(f333(f333(f247(x78101),x78102),x78104))+P1(f333(f333(f247(x78101),f333(f333(f104(x78101),x78102),x78103)),f333(f333(f104(x78101),x78104),x78105))) % 183.90/184.45 [7811]~P81(x78111)+~P1(f333(f333(f247(x78111),x78113),x78115))+~P1(f333(f333(f247(x78111),x78112),x78114))+P1(f333(f333(f247(x78111),f333(f333(f79(x78111),x78112),x78113)),f333(f333(f79(x78111),x78114),x78115))) % 183.90/184.45 [7812]~P106(x78121)+~P1(f333(f333(f247(x78121),x78123),x78125))+~P1(f333(f333(f247(x78121),x78122),x78124))+P1(f333(f333(f247(x78121),f333(f333(f245(x78121),x78122),x78123)),f333(f333(f245(x78121),x78124),x78125))) % 183.90/184.45 [7813]~P106(x78131)+~P1(f333(f333(f247(x78131),x78133),x78135))+~P1(f333(f333(f247(x78131),x78132),x78134))+P1(f333(f333(f247(x78131),f333(f333(f246(x78131),x78132),x78133)),f333(f333(f246(x78131),x78134),x78135))) % 183.90/184.45 [7950]~P139(x79505)+E(x79501,x79502)+E(x79503,x79504)+~E(f333(f333(f79(x79505),f333(f333(f80(x79505),x79503),x79501)),f333(f333(f80(x79505),x79504),x79502)),f333(f333(f79(x79505),f333(f333(f80(x79505),x79503),x79502)),f333(f333(f80(x79505),x79504),x79501))) % 183.90/184.45 [8092]P27(x80921,x80922,x80923)+~P28(x80921,x80924,x80925)+~P27(x80921,x80922,f606(x80925,x80924,x80921,x80922))+~P1(f333(f333(f335(f874(x80921)),x80923),x80925)) % 183.90/184.45 [8161]~P106(x81614)+~P1(f333(f138(x81611),x81613))+P1(f333(f333(f335(x81611),x81612),f333(f174(x81611),x81613)))+P1(f333(f138(x81611),f333(f333(f149(x81611,x81614,x81615),x81612),x81613))) % 183.90/184.45 [8309]~P65(x83091)+E(f333(f333(f22(x83091),f333(f333(f6(a875,x83091),x83092),f333(f303(a875,x83093),x83094))),f333(f333(f6(a875,x83091),x83092),f333(f303(a875,x83093),x83095))),f333(f333(f6(a875,x83091),x83092),f333(f303(a875,x83095),x83094)))+~P1(f333(f333(f247(a875),x83095),x83094))+~P1(f333(f333(f247(a875),x83093),x83095)) % 183.90/184.45 [8310]~P66(x83101)+E(f333(f333(f79(x83101),f333(f333(f6(a875,x83101),x83102),f333(f303(a875,x83103),x83104))),f333(f333(f6(a875,x83101),x83102),f333(f303(a875,x83104),x83105))),f333(f333(f6(a875,x83101),x83102),f333(f303(a875,x83103),x83105)))+~P1(f333(f333(f247(a875),x83104),x83105))+~P1(f333(f333(f247(a875),x83103),x83104)) % 183.90/184.45 [8639]~P59(x86392)+E(x86391,f2(x86392))+E(x86393,f2(x86392))+E(f333(f333(f291(x86392),f333(f333(f22(x86392),f333(f333(f80(x86392),x86394),x86391)),f333(f333(f80(x86392),x86395),x86393))),f333(f333(f80(x86392),x86393),x86391)),f333(f333(f22(x86392),f333(f333(f291(x86392),x86394),x86393)),f333(f333(f291(x86392),x86395),x86391))) % 183.90/184.45 [8640]~P59(x86402)+E(x86401,f2(x86402))+E(x86403,f2(x86402))+E(f333(f333(f291(x86402),f333(f333(f79(x86402),f333(f333(f80(x86402),x86404),x86401)),f333(f333(f80(x86402),x86405),x86403))),f333(f333(f80(x86402),x86403),x86401)),f333(f333(f79(x86402),f333(f333(f291(x86402),x86404),x86403)),f333(f333(f291(x86402),x86405),x86401))) % 183.90/184.45 [8649]~E(x86492,f333(x86493,x86491))+E(x86491,f828(x86492,x86493,x86494,x86495))+~P25(x86495,x86494,x86493,f256(f882(x86495,a870)))+~P1(f333(f333(f335(x86494),x86492),f333(f312(x86495,x86494,x86493),f256(f882(x86495,a870))))) % 183.90/184.45 [8844]~P114(x88441)+~P1(f333(f333(f248(x88441),f333(f74(x88441),x88442)),x88444))+P1(f333(f333(f248(x88441),f333(f333(f80(x88441),f333(f74(x88441),x88442)),f333(f74(x88441),x88443))),f333(f333(f80(x88441),x88444),x88445)))+~P1(f333(f333(f248(x88441),f333(f74(x88441),x88443)),x88445)) % 183.90/184.45 [8861]~P28(x88611,x88615,x88614)+P27(x88611,x88612,x88613)+P1(f333(f333(f335(f874(x88611)),f606(x88614,x88615,x88611,x88612)),x88615))+~P1(f333(f333(f335(f874(x88611)),x88613),x88614)) % 183.90/184.45 [8968]~P25(x89681,x89683,x89685,x89682)+~P1(f333(f61(x89683),x89684))+P1(f333(f333(f247(a875),f333(f37(x89681),x89682)),f333(f37(x89683),x89684)))+~P1(f333(f333(f247(f882(x89683,a870)),f333(f312(x89681,x89683,x89685),x89682)),x89684)) % 183.90/184.45 [9037]~P66(x90372)+~P25(x90371,x90371,x90374,x90375)+~P1(f333(f61(x90371),x90375))+E(f333(f333(f6(x90371,x90372),f333(f72(x90371,x90372,x90371,x90373),x90374)),x90375),f333(f333(f6(x90371,x90372),x90373),f333(f312(x90371,x90371,x90374),x90375))) % 183.90/184.45 [9038]~P73(x90382)+~P25(x90381,x90381,x90384,x90385)+~P1(f333(f61(x90381),x90385))+E(f333(f333(f9(x90381,x90382),f333(f72(x90381,x90382,x90381,x90383),x90384)),x90385),f333(f333(f9(x90381,x90382),x90383),f333(f312(x90381,x90381,x90384),x90385))) % 183.90/184.45 [9152]~P37(x91521,x91522)+~P1(f333(f333(f335(x91521),x91523),x91524))+~P1(f333(f333(f335(x91521),x91525),x91524))+~P1(f333(f333(f335(f881(x91521,x91521)),f333(f333(f268(x91521,x91521),x91525),f631(x91522,x91521,x91524))),x91522)) % 183.90/184.45 [9190]~P25(x91902,x91903,x91905,x91901)+E(x91901,f196(f882(x91902,a870)))+E(f333(f312(x91903,x91902,f353(x91904,x91903,x91902,x91901)),x91904),x91901)+~P1(f333(f333(f247(f882(x91903,a870)),f333(f312(x91902,x91903,x91905),x91901)),x91904)) % 183.90/184.45 [9666]~P4(x96665)+~P106(x96665)+P1(f333(f333(f335(x96661),f867(x96662,x96663,x96661,x96664,x96665)),x96663))+~P1(f333(f333(f248(x96665),x96664),f333(f333(f41(x96661,x96665),x96663),x96662))) % 183.90/184.45 [9671]~P4(x96711)+~P106(x96711)+P1(f333(f333(f248(x96711),x96712),f333(x96713,f867(x96713,x96714,x96715,x96712,x96711))))+~P1(f333(f333(f248(x96711),x96712),f333(f333(f41(x96715,x96711),x96714),x96713))) % 183.90/184.45 [9748]~P67(x97481)+~P1(f333(f66(x97481,x97481,f80(x97481),x97482,x97483),x97485))+P1(f333(f333(f335(x97481),x97482),x97483))+P1(f333(f66(x97481,x97481,f80(x97481),x97484,f333(f333(f311(x97481),x97482),x97483)),f333(f333(f80(x97481),x97484),x97485))) % 183.90/184.45 [9965]~P66(x99652)+~P1(f333(f61(x99651),x99655))+E(f333(f333(f6(x99651,x99652),f333(f333(f7(x99651,x99652,x99652),f333(f333(f18(x99651,x99652,f882(x99652,x99652)),f333(f333(f8(a870,f882(x99652,f882(x99652,x99652)),x99651),f99(x99652)),f333(a330,x99653))),x99654)),f2(x99652))),x99655),f2(x99652))+P1(f333(f333(f335(x99651),x99653),x99655)) % 183.90/184.45 [9966]~P73(x99662)+~P1(f333(f61(x99661),x99665))+E(f333(f333(f9(x99661,x99662),f333(f333(f7(x99661,x99662,x99662),f333(f333(f18(x99661,x99662,f882(x99662,x99662)),f333(f333(f8(a870,f882(x99662,f882(x99662,x99662)),x99661),f99(x99662)),f333(a330,x99663))),x99664)),f77(x99662))),x99665),f77(x99662))+P1(f333(f333(f335(x99661),x99663),x99665)) % 183.90/184.45 [9967]~P66(x99672)+~P1(f333(f61(x99671),x99675))+E(f333(f333(f6(x99671,x99672),f333(f333(f7(x99671,x99672,x99672),f333(f333(f18(x99671,x99672,f882(x99672,x99672)),f333(f333(f8(a870,f882(x99672,f882(x99672,x99672)),x99671),f99(x99672)),f333(a330,x99673))),x99674)),f2(x99672))),x99675),f333(x99674,x99673))+~P1(f333(f333(f335(x99671),x99673),x99675)) % 183.90/184.45 [9968]~P73(x99682)+~P1(f333(f61(x99681),x99685))+E(f333(f333(f9(x99681,x99682),f333(f333(f7(x99681,x99682,x99682),f333(f333(f18(x99681,x99682,f882(x99682,x99682)),f333(f333(f8(a870,f882(x99682,f882(x99682,x99682)),x99681),f99(x99682)),f333(a330,x99683))),x99684)),f77(x99682))),x99685),f333(x99684,x99683))+~P1(f333(f333(f335(x99681),x99683),x99685)) % 183.90/184.45 [10023]~P66(x100232)+~P1(f333(f61(x100231),x100235))+E(f333(f333(f6(x100231,x100232),f333(f333(f7(x100231,x100232,x100232),f333(f333(f18(x100231,x100232,f882(x100232,x100232)),f333(f333(f8(a870,f882(x100232,f882(x100232,x100232)),x100231),f99(x100232)),f333(f333(f7(x100231,x100231,a870),a330),x100233))),x100234)),f2(x100232))),x100235),f2(x100232))+P1(f333(f333(f335(x100231),x100233),x100235)) % 183.90/184.45 [10024]~P73(x100242)+~P1(f333(f61(x100241),x100245))+E(f333(f333(f9(x100241,x100242),f333(f333(f7(x100241,x100242,x100242),f333(f333(f18(x100241,x100242,f882(x100242,x100242)),f333(f333(f8(a870,f882(x100242,f882(x100242,x100242)),x100241),f99(x100242)),f333(f333(f7(x100241,x100241,a870),a330),x100243))),x100244)),f77(x100242))),x100245),f77(x100242))+P1(f333(f333(f335(x100241),x100243),x100245)) % 183.90/184.45 [10026]~P66(x100262)+~P1(f333(f61(x100261),x100265))+E(f333(f333(f6(x100261,x100262),f333(f333(f7(x100261,x100262,x100262),f333(f333(f18(x100261,x100262,f882(x100262,x100262)),f333(f333(f8(a870,f882(x100262,f882(x100262,x100262)),x100261),f99(x100262)),f333(f333(f7(x100261,x100261,a870),a330),x100263))),x100264)),f2(x100262))),x100265),f333(x100264,x100263))+~P1(f333(f333(f335(x100261),x100263),x100265)) % 183.90/184.45 [10027]~P73(x100272)+~P1(f333(f61(x100271),x100275))+E(f333(f333(f9(x100271,x100272),f333(f333(f7(x100271,x100272,x100272),f333(f333(f18(x100271,x100272,f882(x100272,x100272)),f333(f333(f8(a870,f882(x100272,f882(x100272,x100272)),x100271),f99(x100272)),f333(f333(f7(x100271,x100271,a870),a330),x100273))),x100274)),f77(x100272))),x100275),f333(x100274,x100273))+~P1(f333(f333(f335(x100271),x100273),x100275)) % 183.90/184.45 [7805]~P65(x78052)+~P1(f333(f61(x78051),x78054))+E(f333(f333(f6(x78051,x78052),x78053),f333(f333(f22(f882(x78051,a870)),x78054),f333(f333(f311(x78051),x78055),f196(f882(x78051,a870))))),f333(f333(f6(x78051,x78052),x78053),x78054))+P1(f333(f333(f335(x78051),x78055),x78054)) % 183.90/184.45 [8315]~P103(x83152)+~P1(f333(f61(x83151),x83154))+E(f333(f333(f6(x83151,x83152),x83153),f333(f333(f22(f882(x83151,a870)),x83154),f333(f333(f311(x83151),x83155),f196(f882(x83151,a870))))),f333(f333(f22(x83152),f333(f333(f6(x83151,x83152),x83153),x83154)),f333(x83153,x83155)))+~P1(f333(f333(f335(x83151),x83155),x83154)) % 183.90/184.45 [8316]~P65(x83162)+~P1(f333(f61(x83161),x83164))+E(f333(f333(f6(x83161,x83162),x83163),f333(f333(f22(f882(x83161,a870)),x83164),f333(f333(f311(x83161),x83165),f196(f882(x83161,a870))))),f333(f333(f22(x83162),f333(f333(f6(x83161,x83162),x83163),x83164)),f333(x83163,x83165)))+~P1(f333(f333(f335(x83161),x83165),x83164)) % 183.90/184.45 [8347]~P65(x83471)+~P1(f333(f61(x83472),x83474))+E(f333(f333(f22(x83471),f333(f333(f6(x83472,x83471),x83473),x83474)),f333(f333(f6(x83472,x83471),x83473),x83475)),f333(f333(f6(x83472,x83471),x83473),f333(f333(f22(f882(x83472,a870)),x83474),x83475)))+~P1(f333(f333(f247(f882(x83472,a870)),x83475),x83474)) % 183.90/184.45 [8367]P1(f333(f61(x83671),f333(x83672,x83673)))+~P1(f333(f61(x83674),x83675))+~P1(f333(f333(f335(x83674),x83673),x83675))+~P1(f333(f61(x83671),f333(f333(f41(x83674,f882(x83671,a870)),x83675),x83672))) % 183.90/184.45 [8807]~P7(x88071,x88075,x88074)+~E(f333(f287(x88071,x88071,x88074),f333(f333(f311(x88071),x88072),f196(f882(x88071,a870)))),f333(f287(x88071,x88071,x88074),f333(f333(f311(x88071),x88073),f196(f882(x88071,a870)))))+~P1(f333(f333(f335(x88071),x88073),x88075))+P1(f333(f333(f335(f881(x88071,x88071)),f333(f333(f268(x88071,x88071),x88072),x88073)),x88074)) % 183.90/184.45 [9109]~P1(f333(x91091,x91095))+P1(f333(x91091,f427(x91091,x91092,x91093,x91094)))+P1(f333(x91091,f409(x91091,x91092,x91093,x91094)))+~P1(f333(f333(f335(x91094),x91095),f333(f333(f113(f882(x91094,a870)),x91093),x91092))) % 183.90/184.45 [9293]~P1(f333(x92931,x92935))+P1(f333(x92931,f409(x92931,x92932,x92933,x92934)))+P1(f333(f333(f335(x92934),f427(x92931,x92932,x92933,x92934)),x92932))+~P1(f333(f333(f335(x92934),x92935),f333(f333(f113(f882(x92934,a870)),x92933),x92932))) % 183.90/184.45 [9294]~P1(f333(x92941,x92945))+P1(f333(x92941,f427(x92941,x92942,x92943,x92944)))+P1(f333(f333(f335(x92944),f409(x92941,x92942,x92943,x92944)),x92943))+~P1(f333(f333(f335(x92944),x92945),f333(f333(f113(f882(x92944,a870)),x92943),x92942))) % 183.90/184.45 [9300]P1(f333(x93001,x93002))+~P1(f333(x93001,f397(x93001,x93003,x93004,x93005)))+~P1(f333(x93001,f386(x93001,x93003,x93004,x93005)))+~P1(f333(f333(f335(x93005),x93002),f333(f333(f113(f882(x93005,a870)),x93004),x93003))) % 183.90/184.45 [9342]E(x93421,x93422)+~P1(f333(f333(f335(f881(x93423,x93423)),f333(f333(f268(x93423,x93423),x93421),x93422)),f309(x93423,x93425)))+P1(f333(f333(f335(x93423),x93421),x93424))+~P1(f333(f333(f247(f882(f881(x93423,x93423),a870)),x93425),f333(f333(f270(x93423,x93423),x93424),f333(f16(f882(x93423,a870),x93423),x93424)))) % 183.90/184.45 [9361]P1(f333(x93611,x93612))+~P1(f333(x93611,f386(x93611,x93614,x93615,x93613)))+P1(f333(f333(f335(x93613),f397(x93611,x93614,x93615,x93613)),x93614))+~P1(f333(f333(f335(x93613),x93612),f333(f333(f113(f882(x93613,a870)),x93615),x93614))) % 183.90/184.45 [9362]P1(f333(x93621,x93622))+~P1(f333(x93621,f397(x93621,x93624,x93625,x93623)))+P1(f333(f333(f335(x93623),f386(x93621,x93624,x93625,x93623)),x93625))+~P1(f333(f333(f335(x93623),x93622),f333(f333(f113(f882(x93623,a870)),x93625),x93624))) % 183.90/184.45 [9423]P1(f333(x94231,x94232))+P1(f333(f333(f335(x94233),f397(x94231,x94234,x94235,x94233)),x94234))+P1(f333(f333(f335(x94233),f386(x94231,x94234,x94235,x94233)),x94235))+~P1(f333(f333(f335(x94233),x94232),f333(f333(f113(f882(x94233,a870)),x94235),x94234))) % 183.90/184.45 [9425]~P1(f333(x94252,x94255))+P1(f333(f333(f335(x94251),f427(x94252,x94253,x94254,x94251)),x94253))+P1(f333(f333(f335(x94251),f409(x94252,x94253,x94254,x94251)),x94254))+~P1(f333(f333(f335(x94251),x94255),f333(f333(f113(f882(x94251,a870)),x94254),x94253))) % 183.90/184.45 [9573]~P7(x95731,x95735,x95734)+~P1(f333(f333(f335(x95731),x95733),x95735))+P1(f333(f333(f335(f881(x95731,x95731)),f333(f333(f268(x95731,x95731),x95732),x95733)),x95734))+~P1(f333(f333(f247(f882(x95731,a870)),f333(f287(x95731,x95731,x95734),f333(f333(f311(x95731),x95733),f196(f882(x95731,a870))))),f333(f287(x95731,x95731,x95734),f333(f333(f311(x95731),x95732),f196(f882(x95731,a870)))))) % 183.90/184.45 [9696]~P4(x96965)+~P106(x96965)+P1(f333(f333(f335(x96961),f869(x96962,x96963,x96964,x96961,x96965)),x96964))+~P1(f333(f333(f248(x96965),f333(f333(f42(x96961,x96965),x96964),x96963)),x96962)) % 183.90/184.45 [9728]~P81(x97285)+~P78(x97285)+P1(f333(f333(f335(x97281),f713(x97282,x97283,x97284,x97281,x97285)),f333(f174(x97281),x97284)))+P1(f333(f333(f247(x97285),f333(f167(x97285),f333(f333(f155(x97281,x97285),x97283),x97284))),f333(f167(x97285),f333(f333(f155(x97281,x97285),x97282),x97284)))) % 183.90/184.45 [9843]~P4(x98431)+~P106(x98431)+P1(f333(f333(f248(x98431),f333(x98432,f869(x98433,x98432,x98434,x98435,x98431))),x98433))+~P1(f333(f333(f248(x98431),f333(f333(f42(x98435,x98431),x98434),x98432)),x98433)) % 183.90/184.45 [9983]~P81(x99831)+~P78(x99831)+~P1(f333(f333(f247(x99831),f333(x99833,f713(x99835,x99833,x99834,x99832,x99831))),f333(x99835,f713(x99835,x99833,x99834,x99832,x99831))))+P1(f333(f333(f247(x99831),f333(f167(x99831),f333(f333(f155(x99832,x99831),x99833),x99834))),f333(f167(x99831),f333(f333(f155(x99832,x99831),x99835),x99834)))) % 183.90/184.45 [8657]~P66(x86571)+~P1(f333(f61(x86574),x86575))+~P1(f333(f333(f335(x86574),x86573),x86575))+E(f333(f333(f79(x86571),f333(x86572,x86573)),f333(f333(f6(x86574,x86571),x86572),f333(f333(f22(f882(x86574,a870)),x86575),f333(f333(f311(x86574),x86573),f196(f882(x86574,a870)))))),f333(f333(f6(x86574,x86571),x86572),x86575)) % 183.90/184.45 [8658]~P73(x86581)+~P1(f333(f61(x86584),x86585))+~P1(f333(f333(f335(x86584),x86583),x86585))+E(f333(f333(f80(x86581),f333(x86582,x86583)),f333(f333(f9(x86584,x86581),x86582),f333(f333(f22(f882(x86584,a870)),x86585),f333(f333(f311(x86584),x86583),f196(f882(x86584,a870)))))),f333(f333(f9(x86584,x86581),x86582),x86585)) % 183.90/184.45 [8713]~P18(x87131,x87134,x87135)+~P1(f333(f61(x87131),x87132))+E(f333(f333(f22(f882(x87131,a870)),x87132),f333(f333(f311(x87131),x87133),f196(f882(x87131,a870)))),f196(f882(x87131,a870)))+E(f333(f333(x87134,x87133),f333(x87135,f333(f333(f22(f882(x87131,a870)),x87132),f333(f333(f311(x87131),x87133),f196(f882(x87131,a870)))))),f333(x87135,f333(f333(f311(x87131),x87133),x87132))) % 183.90/184.45 [9089]~P66(x90891)+~P1(f333(f61(x90892),x90895))+~P1(f333(f61(x90892),x90894))+E(f333(f333(f79(x90891),f333(f333(f6(x90892,x90891),x90893),f333(f333(f113(f882(x90892,a870)),x90894),x90895))),f333(f333(f6(x90892,x90891),x90893),f333(f333(f104(f882(x90892,a870)),x90894),x90895))),f333(f333(f79(x90891),f333(f333(f6(x90892,x90891),x90893),x90894)),f333(f333(f6(x90892,x90891),x90893),x90895))) % 183.90/184.45 [9091]~P73(x90911)+~P1(f333(f61(x90912),x90915))+~P1(f333(f61(x90912),x90914))+E(f333(f333(f80(x90911),f333(f333(f9(x90912,x90911),x90913),f333(f333(f113(f882(x90912,a870)),x90914),x90915))),f333(f333(f9(x90912,x90911),x90913),f333(f333(f104(f882(x90912,a870)),x90914),x90915))),f333(f333(f80(x90911),f333(f333(f9(x90912,x90911),x90913),x90914)),f333(f333(f9(x90912,x90911),x90913),x90915))) % 183.90/184.45 [9232]~P65(x92321)+~P1(f333(f61(x92322),x92325))+~P1(f333(f61(x92322),x92324))+E(f333(f333(f22(x92321),f333(f333(f79(x92321),f333(f333(f6(x92322,x92321),x92323),x92324)),f333(f333(f6(x92322,x92321),x92323),x92325))),f333(f333(f6(x92322,x92321),x92323),f333(f333(f104(f882(x92322,a870)),x92324),x92325))),f333(f333(f6(x92322,x92321),x92323),f333(f333(f113(f882(x92322,a870)),x92324),x92325))) % 183.90/184.45 [9434]~P25(x94341,x94342,x94343,x94345)+~P25(x94341,x94342,x94343,x94344)+P25(x94341,x94342,x94343,f333(f333(f113(f882(x94341,a870)),x94344),x94345))+~E(f333(f333(f104(f882(x94342,a870)),f333(f312(x94341,x94342,x94343),f333(f333(f22(f882(x94341,a870)),x94344),x94345))),f333(f312(x94341,x94342,x94343),f333(f333(f22(f882(x94341,a870)),x94345),x94344))),f196(f882(x94342,a870))) % 183.90/184.45 [9548]E(x95481,f2(a1))+~P1(f333(f333(f248(a1),f2(a1)),x95483))+~P1(f333(f48(x95482,x95481),f333(f333(f268(a1,a1),x95484),x95485)))+P1(f333(f48(x95482,f333(f333(f80(a1),x95481),x95483)),f333(f333(f268(a1,a1),f333(f333(f38(a1),x95484),x95483)),f333(f333(f79(a1),f333(f333(f80(a1),x95481),f44(a1,x95484,x95483))),x95485)))) % 183.90/184.45 [9556]~P1(f333(f333(f248(a875),f2(a875)),x95563))+~P1(f333(f333(f248(a875),f2(a875)),x95562))+~P1(f333(f47(x95561,x95562),f333(f333(f268(a875,a875),x95564),x95565)))+P1(f333(f47(x95561,f333(f333(f80(a875),x95562),x95563)),f333(f333(f268(a875,a875),f333(f333(f38(a875),x95564),x95563)),f333(f333(f79(a875),f333(f333(f80(a875),x95562),f44(a875,x95564,x95563))),x95565)))) % 183.90/184.45 [9605]~P73(x96051)+~P1(f333(f61(x96052),x96055))+~P1(f333(f61(x96052),x96054))+E(f333(f333(f80(x96051),f333(f333(f333(f65(x96051,x96052,f80(x96051)),x96053),f77(x96051)),f333(f333(f113(f882(x96052,a870)),x96054),x96055))),f333(f333(f333(f65(x96051,x96052,f80(x96051)),x96053),f77(x96051)),f333(f333(f104(f882(x96052,a870)),x96054),x96055))),f333(f333(f80(x96051),f333(f333(f333(f65(x96051,x96052,f80(x96051)),x96053),f77(x96051)),x96054)),f333(f333(f333(f65(x96051,x96052,f80(x96051)),x96053),f77(x96051)),x96055))) % 183.90/184.45 [9607]~E(f333(f333(f177(x96071),x96075),x96072),f333(f333(f177(x96071),x96075),x96073))+P1(f333(f333(f335(f881(f876(x96071),f876(x96071))),f333(f333(f268(f876(x96071),f876(x96071)),x96072),x96073)),f148(x96071,x96074)))+~P1(f333(f333(f248(a875),x96075),f333(f333(f245(a875),f333(f197(f876(x96071)),x96072)),f333(f197(f876(x96071)),x96073))))+~P1(f333(f333(f335(f881(x96071,x96071)),f333(f333(f268(x96071,x96071),f333(f333(f166(x96071),x96072),x96075)),f333(f333(f166(x96071),x96073),x96075))),x96074)) % 183.90/184.45 [9716]~P81(x97165)+~P141(x97165)+P1(f333(f333(f335(x97161),f382(x97162,x97163,x97164,x97161,x97165)),x97164))+P1(f333(f333(f247(x97165),f333(f333(f6(x97161,x97165),x97163),x97164)),f333(f333(f80(x97165),f333(f103(x97165),f333(f37(x97161),x97164))),x97162))) % 183.90/184.45 [9911]~P81(x99111)+~P141(x99111)+~P1(f333(f333(f247(x99111),f333(x99113,f382(x99115,x99113,x99114,x99112,x99111))),x99115))+P1(f333(f333(f247(x99111),f333(f333(f6(x99112,x99111),x99113),x99114)),f333(f333(f80(x99111),f333(f103(x99111),f333(f37(x99112),x99114))),x99115))) % 183.90/184.45 [8685]E(f333(f333(f135(x86851),x86852),x86853),f333(f333(f135(x86851),x86854),x86855))+~E(f333(f333(f177(x86851),f333(f197(f876(x86851)),x86852)),x86854),x86852)+~E(f333(f333(f135(x86851),f333(f333(f139(x86851),f333(f197(f876(x86851)),x86852)),x86854)),x86855),x86853)+P1(f333(f333(f247(a875),f333(f197(f876(x86851)),x86854)),f333(f197(f876(x86851)),x86852))) % 183.90/184.45 [8805]E(f333(f333(f135(x88051),x88052),x88053),f333(f333(f135(x88051),x88054),x88055))+~E(f333(f333(f177(x88051),f333(f197(f876(x88051)),x88052)),x88054),x88052)+~E(x88053,f333(f333(f135(x88051),f333(f333(f139(x88051),f333(f197(f876(x88051)),x88052)),x88054)),x88055))+~P1(f333(f333(f247(a875),f333(f197(f876(x88051)),x88052)),f333(f197(f876(x88051)),x88054))) % 183.90/184.45 [10046]~P1(f333(x100465,x100464))+~P1(f333(f61(x100462),f333(f253(x100462),x100465)))+P1(f333(f61(x100461),f333(f253(x100461),f333(f333(f7(x100461,x100462,a870),x100463),x100464))))+~P1(f333(f61(x100461),f333(f253(x100461),f333(f333(f8(f882(x100462,a870),a870,x100461),f86(x100462)),f333(f333(f8(f882(x100462,a870),f882(x100462,a870),x100461),f333(f18(x100462,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100462),a331),x100465))),x100463))))) % 183.90/184.45 [8482]~P19(x84825,x84821,x84826,x84822)+E(f333(f72(x84821,x84821,x84821,f333(x84822,x84823)),f333(x84822,x84824)),f333(f72(x84821,x84821,x84821,f333(x84822,x84824)),f333(x84822,x84823)))+~P1(f333(f61(x84825),x84824))+~P1(f333(f61(x84825),x84823)) % 183.90/184.45 [7861]~P25(x78611,x78612,x78614,x78613)+~E(f333(x78614,x78616),x78615)+E(f333(f76(x78611,x78612,x78613,x78614),x78615),x78616)+~P1(f333(f333(f335(x78611),x78616),x78613)) % 183.90/184.45 [8061]~P20(x80616,x80611,x80614,x80612)+E(f333(f72(x80611,x80611,x80611,f333(x80612,x80613)),f333(x80614,x80615)),f333(x80612,x80613))+~P1(f333(f61(x80616),x80613))+~P1(f333(f333(f335(x80616),x80615),x80613)) % 183.90/184.45 [9279]~P19(x92793,x92791,x92796,x92792)+E(f333(f72(x92791,x92791,x92791,f333(x92792,f333(f333(f22(f882(x92793,a870)),x92794),f333(f333(f311(x92793),x92795),f196(f882(x92793,a870)))))),f333(x92796,x92795)),f333(x92792,x92794))+~P1(f333(f61(x92793),x92794))+~P1(f333(f333(f335(x92793),x92795),x92794)) % 183.90/184.45 [6935]~P56(x69351)+~E(f44(x69351,x69353,x69354),f44(x69351,x69356,x69354))+~E(f44(x69351,x69352,x69354),f44(x69351,x69355,x69354))+E(f44(x69351,f333(f333(f22(x69351),x69352),x69353),x69354),f44(x69351,f333(f333(f22(x69351),x69355),x69356),x69354)) % 183.90/184.45 [6936]~P55(x69361)+~E(f44(x69361,x69363,x69364),f44(x69361,x69366,x69364))+~E(f44(x69361,x69362,x69364),f44(x69361,x69365,x69364))+E(f44(x69361,f333(f333(f79(x69361),x69362),x69363),x69364),f44(x69361,f333(f333(f79(x69361),x69365),x69366),x69364)) % 183.90/184.45 [6937]~P55(x69371)+~E(f44(x69371,x69373,x69374),f44(x69371,x69376,x69374))+~E(f44(x69371,x69372,x69374),f44(x69371,x69375,x69374))+E(f44(x69371,f333(f333(f80(x69371),x69372),x69373),x69374),f44(x69371,f333(f333(f80(x69371),x69375),x69376),x69374)) % 183.90/184.45 [7754]~P16(x77541,x77542,x77543)+~P1(f333(f61(x77541),x77546))+E(f333(f333(f64(x77541,x77542,x77543),x77544),f333(f333(f311(x77541),x77545),x77546)),f333(f333(f64(x77541,x77542,x77543),f333(f333(x77543,x77545),x77544)),x77546))+P1(f333(f333(f335(x77541),x77545),x77546)) % 183.90/184.45 [7819]~P4(x78191)+P1(f333(f333(f247(x78191),x78192),f333(x78193,x78194)))+~P1(f333(f333(f335(x78195),x78194),x78196))+~P1(f333(f333(f247(x78191),x78192),f333(f333(f42(x78195,x78191),x78196),x78193))) % 183.90/184.45 [7980]~P16(x79801,x79802,x79803)+~P1(f333(f61(x79801),x79806))+E(f333(f333(f64(x79801,x79802,x79803),x79804),f333(f333(f311(x79801),x79805),x79806)),f333(f333(x79803,x79805),f333(f333(f64(x79801,x79802,x79803),x79804),x79806)))+P1(f333(f333(f335(x79801),x79805),x79806)) % 183.90/184.45 [8077]~P106(x80773)+~P1(f333(x80772,x80775))+~P14(x80773,f333(f333(f155(x80771,x80773),x80774),x80776))+E(f333(f137(x80771,x80772),f333(f333(f149(x80771,x80773,x80774),x80775),x80776)),f333(f333(f149(x80771,x80773,x80774),x80775),f333(f137(x80771,x80772),x80776))) % 183.90/184.45 [8100]E(x81001,x81002)+E(x81003,f2(a1))+~P1(f333(f48(x81004,x81003),f333(f333(f268(a1,a1),x81005),x81002)))+~P1(f333(f48(x81004,x81003),f333(f333(f268(a1,a1),x81006),x81001))) % 183.90/184.45 [8101]E(x81011,x81012)+E(x81013,f2(a1))+~P1(f333(f48(x81014,x81013),f333(f333(f268(a1,a1),x81012),x81015)))+~P1(f333(f48(x81014,x81013),f333(f333(f268(a1,a1),x81011),x81016))) % 183.90/184.45 [8121]~P19(x81212,x81215,x81216,x81211)+~P1(f333(f61(x81212),x81214))+E(f333(x81211,f333(f333(f311(x81212),x81213),x81214)),f333(f72(x81215,x81215,x81215,f333(x81211,x81214)),f333(x81216,x81213)))+P1(f333(f333(f335(x81212),x81213),x81214)) % 183.90/184.45 [8350]~P20(x83505,x83501,x83506,x83502)+E(f333(f72(x83501,x83501,x83501,f333(x83502,x83503)),f333(x83502,x83504)),f333(x83502,x83503))+~P1(f333(f61(x83505),x83503))+~P1(f333(f333(f247(f882(x83505,a870)),x83504),x83503)) % 183.90/184.45 [9480]~P25(x94801,x94802,x94804,x94803)+~P1(f333(f333(f335(x94802),x94805),f333(f312(x94801,x94802,x94804),x94803)))+P1(f333(f333(f335(x94801),f333(f76(x94801,x94802,x94803,x94804),x94805)),x94806))+~P1(f333(f333(f247(f882(x94801,a870)),x94803),x94806)) % 183.90/184.45 [9856]~P66(x98562)+~E(f380(x98561,x98563,x98565,x98566,x98564,x98562),f381(x98561,x98563,x98565,x98566,x98564,x98562))+~P1(f333(f61(x98564),x98566))+E(f333(f333(f6(x98561,x98562),x98563),f333(f312(x98564,x98561,x98565),x98566)),f333(f333(f6(x98564,x98562),f333(f72(x98561,x98562,x98564,x98563),x98565)),x98566)) % 183.90/184.45 [9893]~P66(x98936)+E(f333(x98931,f380(x98932,x98933,x98931,x98934,x98935,x98936)),f333(x98931,f381(x98932,x98933,x98931,x98934,x98935,x98936)))+E(f333(f333(f6(x98932,x98936),x98933),f333(f312(x98935,x98932,x98931),x98934)),f333(f333(f6(x98935,x98936),f333(f72(x98932,x98936,x98935,x98933),x98931)),x98934))+~P1(f333(f61(x98935),x98934)) % 183.90/184.45 [9933]~P66(x99332)+~E(f333(x99333,f333(x99335,f381(x99331,x99333,x99335,x99336,x99334,x99332))),f2(x99332))+~P1(f333(f61(x99334),x99336))+E(f333(f333(f6(x99331,x99332),x99333),f333(f312(x99334,x99331,x99335),x99336)),f333(f333(f6(x99334,x99332),f333(f72(x99331,x99332,x99334,x99333),x99335)),x99336)) % 183.90/184.45 [9991]~P66(x99912)+~P1(f333(f61(x99914),x99916))+E(f333(f333(f6(x99911,x99912),x99913),f333(f312(x99914,x99911,x99915),x99916)),f333(f333(f6(x99914,x99912),f333(f72(x99911,x99912,x99914,x99913),x99915)),x99916))+P1(f333(f333(f335(x99914),f381(x99911,x99913,x99915,x99916,x99914,x99912)),x99916)) % 183.90/184.45 [9992]~P66(x99922)+~P1(f333(f61(x99924),x99926))+E(f333(f333(f6(x99921,x99922),x99923),f333(f312(x99924,x99921,x99925),x99926)),f333(f333(f6(x99924,x99922),f333(f72(x99921,x99922,x99924,x99923),x99925)),x99926))+P1(f333(f333(f335(x99924),f380(x99921,x99923,x99925,x99926,x99924,x99922)),x99926)) % 183.90/184.45 [10105]~P73(x101051)+~P1(f333(f61(x101052),x101056))+E(f333(f333(f333(f65(x101051,x101052,f80(x101051)),f333(f333(f18(x101052,f882(x101053,a870),x101051),f333(f333(f7(x101052,x101051,f882(f882(x101053,a870),x101051)),f333(f333(f8(f882(x101053,x101051),f882(x101051,f882(f882(x101053,a870),x101051)),x101052),f65(x101051,x101053,f80(x101051))),x101054)),f77(x101051))),x101055)),f77(x101051)),x101056),f333(f333(f333(f65(x101051,f881(x101052,x101053),f80(x101051)),f333(f272(x101052,x101053,x101051),x101054)),f77(x101051)),f333(f333(f270(x101052,x101053),x101056),x101055)))+P1(f333(f333(f335(x101052),f581(x101054,x101055,x101053,x101056,x101052,x101051)),x101056)) % 183.90/184.45 [10123]~P73(x101231)+~P1(f333(f61(x101232),x101236))+E(f333(f333(f333(f65(x101231,x101232,f80(x101231)),f333(f333(f18(x101232,f882(x101233,a870),x101231),f333(f333(f7(x101232,x101231,f882(f882(x101233,a870),x101231)),f333(f333(f8(f882(x101233,x101231),f882(x101231,f882(f882(x101233,a870),x101231)),x101232),f65(x101231,x101233,f80(x101231))),x101234)),f77(x101231))),x101235)),f77(x101231)),x101236),f333(f333(f333(f65(x101231,f881(x101232,x101233),f80(x101231)),f333(f272(x101232,x101233,x101231),x101234)),f77(x101231)),f333(f333(f270(x101232,x101233),x101236),x101235)))+~P1(f333(f61(x101233),f333(x101235,f581(x101234,x101235,x101233,x101236,x101232,x101231)))) % 183.90/184.45 [8262]~P20(x82622,x82625,x82626,x82621)+~P1(f333(f61(x82622),x82624))+~P1(f333(f61(x82622),x82623))+E(f333(x82621,f333(f333(f113(f882(x82622,a870)),x82623),x82624)),f333(f72(x82625,x82625,x82625,f333(x82621,x82623)),f333(x82621,x82624))) % 183.90/184.45 [8483]~P4(x84831)+P1(f333(f333(f247(x84831),f333(x84832,x84833)),x84834))+~P1(f333(f333(f335(x84835),x84833),x84836))+~P1(f333(f333(f247(x84831),f333(f333(f41(x84835,x84831),x84836),x84832)),x84834)) % 183.90/184.45 [8885]~P25(x88852,x88851,x88853,x88856)+E(f333(f333(f22(f882(x88851,a870)),f333(f312(x88852,x88851,x88853),x88854)),f333(f312(x88852,x88851,x88853),x88855)),f333(f312(x88852,x88851,x88853),f333(f333(f22(f882(x88852,a870)),x88854),x88855)))+~P1(f333(f333(f247(f882(x88852,a870)),x88855),x88856))+~P1(f333(f333(f247(f882(x88852,a870)),x88854),x88856)) % 183.90/184.45 [8886]~P25(x88862,x88861,x88863,x88866)+E(f333(f333(f104(f882(x88861,a870)),f333(f312(x88862,x88861,x88863),x88864)),f333(f312(x88862,x88861,x88863),x88865)),f333(f312(x88862,x88861,x88863),f333(f333(f104(f882(x88862,a870)),x88864),x88865)))+~P1(f333(f333(f247(f882(x88862,a870)),x88865),x88866))+~P1(f333(f333(f247(f882(x88862,a870)),x88864),x88866)) % 183.90/184.45 [8926]~P1(f333(x89261,x89263))+~P1(f333(f333(f333(f333(a204,x89262),x89263),x89264),x89266))+~P1(f333(f333(f333(f333(a204,f31(x89261,x89262)),x89266),x89264),x89265))+P1(f333(f333(f333(f333(a204,f31(x89261,x89262)),x89263),x89264),x89265)) % 183.90/184.45 [9154]E(x91541,x91542)+~P49(x91543,x91544,x91545)+~P1(f333(f333(f335(f881(x91543,x91544)),f333(f333(f268(x91543,x91544),x91546),x91542)),x91545))+~P1(f333(f333(f335(f881(x91543,x91544)),f333(f333(f268(x91543,x91544),x91546),x91541)),x91545)) % 183.90/184.45 [9928]~P67(x99281)+~E(f333(x99283,f846(x99284,x99286,x99283,x99285,x99282,x99281)),f333(x99286,f846(x99284,x99286,x99283,x99285,x99282,x99281)))+~P1(f333(f61(x99282),x99285))+E(f333(f333(f333(f65(x99281,x99282,f80(x99281)),x99283),x99284),x99285),f333(f333(f333(f65(x99281,x99282,f80(x99281)),x99286),x99284),x99285)) % 183.90/184.45 [9989]~P67(x99891)+~P1(f333(f61(x99892),x99895))+E(f333(f333(f333(f65(x99891,x99892,f80(x99891)),x99893),x99894),x99895),f333(f333(f333(f65(x99891,x99892,f80(x99891)),x99896),x99894),x99895))+P1(f333(f333(f335(x99892),f846(x99894,x99893,x99896,x99895,x99892,x99891)),x99895)) % 183.90/184.45 [8698]~P67(x86981)+~P1(f333(f61(x86982),x86986))+P1(f333(f333(f335(x86982),x86985),x86986))+E(f333(f333(f333(f65(x86981,x86982,f80(x86981)),x86983),x86984),f333(f333(f311(x86982),x86985),x86986)),f333(f333(f80(x86981),f333(x86983,x86985)),f333(f333(f333(f65(x86981,x86982,f80(x86981)),x86983),x86984),x86986))) % 183.90/184.45 [8744]~P7(x87441,x87446,x87443)+~P12(x87441,f882(x87442,a870),x87443,x87445)+~P1(f333(f333(f335(x87441),x87444),x87446))+E(f333(f333(f41(x87441,f882(x87442,a870)),f333(f287(x87441,x87441,x87443),f333(f333(f311(x87441),x87444),f196(f882(x87441,a870))))),x87445),f333(x87445,x87444)) % 183.90/184.45 [8862]~P16(x88623,x88624,x88621)+~P1(f333(f61(x88623),x88626))+~P1(f333(f333(f335(x88623),x88622),x88626))+E(f333(f333(x88621,x88622),f333(f333(f64(x88623,x88624,x88621),x88625),f333(f333(f22(f882(x88623,a870)),x88626),f333(f333(f311(x88623),x88622),f196(f882(x88623,a870)))))),f333(f333(f64(x88623,x88624,x88621),x88625),x88626)) % 183.90/184.45 [9167]~P19(x91673,x91671,x91676,x91672)+~P1(f333(f61(x91673),x91675))+~P1(f333(f61(x91673),x91674))+E(f333(f72(x91671,x91671,x91671,f333(x91672,f333(f333(f113(f882(x91673,a870)),x91674),x91675))),f333(x91672,f333(f333(f104(f882(x91673,a870)),x91674),x91675))),f333(f72(x91671,x91671,x91671,f333(x91672,x91674)),f333(x91672,x91675))) % 183.90/184.45 [9500]~E(x95003,f333(f333(f160(x95001,x95002),x95005),x95006))+P1(f333(f333(f335(f881(f876(x95001),f876(x95001))),f333(f333(f268(f876(x95001),f876(x95001)),x95002),x95003)),f158(x95001,x95004)))+~P1(f333(f333(f248(a875),x95005),f333(f197(f876(x95001)),x95002)))+~P1(f333(f333(f335(f881(x95001,x95001)),f333(f333(f268(x95001,x95001),f333(f333(f166(x95001),x95002),x95005)),x95006)),x95004)) % 183.90/184.45 [10002]~P66(x100022)+~P1(f333(f61(x100021),x100026))+P1(f333(f333(f335(x100021),f579(x100024,x100025,x100023,x100026,x100021,x100022)),x100026))+E(f333(f333(f6(x100021,x100022),f333(f333(f18(x100021,f882(x100023,a870),x100022),f333(f333(f8(f882(x100023,x100022),f882(f882(x100023,a870),x100022),x100021),f6(x100023,x100022)),x100024)),x100025)),x100026),f333(f333(f6(f881(x100021,x100023),x100022),f333(f272(x100021,x100023,x100022),x100024)),f333(f333(f270(x100021,x100023),x100026),x100025))) % 183.90/184.45 [10003]~P73(x100032)+~P1(f333(f61(x100031),x100036))+P1(f333(f333(f335(x100031),f580(x100034,x100035,x100033,x100036,x100031,x100032)),x100036))+E(f333(f333(f9(x100031,x100032),f333(f333(f18(x100031,f882(x100033,a870),x100032),f333(f333(f8(f882(x100033,x100032),f882(f882(x100033,a870),x100032),x100031),f9(x100033,x100032)),x100034)),x100035)),x100036),f333(f333(f9(f881(x100031,x100033),x100032),f333(f272(x100031,x100033,x100032),x100034)),f333(f333(f270(x100031,x100033),x100036),x100035))) % 183.90/184.45 [10043]~P66(x100432)+~P1(f333(f61(x100431),x100436))+~P1(f333(f61(x100433),f333(x100435,f579(x100434,x100435,x100433,x100436,x100431,x100432))))+E(f333(f333(f6(x100431,x100432),f333(f333(f18(x100431,f882(x100433,a870),x100432),f333(f333(f8(f882(x100433,x100432),f882(f882(x100433,a870),x100432),x100431),f6(x100433,x100432)),x100434)),x100435)),x100436),f333(f333(f6(f881(x100431,x100433),x100432),f333(f272(x100431,x100433,x100432),x100434)),f333(f333(f270(x100431,x100433),x100436),x100435))) % 183.90/184.45 [10044]~P73(x100442)+~P1(f333(f61(x100441),x100446))+~P1(f333(f61(x100443),f333(x100445,f580(x100444,x100445,x100443,x100446,x100441,x100442))))+E(f333(f333(f9(x100441,x100442),f333(f333(f18(x100441,f882(x100443,a870),x100442),f333(f333(f8(f882(x100443,x100442),f882(f882(x100443,a870),x100442),x100441),f9(x100443,x100442)),x100444)),x100445)),x100446),f333(f333(f9(f881(x100441,x100443),x100442),f333(f272(x100441,x100443,x100442),x100444)),f333(f333(f270(x100441,x100443),x100446),x100445))) % 183.90/184.45 [10025]~P73(x100252)+~P1(f333(f61(x100251),x100256))+P1(f333(f333(f335(x100251),x100253),x100256))+E(f333(f333(f9(x100251,x100252),f333(f333(f7(x100251,x100252,x100252),f333(f333(f18(x100251,x100252,f882(x100252,x100252)),f333(f333(f8(a870,f882(x100252,f882(x100252,x100252)),x100251),f99(x100252)),f333(f333(f7(x100251,x100251,a870),a330),x100253))),x100254)),x100255)),x100256),f333(f333(f258(x100252),x100255),f333(f37(x100251),x100256))) % 183.90/184.45 [10030]~P73(x100302)+~P1(f333(f61(x100301),x100306))+~P1(f333(f333(f335(x100301),x100303),x100306))+E(f333(f333(f9(x100301,x100302),f333(f333(f7(x100301,x100302,x100302),f333(f333(f18(x100301,x100302,f882(x100302,x100302)),f333(f333(f8(a870,f882(x100302,f882(x100302,x100302)),x100301),f99(x100302)),f333(f333(f7(x100301,x100301,a870),a330),x100303))),x100304)),x100305)),x100306),f333(f333(f80(x100302),f333(x100304,x100303)),f333(f333(f258(x100302),x100305),f333(f333(f22(a875),f333(f37(x100301),x100306)),f77(a875))))) % 183.90/184.45 [10098]~P1(f333(f61(x100981),x100985))+~P1(f333(f61(x100982),x100983))+P1(f333(f333(f335(x100982),f494(x100986,x100984,x100983,x100982,x100985,x100981)),x100983))+E(f333(f333(f6(x100981,a875),f333(f333(f8(f882(x100982,a870),a875,x100981),f37(x100982)),f333(f333(f8(f882(x100982,a870),f882(x100982,a870),x100981),f253(x100982)),f333(f333(f8(f882(x100982,a870),f882(x100982,a870),x100981),f333(f18(x100982,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100982),a331),f333(f333(f7(x100982,f882(x100982,a870),a870),f335(x100982)),x100983)))),x100984)))),x100985),f333(f333(f80(a875),x100986),f333(f37(x100982),x100983))) % 183.90/184.45 [10099]~P1(f333(f61(x100991),x100995))+~P1(f333(f61(x100992),x100993))+P1(f333(f333(f335(x100992),f495(x100996,x100994,x100993,x100992,x100995,x100991)),x100993))+E(f333(f333(f6(x100991,a875),f333(f333(f8(f882(x100992,a870),a875,x100991),f37(x100992)),f333(f333(f8(f882(x100992,a870),f882(x100992,a870),x100991),f253(x100992)),f333(f333(f8(f882(x100992,a870),f882(x100992,a870),x100991),f333(f18(x100992,a870,a870),f333(f333(f8(a870,f882(a870,a870),x100992),a331),f333(f333(f7(x100992,f882(x100992,a870),a870),f335(x100992)),x100993)))),x100994)))),x100995),f333(f333(f6(x100992,a875),x100996),x100993)) % 183.90/184.45 [10129]~P1(f333(f61(x101292),x101293))+~P1(f333(f61(x101291),x101295))+~E(f333(f37(x101291),f333(f253(x101291),f333(f333(f18(x101291,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101291),a331),f333(f333(f7(x101291,f882(x101291,a870),a870),f335(x101291)),x101295))),f333(f333(f7(x101291,x101292,a870),x101294),f494(x101296,x101294,x101293,x101292,x101295,x101291))))),x101296)+E(f333(f333(f6(x101291,a875),f333(f333(f8(f882(x101292,a870),a875,x101291),f37(x101292)),f333(f333(f8(f882(x101292,a870),f882(x101292,a870),x101291),f253(x101292)),f333(f333(f8(f882(x101292,a870),f882(x101292,a870),x101291),f333(f18(x101292,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101292),a331),f333(f333(f7(x101292,f882(x101292,a870),a870),f335(x101292)),x101293)))),x101294)))),x101295),f333(f333(f80(a875),x101296),f333(f37(x101292),x101293))) % 183.90/184.45 [10131]~P1(f333(f61(x101312),x101313))+~P1(f333(f61(x101311),x101315))+~E(f333(f37(x101311),f333(f253(x101311),f333(f333(f18(x101311,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101311),a331),f333(f333(f7(x101311,f882(x101311,a870),a870),f335(x101311)),x101315))),f333(f333(f7(x101311,x101312,a870),x101314),f495(x101316,x101314,x101313,x101312,x101315,x101311))))),f333(x101316,f495(x101316,x101314,x101313,x101312,x101315,x101311)))+E(f333(f333(f6(x101311,a875),f333(f333(f8(f882(x101312,a870),a875,x101311),f37(x101312)),f333(f333(f8(f882(x101312,a870),f882(x101312,a870),x101311),f253(x101312)),f333(f333(f8(f882(x101312,a870),f882(x101312,a870),x101311),f333(f18(x101312,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101312),a331),f333(f333(f7(x101312,f882(x101312,a870),a870),f335(x101312)),x101313)))),x101314)))),x101315),f333(f333(f6(x101312,a875),x101316),x101313)) % 183.90/184.45 [9783]E(x97831,x97832)+~P16(x97833,x97834,x97835)+~P1(f333(f66(x97833,x97834,x97835,x97836,x97837),x97832))+~P1(f333(f66(x97833,x97834,x97835,x97836,x97837),x97831)) % 183.90/184.45 [9576]P1(f333(x95761,x95762))+~P1(f333(f333(f335(x95767),x95762),f333(x95766,x95764)))+~P1(f333(x95761,f835(x95761,x95766,x95765,x95763,x95767)))+~P1(f333(f333(f335(x95763),x95764),x95765)) % 183.90/184.45 [10017]~P16(x100177,x100176,x100171)+E(f333(f333(x100171,x100172),f739(x100172,x100173,x100174,x100175,x100171,x100176,x100177)),x100173)+~P1(f333(f66(x100177,x100176,x100171,x100175,x100174),x100173))+~P1(f333(f333(f335(x100177),x100172),x100174)) % 183.90/184.45 [10083]~P16(x100831,x100832,x100833)+~P1(f333(f66(x100831,x100832,x100833,x100834,x100835),x100837))+P1(f333(f66(x100831,x100832,x100833,x100834,f333(f333(f22(f882(x100831,a870)),x100835),f333(f333(f311(x100831),x100836),f196(f882(x100831,a870))))),f739(x100836,x100837,x100835,x100834,x100833,x100832,x100831)))+~P1(f333(f333(f335(x100831),x100836),x100835)) % 183.90/184.45 [9476]~P67(x94761)+~P25(x94765,x94762,x94766,x94767)+~P1(f333(f61(x94765),x94767))+E(f333(f333(f333(f65(x94761,x94762,f80(x94761)),x94763),x94764),f333(f312(x94765,x94762,x94766),x94767)),f333(f333(f333(f65(x94761,x94765,f80(x94761)),f333(f72(x94762,x94761,x94765,x94763),x94766)),x94764),x94767)) % 183.90/184.45 [9600]~E(f333(f333(f311(x96001),x96005),x96006),f333(f333(f311(x96001),x96002),x96003))+~P1(f333(f66(x96001,x96001,x96004,x96002,x96003),x96007))+P1(f333(f333(f335(x96001),x96002),x96003))+P1(f333(f62(x96001,x96004,f333(f333(f311(x96001),x96005),x96006)),x96007)) % 183.90/184.45 [9683]P1(f333(x96831,x96832))+~P1(f333(f333(f335(x96833),x96832),f333(x96834,x96837)))+~P1(f333(f333(f335(x96836),x96837),x96835))+P1(f333(f333(f335(x96833),f835(x96831,x96834,x96835,x96836,x96833)),f333(f333(f41(x96836,f882(x96833,a870)),x96835),x96834))) % 183.90/184.45 [9697]~P25(x96972,x96971,x96975,x96974)+~P25(x96971,x96973,x96976,f333(f312(x96972,x96971,x96975),x96974))+E(f333(f333(f72(x96971,x96972,x96973,f76(x96972,x96971,x96974,x96975)),f76(x96971,x96973,f333(f312(x96972,x96971,x96975),x96974),x96976)),x96977),f333(f76(x96972,x96973,x96974,f333(f72(x96971,x96973,x96972,x96976),x96975)),x96977))+~P1(f333(f333(f335(x96973),x96977),f333(f312(x96971,x96973,x96976),f333(f312(x96972,x96971,x96975),x96974)))) % 183.90/184.45 [10018]~P16(x100187,x100186,x100181)+E(f333(f333(x100181,x100182),f793(x100183,x100184,x100182,x100185,x100181,x100186,x100187)),x100183)+P1(f333(f333(f335(x100187),x100182),x100184))+~P1(f333(f66(x100187,x100186,x100181,x100185,f333(f333(f311(x100187),x100182),x100184)),x100183)) % 183.90/184.45 [10082]~P16(x100821,x100824,x100825)+P1(f333(f66(x100821,x100824,x100825,x100826,x100823),f793(x100827,x100823,x100822,x100826,x100825,x100824,x100821)))+P1(f333(f333(f335(x100821),x100822),x100823))+~P1(f333(f66(x100821,x100824,x100825,x100826,f333(f333(f311(x100821),x100822),x100823)),x100827)) % 183.90/184.45 [9765]E(x97651,f2(a1))+~P1(f333(f48(x97653,x97651),f333(f333(f268(a1,a1),x97655),x97657)))+~P1(f333(f48(x97652,x97651),f333(f333(f268(a1,a1),x97654),x97656)))+P1(f333(f48(f333(f333(f79(a1),x97652),x97653),x97651),f333(f333(f268(a1,a1),f333(f333(f79(a1),f333(f333(f79(a1),x97654),x97655)),f333(f333(f38(a1),f333(f333(f79(a1),x97656),x97657)),x97651))),f44(a1,f333(f333(f79(a1),x97656),x97657),x97651)))) % 183.90/184.45 [9767]~P1(f333(f333(f248(a875),f2(a875)),x97673))+~P1(f333(f47(x97672,x97673),f333(f333(f268(a875,a875),x97675),x97677)))+~P1(f333(f47(x97671,x97673),f333(f333(f268(a875,a875),x97674),x97676)))+P1(f333(f47(f333(f333(f79(a875),x97671),x97672),x97673),f333(f333(f268(a875,a875),f333(f333(f79(a875),f333(f333(f79(a875),x97674),x97675)),f333(f333(f38(a875),f333(f333(f79(a875),x97676),x97677)),x97673))),f44(a875,f333(f333(f79(a875),x97676),x97677),x97673)))) % 183.90/184.45 [10128]~P66(x101282)+~P1(f333(f61(x101283),x101285))+~P1(f333(f61(x101281),x101287))+E(f333(f333(f6(x101281,x101282),f333(f333(f18(x101281,f882(x101283,a870),x101282),f333(f333(f8(f882(x101283,x101282),f882(f882(x101283,a870),x101282),x101281),f6(x101283,x101282)),x101284)),f333(f333(f8(f882(x101283,a870),f882(x101283,a870),x101281),f253(x101283)),f333(f333(f8(f882(x101283,a870),f882(x101283,a870),x101281),f333(f18(x101283,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101283),a331),f333(f333(f7(x101283,f882(x101283,a870),a870),f335(x101283)),x101285)))),x101286)))),x101287),f333(f333(f6(x101283,x101282),f333(f333(f18(x101283,f882(x101281,a870),x101282),f333(f333(f8(f882(x101281,x101282),f882(f882(x101281,a870),x101282),x101283),f6(x101281,x101282)),f333(f7(x101281,x101283,x101282),x101284))),f333(f333(f8(f882(x101281,a870),f882(x101281,a870),x101283),f253(x101281)),f333(f333(f8(f882(x101281,a870),f882(x101281,a870),x101283),f333(f18(x101281,a870,a870),f333(f333(f8(a870,f882(a870,a870),x101281),a331),f333(f333(f7(x101281,f882(x101281,a870),a870),f335(x101281)),x101287)))),f333(f7(x101281,x101283,a870),x101286))))),x101285)) % 183.90/184.45 [9636]~P22(x96367,x96366,x96361,x96368,x96362,x96364)+E(f333(f333(x96361,f333(x96362,x96363)),f333(x96364,x96365)),f333(x96364,x96365))+~P1(f333(f61(x96366),x96365))+~P1(f333(f333(f335(x96366),x96363),x96365)) % 183.90/184.45 [9640]~P13(x96406,x96401,x96402,x96408,x96403,x96404)+~P7(x96406,x96407,x96408)+P12(x96401,x96402,x96403,f333(x96404,x96405))+~P1(f333(f333(f335(x96406),x96405),x96407)) % 183.90/184.45 [8078]~P27(x80788,x80787,f333(f333(f333(f91(x80788),x80784),x80786),x80781))+P1(f333(f333(x80781,x80782),x80783))+~P1(f333(f333(x80784,x80782),x80785))+~P1(f333(f333(f333(f333(a204,x80786),x80785),x80787),x80783)) % 183.90/184.45 [9261]~P19(x92617,x92611,x92618,x92613)+~P1(f333(f61(x92617),x92615))+~P1(f333(f61(x92617),x92614))+E(f333(f72(x92611,x92611,x92612,f333(x92613,x92614)),f333(f72(x92611,x92611,x92612,f333(x92613,x92615)),x92616)),f333(f72(x92611,x92611,x92612,f333(x92613,x92615)),f333(f72(x92611,x92611,x92612,f333(x92613,x92614)),x92616))) % 183.90/184.45 [9269]~P34(x92691,x92692,x92693,x92694,x92697)+P34(x92691,x92692,x92693,f333(f333(f160(x92691,x92694),x92695),x92696),f333(f333(f160(x92692,x92697),x92695),x92698))+~P1(f333(f333(x92693,x92696),x92698))+~P1(f333(f333(f248(a875),x92695),f333(f197(f876(x92691)),x92694))) % 183.90/184.45 [9270]~P34(x92701,x92702,x92703,x92704,x92707)+P34(x92701,x92702,x92703,f333(f333(f160(x92701,x92704),x92705),x92706),f333(f333(f160(x92702,x92707),x92705),x92708))+~P1(f333(f333(x92703,x92706),x92708))+~P1(f333(f333(f248(a875),x92705),f333(f197(f876(x92702)),x92707))) % 183.90/184.45 [9349]~P25(x93492,x93492,x93495,x93496)+~P21(x93493,x93492,x93497,x93498,x93491)+~P1(f333(f61(x93492),x93496))+E(f333(f333(x93491,f333(f72(x93492,x93493,x93492,x93494),x93495)),x93496),f333(f333(x93491,x93494),f333(f312(x93492,x93492,x93495),x93496))) % 183.90/184.45 [9638]~P23(x96387,x96382,x96385,x96388,x96386,x96381)+~P1(f333(f61(x96382),x96384))+E(f333(x96381,f333(f333(f311(x96382),x96383),x96384)),f333(f333(x96385,f333(x96386,x96383)),f333(x96381,x96384)))+P1(f333(f333(f335(x96382),x96383),x96384)) % 183.90/184.45 [9649]~P22(x96496,x96495,x96491,x96497,x96498,x96492)+E(f333(f333(x96491,f333(x96492,x96493)),f333(x96492,x96494)),f333(x96492,x96494))+~P1(f333(f61(x96495),x96494))+~P1(f333(f333(f247(f882(x96495,a870)),x96493),x96494)) % 183.90/184.45 [9247]P1(f333(f333(f335(f881(f876(x92471),f876(x92471))),f333(f333(f268(f876(x92471),f876(x92471)),x92472),x92473)),f158(x92471,x92474)))+~E(x92473,f333(f333(f135(x92471),x92475),f333(f333(f152(x92471),x92476),x92477)))+~E(x92472,f333(f333(f135(x92471),x92475),f333(f333(f152(x92471),x92478),x92477)))+~P1(f333(f333(f335(f881(x92471,x92471)),f333(f333(f268(x92471,x92471),x92478),x92476)),x92474)) % 183.90/184.45 [9643]~P22(x96436,x96432,x96435,x96437,x96438,x96431)+~P1(f333(f61(x96432),x96434))+~P1(f333(f61(x96432),x96433))+E(f333(x96431,f333(f333(f113(f882(x96432,a870)),x96433),x96434)),f333(f333(x96435,f333(x96431,x96433)),f333(x96431,x96434))) % 183.90/184.45 [10166]~P25(x101664,x101662,x101665,x101668)+E(f333(f333(f42(x101661,f882(x101662,a870)),x101663),f333(f333(f8(f882(x101664,a870),f882(x101662,a870),x101661),f312(x101664,x101662,x101665)),x101666)),f333(f312(x101664,x101662,x101665),f333(f333(f42(x101661,f882(x101664,a870)),x101663),x101666)))+~P1(f333(f333(f335(x101661),x101667),x101663))+P1(f333(f333(f335(x101661),f387(x101667,x101666,x101663,x101661,x101668,x101665,x101662,x101664)),x101663)) % 183.90/184.45 [10190]~P25(x101904,x101902,x101905,x101907)+E(f333(f333(f42(x101901,f882(x101902,a870)),x101903),f333(f333(f8(f882(x101904,a870),f882(x101902,a870),x101901),f312(x101904,x101902,x101905)),x101906)),f333(f312(x101904,x101902,x101905),f333(f333(f42(x101901,f882(x101904,a870)),x101903),x101906)))+~P1(f333(f333(f335(x101901),x101908),x101903))+~P1(f333(f333(f247(f882(x101904,a870)),f333(x101906,f387(x101908,x101906,x101903,x101901,x101907,x101905,x101902,x101904))),x101907)) % 183.90/184.45 [9706]~P23(x97067,x97065,x97061,x97068,x97062,x97064)+~P1(f333(f61(x97065),x97066))+~P1(f333(f333(f335(x97065),x97063),x97066))+E(f333(f333(x97061,f333(x97062,x97063)),f333(x97064,f333(f333(f22(f882(x97065,a870)),x97066),f333(f333(f311(x97065),x97063),f196(f882(x97065,a870)))))),f333(x97064,x97066)) % 183.90/184.45 [9714]~P23(x97146,x97143,x97141,x97147,x97148,x97142)+~P1(f333(f61(x97143),x97145))+~P1(f333(f61(x97143),x97144))+E(f333(f333(x97141,f333(x97142,f333(f333(f113(f882(x97143,a870)),x97144),x97145))),f333(x97142,f333(f333(f104(f882(x97143,a870)),x97144),x97145))),f333(f333(x97141,f333(x97142,x97144)),f333(x97142,x97145))) % 183.90/184.45 [9806]P42(x98061,x98062,x98063,x98064,x98065,f333(f333(x98063,x98066),x98067))+~P42(x98061,x98062,x98063,x98064,f333(f333(f22(f882(x98061,a870)),x98065),f333(f333(f311(x98061),x98068),f196(f882(x98061,a870)))),x98069)+~E(f333(f333(x98063,x98066),x98067),f333(f333(x98063,x98068),x98069))+~P1(f333(f333(f335(x98061),x98068),x98065)) % 183.90/184.45 [10205]P24(x102051,x102052,f333(f333(f311(f874(x102051)),f333(f333(f333(f91(x102051),f333(x102053,f443(x102054,x102055,x102056,x102057,x102053,x102052,x102051,x102058,x102059))),f333(x102057,f443(x102054,x102055,x102056,x102057,x102053,x102052,x102051,x102058,x102059))),f333(x102056,f443(x102054,x102055,x102056,x102057,x102053,x102052,x102051,x102058,x102059)))),f196(f882(f874(x102051),a870))))+~P1(f333(f61(x102059),x102058))+~P24(x102051,x102052,f333(f312(x102059,f874(x102051),f333(f333(f18(x102059,f882(x102051,f882(a872,a870)),f874(x102051)),f333(f333(f18(x102059,a871,f882(f882(x102051,f882(a872,a870)),f874(x102051))),f333(f333(f8(f882(x102051,f882(a872,a870)),f882(a871,f882(f882(x102051,f882(a872,a870)),f874(x102051))),x102059),f91(x102051)),x102053)),x102057)),x102056)),x102058))+P24(x102051,x102052,f333(f312(x102059,f874(x102051),f333(f333(f18(x102059,f882(x102051,f882(a872,a870)),f874(x102051)),f333(f333(f18(x102059,a871,f882(f882(x102051,f882(a872,a870)),f874(x102051))),f333(f333(f8(f882(x102051,f882(a872,a870)),f882(a871,f882(f882(x102051,f882(a872,a870)),f874(x102051))),x102059),f91(x102051)),x102055)),x102057)),x102054)),x102058)) % 183.90/184.45 [10206]~P24(x102061,x102062,f333(f333(f311(f874(x102061)),f333(f333(f333(f91(x102061),f333(x102064,f443(x102066,x102064,x102068,x102065,x102069,x102062,x102061,x102067,x102063))),f333(x102065,f443(x102066,x102064,x102068,x102065,x102069,x102062,x102061,x102067,x102063))),f333(x102066,f443(x102066,x102064,x102068,x102065,x102069,x102062,x102061,x102067,x102063)))),f196(f882(f874(x102061),a870))))+~P1(f333(f61(x102063),x102067))+~P24(x102061,x102062,f333(f312(x102063,f874(x102061),f333(f333(f18(x102063,f882(x102061,f882(a872,a870)),f874(x102061)),f333(f333(f18(x102063,a871,f882(f882(x102061,f882(a872,a870)),f874(x102061))),f333(f333(f8(f882(x102061,f882(a872,a870)),f882(a871,f882(f882(x102061,f882(a872,a870)),f874(x102061))),x102063),f91(x102061)),x102069)),x102065)),x102068)),x102067))+P24(x102061,x102062,f333(f312(x102063,f874(x102061),f333(f333(f18(x102063,f882(x102061,f882(a872,a870)),f874(x102061)),f333(f333(f18(x102063,a871,f882(f882(x102061,f882(a872,a870)),f874(x102061))),f333(f333(f8(f882(x102061,f882(a872,a870)),f882(a871,f882(f882(x102061,f882(a872,a870)),f874(x102061))),x102063),f91(x102061)),x102064)),x102065)),x102066)),x102067)) % 183.90/184.45 [9740]~P13(x97406,x97407,x97408,x97409,x974010,x97401)+E(f333(f333(x97401,x97402),x97403),f333(f333(x97401,x97404),x97405))+~P1(f333(f333(f335(f881(x97407,x97407)),f333(f333(f268(x97407,x97407),x97403),x97405)),x974010))+~P1(f333(f333(f335(f881(x97406,x97406)),f333(f333(f268(x97406,x97406),x97402),x97404)),x97409)) % 183.90/184.45 [9351]~P62(x93512)+E(x93511,f196(f882(x93512,a870)))+~P1(f333(f61(x93512),x93511))+P1(f333(f333(f335(x93512),f13(x93512,x93511)),x93511))+~P1(f333(f333(f335(x93512),f333(f333(f113(x93512),f571(x93511,x93512)),f583(x93511,x93512))),f333(f333(f311(x93512),f571(x93511,x93512)),f333(f333(f311(x93512),f583(x93511,x93512)),f196(f882(x93512,a870)))))) % 183.90/184.45 [9352]~P62(x93522)+E(x93521,f196(f882(x93522,a870)))+~P1(f333(f61(x93522),x93521))+P1(f333(f333(f335(x93522),f10(x93522,x93521)),x93521))+~P1(f333(f333(f335(x93522),f333(f333(f104(x93522),f636(x93521,x93522)),f661(x93521,x93522))),f333(f333(f311(x93522),f636(x93521,x93522)),f333(f333(f311(x93522),f661(x93521,x93522)),f196(f882(x93522,a870)))))) % 183.90/184.45 [9384]~P67(x93842)+E(x93841,f196(f882(x93842,a870)))+~P1(f333(f61(x93842),x93841))+P1(f333(f333(f335(x93842),f333(f63(x93842,f80(x93842)),x93841)),x93841))+~P1(f333(f333(f335(x93842),f333(f333(f80(x93842),f853(x93841,x93842)),f855(x93841,x93842))),f333(f333(f311(x93842),f853(x93841,x93842)),f333(f333(f311(x93842),f855(x93841,x93842)),f196(f882(x93842,a870)))))) % 183.90/184.45 [9390]~P106(x93902)+E(x93901,f196(f882(x93902,a870)))+~P1(f333(f61(x93902),x93901))+P1(f333(f333(f335(x93902),f11(x93902,f245(x93902),x93901)),x93901))+~P1(f333(f333(f335(x93902),f333(f333(f245(x93902),f503(x93901,x93902)),f506(x93901,x93902))),f333(f333(f311(x93902),f503(x93901,x93902)),f333(f333(f311(x93902),f506(x93901,x93902)),f196(f882(x93902,a870)))))) % 183.90/184.45 [9391]~P106(x93912)+E(x93911,f196(f882(x93912,a870)))+~P1(f333(f61(x93912),x93911))+P1(f333(f333(f335(x93912),f12(x93912,f246(x93912),x93911)),x93911))+~P1(f333(f333(f335(x93912),f333(f333(f246(x93912),f504(x93911,x93912)),f505(x93911,x93912))),f333(f333(f311(x93912),f504(x93911,x93912)),f333(f333(f311(x93912),f505(x93911,x93912)),f196(f882(x93912,a870)))))) % 183.90/184.45 [6503]~P85(x65032)+E(x65031,f2(x65032))+~E(f333(f333(f79(x65032),x65033),x65031),f2(x65032))+~P1(f333(f333(f247(x65032),f2(x65032)),x65033))+~P1(f333(f333(f247(x65032),f2(x65032)),x65031)) % 183.90/184.45 [6504]~P85(x65042)+E(x65041,f2(x65042))+~E(f333(f333(f79(x65042),x65041),x65043),f2(x65042))+~P1(f333(f333(f247(x65042),f2(x65042)),x65043))+~P1(f333(f333(f247(x65042),f2(x65042)),x65041)) % 183.90/184.45 [7037]~P106(x70372)+~P14(x70372,x70371)+E(x70371,f116(x70372))+~P1(f333(f333(f335(x70372),x70373),f333(f174(x70372),f742(x70371,x70372))))+P1(f333(f333(f247(x70372),f761(x70371,x70372)),x70373)) % 183.90/184.45 [7203]~P106(x72031)+E(f14(x72031,x72032),x72033)+~P1(f333(f61(x72031),x72032))+~P1(f333(f333(f247(x72031),x72033),f526(x72033,x72032,x72031)))+~P1(f333(f333(f335(x72031),x72033),x72032)) % 183.90/184.45 [7234]~P106(x72341)+~P14(x72341,x72342)+~P14(x72341,x72343)+P14(x72341,f333(f333(f135(x72341),x72342),x72343))+P1(f333(f333(f335(x72341),f748(x72343,x72342,x72341)),f333(f174(x72341),x72342))) % 183.90/184.45 [7235]~P106(x72351)+~P14(x72351,x72352)+~P14(x72351,x72353)+P14(x72351,f333(f333(f135(x72351),x72352),x72353))+P1(f333(f333(f335(x72351),f749(x72353,x72352,x72351)),f333(f174(x72351),x72353))) % 183.90/184.45 [7291]~P106(x72911)+E(f14(x72911,x72912),x72913)+~P1(f333(f61(x72911),x72912))+P1(f333(f333(f335(x72911),f526(x72913,x72912,x72911)),x72912))+~P1(f333(f333(f335(x72911),x72913),x72912)) % 183.90/184.45 [7292]~P106(x72921)+E(f15(x72921,x72922),x72923)+~P1(f333(f61(x72921),x72922))+P1(f333(f333(f335(x72921),f528(x72923,x72922,x72921)),x72922))+~P1(f333(f333(f335(x72921),x72923),x72922)) % 183.90/184.45 [7879]~P106(x78791)+E(f15(x78791,x78792),x78793)+~P1(f333(f61(x78791),x78792))+~P1(f333(f333(f335(x78791),x78793),x78792))+~P1(f333(f333(f247(x78791),f528(x78793,x78792,x78791)),x78793)) % 183.90/184.45 [8210]~P106(x82101)+~P14(x82101,x82102)+~P14(x82101,x82103)+P14(x82101,f333(f333(f135(x82101),x82102),x82103))+~P1(f333(f333(f247(x82101),f748(x82103,x82102,x82101)),f749(x82103,x82102,x82101))) % 183.90/184.45 [8992]~P62(x89922)+E(x89921,f196(f882(x89922,a870)))+~E(f333(f333(f113(x89922),f333(x89923,f594(x89921,x89923,x89922))),f333(x89923,f605(x89921,x89923,x89922))),f333(x89923,f333(f333(f113(x89922),f594(x89921,x89923,x89922)),f605(x89921,x89923,x89922))))+E(f13(x89922,f333(f312(x89922,x89922,x89923),x89921)),f333(x89923,f13(x89922,x89921)))+~P1(f333(f61(x89922),x89921)) % 183.90/184.45 [8993]~P62(x89932)+E(x89931,f196(f882(x89932,a870)))+~E(f333(f333(f104(x89932),f333(x89933,f667(x89931,x89933,x89932))),f333(x89933,f682(x89931,x89933,x89932))),f333(x89933,f333(f333(f104(x89932),f667(x89931,x89933,x89932)),f682(x89931,x89933,x89932))))+E(f10(x89932,f333(f312(x89932,x89932,x89933),x89931)),f333(x89933,f10(x89932,x89931)))+~P1(f333(f61(x89932),x89931)) % 183.90/184.45 [8994]~P106(x89942)+E(x89941,f196(f882(x89942,a870)))+~E(f333(f333(f245(x89942),f333(x89943,f508(x89941,x89943,x89942))),f333(x89943,f517(x89941,x89943,x89942))),f333(x89943,f333(f333(f245(x89942),f508(x89941,x89943,x89942)),f517(x89941,x89943,x89942))))+E(f14(x89942,f333(f312(x89942,x89942,x89943),x89941)),f333(x89943,f14(x89942,x89941)))+~P1(f333(f61(x89942),x89941)) % 183.90/184.45 [8995]~P106(x89952)+E(x89951,f196(f882(x89952,a870)))+~E(f333(f333(f246(x89952),f333(x89953,f509(x89951,x89953,x89952))),f333(x89953,f516(x89951,x89953,x89952))),f333(x89953,f333(f333(f246(x89952),f509(x89951,x89953,x89952)),f516(x89951,x89953,x89952))))+E(f15(x89952,f333(f312(x89952,x89952,x89953),x89951)),f333(x89953,f15(x89952,x89951)))+~P1(f333(f61(x89952),x89951)) % 183.90/184.45 [9065]~P106(x90652)+E(x90651,f196(f882(x90652,a870)))+~E(f333(f333(f245(x90652),f333(x90653,f510(x90651,x90653,x90652))),f333(x90653,f515(x90651,x90653,x90652))),f333(x90653,f333(f333(f245(x90652),f510(x90651,x90653,x90652)),f515(x90651,x90653,x90652))))+E(f11(x90652,f245(x90652),f333(f312(x90652,x90652,x90653),x90651)),f333(x90653,f11(x90652,f245(x90652),x90651)))+~P1(f333(f61(x90652),x90651)) % 183.90/184.45 [9066]~P106(x90662)+E(x90661,f196(f882(x90662,a870)))+~E(f333(f333(f246(x90662),f333(x90663,f511(x90661,x90663,x90662))),f333(x90663,f514(x90661,x90663,x90662))),f333(x90663,f333(f333(f246(x90662),f511(x90661,x90663,x90662)),f514(x90661,x90663,x90662))))+E(f12(x90662,f246(x90662),f333(f312(x90662,x90662,x90663),x90661)),f333(x90663,f12(x90662,f246(x90662),x90661)))+~P1(f333(f61(x90662),x90661)) % 183.90/184.45 [6519]~P67(x65192)+E(x65191,f196(f882(x65192,a870)))+~P1(f333(f61(x65192),x65191))+E(f333(f63(x65192,f80(x65192)),f333(f333(f311(x65192),x65193),x65191)),f333(f333(f80(x65192),x65193),f333(f63(x65192,f80(x65192)),x65191)))+P1(f333(f333(f335(x65192),x65193),x65191)) % 183.90/184.45 [7043]~P62(x70432)+E(f333(f333(f113(x70432),f13(x70432,x70431)),f13(x70432,x70433)),f13(x70432,x70433))+E(x70431,f196(f882(x70432,a870)))+~P1(f333(f61(x70432),x70433))+~P1(f333(f333(f247(f882(x70432,a870)),x70431),x70433)) % 183.90/184.45 [7044]~P62(x70442)+E(f333(f333(f104(x70442),f10(x70442,x70441)),f10(x70442,x70443)),f10(x70442,x70443))+E(x70441,f196(f882(x70442,a870)))+~P1(f333(f61(x70442),x70443))+~P1(f333(f333(f247(f882(x70442,a870)),x70441),x70443)) % 183.90/184.45 [7045]~P106(x70452)+E(f333(f333(f245(x70452),f14(x70452,x70451)),f14(x70452,x70453)),f14(x70452,x70453))+E(x70451,f196(f882(x70452,a870)))+~P1(f333(f61(x70452),x70453))+~P1(f333(f333(f247(f882(x70452,a870)),x70451),x70453)) % 183.90/184.45 [7046]~P106(x70462)+E(f333(f333(f246(x70462),f15(x70462,x70461)),f15(x70462,x70463)),f15(x70462,x70463))+E(x70461,f196(f882(x70462,a870)))+~P1(f333(f61(x70462),x70463))+~P1(f333(f333(f247(f882(x70462,a870)),x70461),x70463)) % 183.90/184.45 [7343]~P106(x73432)+E(x73431,f196(f882(x73432,a870)))+~P1(f333(f61(x73432),x73433))+P1(f333(f333(f247(x73432),f14(x73432,x73433)),f14(x73432,x73431)))+~P1(f333(f333(f247(f882(x73432,a870)),x73431),x73433)) % 183.90/184.45 [7344]~P106(x73442)+E(x73441,f196(f882(x73442,a870)))+~P1(f333(f61(x73442),x73443))+P1(f333(f333(f247(x73442),f15(x73442,x73441)),f15(x73442,x73443)))+~P1(f333(f333(f247(f882(x73442,a870)),x73441),x73443)) % 183.90/184.45 [7402]~P62(x74021)+E(f13(x74021,x74022),x74023)+~P1(f333(f61(x74021),x74022))+~E(f333(f333(f22(f882(x74021,a870)),x74022),f333(f333(f311(x74021),x74023),f196(f882(x74021,a870)))),f196(f882(x74021,a870)))+~P1(f333(f333(f335(x74021),x74023),x74022)) % 183.90/184.45 [7403]~P62(x74031)+E(f10(x74031,x74032),x74033)+~P1(f333(f61(x74031),x74032))+~E(f333(f333(f22(f882(x74031,a870)),x74032),f333(f333(f311(x74031),x74033),f196(f882(x74031,a870)))),f196(f882(x74031,a870)))+~P1(f333(f333(f335(x74031),x74033),x74032)) % 183.90/184.45 [7404]~P106(x74041)+E(f14(x74041,x74042),x74043)+~P1(f333(f61(x74041),x74042))+~E(f333(f333(f22(f882(x74041,a870)),x74042),f333(f333(f311(x74041),x74043),f196(f882(x74041,a870)))),f196(f882(x74041,a870)))+~P1(f333(f333(f335(x74041),x74043),x74042)) % 183.90/184.45 [7405]~P106(x74051)+E(f15(x74051,x74052),x74053)+~P1(f333(f61(x74051),x74052))+~E(f333(f333(f22(f882(x74051,a870)),x74052),f333(f333(f311(x74051),x74053),f196(f882(x74051,a870)))),f196(f882(x74051,a870)))+~P1(f333(f333(f335(x74051),x74053),x74052)) % 183.90/184.45 [7504]~P106(x75041)+E(f11(x75041,f245(x75041),x75042),x75043)+~P1(f333(f61(x75041),x75042))+~E(f333(f333(f22(f882(x75041,a870)),x75042),f333(f333(f311(x75041),x75043),f196(f882(x75041,a870)))),f196(f882(x75041,a870)))+~P1(f333(f333(f335(x75041),x75043),x75042)) % 183.90/184.45 [7505]~P106(x75051)+E(f12(x75051,f246(x75051),x75052),x75053)+~P1(f333(f61(x75051),x75052))+~E(f333(f333(f22(f882(x75051,a870)),x75052),f333(f333(f311(x75051),x75053),f196(f882(x75051,a870)))),f196(f882(x75051,a870)))+~P1(f333(f333(f335(x75051),x75053),x75052)) % 183.90/184.45 [7542]~P106(x75422)+E(x75421,f196(f882(x75422,a870)))+~P1(f333(f61(x75422),x75421))+~P1(f333(f333(f248(x75422),x75423),f488(x75423,x75421,x75422)))+P1(f333(f333(f248(x75422),x75423),f333(f63(x75422,f245(x75422)),x75421))) % 183.90/184.45 [7543]~P99(x75432)+E(x75431,f196(f882(x75432,a870)))+~P1(f333(f61(x75432),x75431))+~P1(f333(f333(f247(x75432),x75433),f346(x75433,x75431,x75432)))+P1(f333(f333(f247(x75432),x75433),f333(f63(x75432,f104(x75432)),x75431))) % 183.90/184.45 [7544]~P106(x75442)+E(x75441,f196(f882(x75442,a870)))+~P1(f333(f61(x75442),x75441))+~P1(f333(f333(f247(x75442),x75443),f489(x75443,x75441,x75442)))+P1(f333(f333(f247(x75442),x75443),f333(f63(x75442,f245(x75442)),x75441))) % 183.90/184.45 [7629]~P99(x76292)+E(x76291,f196(f882(x76292,a870)))+~P1(f333(f61(x76292),x76291))+P1(f333(f333(f335(x76292),f346(x76293,x76291,x76292)),x76291))+P1(f333(f333(f247(x76292),x76293),f333(f63(x76292,f104(x76292)),x76291))) % 183.90/184.45 [7630]~P106(x76302)+E(x76301,f196(f882(x76302,a870)))+~P1(f333(f61(x76302),x76301))+P1(f333(f333(f335(x76302),f489(x76303,x76301,x76302)),x76301))+P1(f333(f333(f247(x76302),x76303),f333(f63(x76302,f245(x76302)),x76301))) % 183.90/184.45 [7631]~P106(x76312)+E(x76311,f196(f882(x76312,a870)))+~P1(f333(f61(x76312),x76311))+P1(f333(f333(f335(x76312),f488(x76313,x76311,x76312)),x76311))+P1(f333(f333(f248(x76312),x76313),f333(f63(x76312,f245(x76312)),x76311))) % 183.90/184.45 [7756]~P106(x77562)+E(x77561,f196(f882(x77562,a870)))+E(f333(f333(f245(x77562),f11(x77562,f245(x77562),x77561)),f11(x77562,f245(x77562),x77563)),f11(x77562,f245(x77562),x77563))+~P1(f333(f61(x77562),x77563))+~P1(f333(f333(f247(f882(x77562,a870)),x77561),x77563)) % 183.90/184.45 [7757]~P106(x77572)+E(x77571,f196(f882(x77572,a870)))+E(f333(f333(f246(x77572),f12(x77572,f246(x77572),x77571)),f12(x77572,f246(x77572),x77573)),f12(x77572,f246(x77572),x77573))+~P1(f333(f61(x77572),x77573))+~P1(f333(f333(f247(f882(x77572,a870)),x77571),x77573)) % 183.90/184.45 [7958]~E(f848(x79581,x79583,x79582),f849(x79581,x79583,x79582))+~E(f333(f37(x79582),f850(x79581,x79583,x79582)),x79581)+E(f333(f333(f80(a875),x79581),f333(f37(f882(x79582,a870)),x79583)),f333(f37(x79582),f39(f882(x79582,a870),x79583)))+~P1(f333(f61(x79582),f39(f882(x79582,a870),x79583)))+~P1(f333(f61(f882(x79582,a870)),x79583)) % 183.90/184.45 [8143]~P106(x81432)+E(x81431,f196(f882(x81432,a870)))+~P1(f333(f61(x81432),x81433))+P1(f333(f333(f247(x81432),f333(f63(x81432,f245(x81432)),x81433)),f333(f63(x81432,f245(x81432)),x81431)))+~P1(f333(f333(f247(f882(x81432,a870)),x81431),x81433)) % 183.90/184.45 [8453]~E(f848(x84531,x84533,x84532),f849(x84531,x84533,x84532))+E(f333(f333(f80(a875),x84531),f333(f37(f882(x84532,a870)),x84533)),f333(f37(x84532),f39(f882(x84532,a870),x84533)))+P1(f333(f333(f335(f882(x84532,a870)),f850(x84531,x84533,x84532)),x84533))+~P1(f333(f61(x84532),f39(f882(x84532,a870),x84533)))+~P1(f333(f61(f882(x84532,a870)),x84533)) % 183.90/184.45 [8479]~E(f333(f37(x84792),f850(x84791,x84793,x84792)),x84791)+E(f333(f333(f80(a875),x84791),f333(f37(f882(x84792,a870)),x84793)),f333(f37(x84792),f39(f882(x84792,a870),x84793)))+P1(f333(f333(f335(f882(x84792,a870)),f849(x84791,x84793,x84792)),x84793))+~P1(f333(f61(x84792),f39(f882(x84792,a870),x84793)))+~P1(f333(f61(f882(x84792,a870)),x84793)) % 183.90/184.45 [8480]~E(f333(f37(x84802),f850(x84801,x84803,x84802)),x84801)+E(f333(f333(f80(a875),x84801),f333(f37(f882(x84802,a870)),x84803)),f333(f37(x84802),f39(f882(x84802,a870),x84803)))+P1(f333(f333(f335(f882(x84802,a870)),f848(x84801,x84803,x84802)),x84803))+~P1(f333(f61(x84802),f39(f882(x84802,a870),x84803)))+~P1(f333(f61(f882(x84802,a870)),x84803)) % 183.90/184.45 [8508]~E(f333(f37(x85082),f850(x85081,x85083,x85082)),x85081)+~E(f333(f333(f104(f882(x85082,a870)),f849(x85081,x85083,x85082)),f848(x85081,x85083,x85082)),f196(f882(x85082,a870)))+E(f333(f333(f80(a875),x85081),f333(f37(f882(x85082,a870)),x85083)),f333(f37(x85082),f39(f882(x85082,a870),x85083)))+~P1(f333(f61(f882(x85082,a870)),x85083))+~P1(f333(f61(x85082),f39(f882(x85082,a870),x85083))) % 183.90/184.45 [8749]E(f333(f333(f80(a875),x87491),f333(f37(f882(x87492,a870)),x87493)),f333(f37(x87492),f39(f882(x87492,a870),x87493)))+P1(f333(f333(f335(f882(x87492,a870)),f850(x87491,x87493,x87492)),x87493))+P1(f333(f333(f335(f882(x87492,a870)),f849(x87491,x87493,x87492)),x87493))+~P1(f333(f61(f882(x87492,a870)),x87493))+~P1(f333(f61(x87492),f39(f882(x87492,a870),x87493))) % 183.90/184.45 [8750]E(f333(f333(f80(a875),x87501),f333(f37(f882(x87502,a870)),x87503)),f333(f37(x87502),f39(f882(x87502,a870),x87503)))+P1(f333(f333(f335(f882(x87502,a870)),f850(x87501,x87503,x87502)),x87503))+P1(f333(f333(f335(f882(x87502,a870)),f848(x87501,x87503,x87502)),x87503))+~P1(f333(f61(f882(x87502,a870)),x87503))+~P1(f333(f61(x87502),f39(f882(x87502,a870),x87503))) % 183.90/184.45 [8775]~E(f333(f333(f104(f882(x87752,a870)),f849(x87751,x87753,x87752)),f848(x87751,x87753,x87752)),f196(f882(x87752,a870)))+E(f333(f333(f80(a875),x87751),f333(f37(f882(x87752,a870)),x87753)),f333(f37(x87752),f39(f882(x87752,a870),x87753)))+~P1(f333(f61(f882(x87752,a870)),x87753))+P1(f333(f333(f335(f882(x87752,a870)),f850(x87751,x87753,x87752)),x87753))+~P1(f333(f61(x87752),f39(f882(x87752,a870),x87753))) % 183.90/184.45 [9039]~P94(x90392)+E(x90391,f196(f882(x90392,a870)))+~E(f333(f333(f80(x90392),f333(x90393,f851(x90391,x90393,x90392))),f333(x90393,f858(x90391,x90393,x90392))),f333(x90393,f333(f333(f80(x90392),f851(x90391,x90393,x90392)),f858(x90391,x90393,x90392))))+~P1(f333(f61(x90392),x90391))+E(f333(f63(x90392,f80(x90392)),f333(f312(x90392,x90392,x90393),x90391)),f333(x90393,f333(f63(x90392,f80(x90392)),x90391))) % 183.90/184.45 [9963]P1(f333(f333(x99631,x99632),x99633))+P1(f333(f333(f248(a1),f545(x99631,x99633,x99632)),f546(x99631,x99633,x99632)))+P1(f333(f333(f247(a1),f546(x99631,x99633,x99632)),f2(a1)))+P1(f333(f333(x99631,f545(x99631,x99633,x99632)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f546(x99631,x99633,x99632))))+~P1(f333(f321(f881(a1,a1),a56),f333(f333(f268(a1,a1),x99632),x99633))) % 183.90/184.45 [9969]P1(f333(f333(x99691,x99692),x99693))+P1(f333(f333(f247(a1),f544(x99691,x99693,x99692)),f2(a1)))+P1(f333(f333(x99691,f537(x99691,x99693,x99692)),f333(f333(f80(a1),f333(f106(a1),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f544(x99691,x99693,x99692))))+P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),f537(x99691,x99693,x99692)),f544(x99691,x99693,x99692))))+~P1(f333(f321(f881(a1,a1),a51),f333(f333(f268(a1,a1),x99692),x99693))) % 183.90/184.45 [7929]~P114(x79291)+~P1(f333(f333(f247(x79291),x79292),f77(x79291)))+~P1(f333(f333(f247(x79291),f2(x79291)),x79292))+~P1(f333(f333(f247(x79291),f2(x79291)),x79293))+P1(f333(f333(f247(x79291),f333(f333(f80(x79291),x79292),x79293)),x79293)) % 183.90/184.45 [7930]~P114(x79301)+~P1(f333(f333(f247(x79301),x79303),f77(x79301)))+~P1(f333(f333(f247(x79301),f2(x79301)),x79303))+~P1(f333(f333(f247(x79301),f2(x79301)),x79302))+P1(f333(f333(f247(x79301),f333(f333(f80(x79301),x79302),x79303)),x79302)) % 183.90/184.45 [8294]~P106(x82942)+E(x82941,f196(f882(x82942,a870)))+~P1(f333(f61(x82942),x82941))+P1(f333(f333(f335(x82942),f497(x82943,x82941,x82942)),x82941))+~P1(f333(f333(f247(x82942),f333(f63(x82942,f245(x82942)),x82941)),x82943)) % 183.90/184.45 [8295]~P106(x82952)+E(x82951,f196(f882(x82952,a870)))+~P1(f333(f61(x82952),x82951))+P1(f333(f333(f335(x82952),f499(x82953,x82951,x82952)),x82951))+~P1(f333(f333(f248(x82952),f333(f63(x82952,f245(x82952)),x82951)),x82953)) % 183.90/184.45 [8296]~P106(x82962)+E(x82961,f196(f882(x82962,a870)))+~P1(f333(f61(x82962),x82961))+P1(f333(f333(f248(x82962),f499(x82963,x82961,x82962)),x82963))+~P1(f333(f333(f248(x82962),f333(f63(x82962,f245(x82962)),x82961)),x82963)) % 183.90/184.45 [8297]~P106(x82972)+E(x82971,f196(f882(x82972,a870)))+~P1(f333(f61(x82972),x82971))+P1(f333(f333(f247(x82972),f497(x82973,x82971,x82972)),x82973))+~P1(f333(f333(f247(x82972),f333(f63(x82972,f245(x82972)),x82971)),x82973)) % 183.90/184.45 [8381]~P1(f333(x83811,x83813))+P1(f333(x83811,f441(x83811,x83812)))+P1(f333(x83811,f434(x83811,x83812)))+~P1(f333(f333(f248(a1),f2(a1)),x83812))+P1(f333(x83811,f333(f333(f22(a1),f434(x83811,x83812)),f333(f333(f80(a1),f442(x83811,x83812)),x83812)))) % 183.90/184.45 [8602]~P1(f333(x86021,x86023))+P1(f333(x86021,f434(x86021,x86022)))+~P1(f333(f333(f248(a1),f2(a1)),x86022))+P1(f333(f333(f335(a1),f441(x86021,x86022)),f304(a1,f77(a1),x86022)))+P1(f333(x86021,f333(f333(f22(a1),f434(x86021,x86022)),f333(f333(f80(a1),f442(x86021,x86022)),x86022)))) % 183.90/184.45 [8797]~P1(f333(x87971,x87973))+~P1(f333(x87971,f434(x87971,x87972)))+P1(f333(x87971,f441(x87971,x87972)))+~P1(f333(f333(f248(a1),f2(a1)),x87972))+~P1(f333(x87971,f333(f333(f22(a1),f434(x87971,x87972)),f333(f333(f80(a1),f442(x87971,x87972)),x87972)))) % 183.90/184.45 [8924]~P1(f333(x89241,x89243))+~P1(f333(x89241,f434(x89241,x89242)))+~P1(f333(f333(f248(a1),f2(a1)),x89242))+P1(f333(f333(f335(a1),f441(x89241,x89242)),f304(a1,f77(a1),x89242)))+~P1(f333(x89241,f333(f333(f22(a1),f434(x89241,x89242)),f333(f333(f80(a1),f442(x89241,x89242)),x89242)))) % 183.90/184.45 [8709]~P62(x87091)+~P1(f333(f61(x87091),x87092))+E(f333(f333(f22(f882(x87091,a870)),x87092),f333(f333(f311(x87091),x87093),f196(f882(x87091,a870)))),f196(f882(x87091,a870)))+~P1(f333(f333(f335(x87091),x87093),x87092))+E(f333(f333(f113(x87091),x87093),f13(x87091,f333(f333(f22(f882(x87091,a870)),x87092),f333(f333(f311(x87091),x87093),f196(f882(x87091,a870)))))),f13(x87091,x87092)) % 183.90/184.45 [8710]~P62(x87101)+~P1(f333(f61(x87101),x87102))+E(f333(f333(f22(f882(x87101,a870)),x87102),f333(f333(f311(x87101),x87103),f196(f882(x87101,a870)))),f196(f882(x87101,a870)))+~P1(f333(f333(f335(x87101),x87103),x87102))+E(f333(f333(f104(x87101),x87103),f10(x87101,f333(f333(f22(f882(x87101,a870)),x87102),f333(f333(f311(x87101),x87103),f196(f882(x87101,a870)))))),f10(x87101,x87102)) % 183.90/184.45 [8711]~P106(x87111)+~P1(f333(f61(x87111),x87112))+E(f333(f333(f22(f882(x87111,a870)),x87112),f333(f333(f311(x87111),x87113),f196(f882(x87111,a870)))),f196(f882(x87111,a870)))+~P1(f333(f333(f335(x87111),x87113),x87112))+E(f333(f333(f245(x87111),x87113),f14(x87111,f333(f333(f22(f882(x87111,a870)),x87112),f333(f333(f311(x87111),x87113),f196(f882(x87111,a870)))))),f14(x87111,x87112)) % 183.90/184.45 [8712]~P106(x87121)+~P1(f333(f61(x87121),x87122))+E(f333(f333(f22(f882(x87121,a870)),x87122),f333(f333(f311(x87121),x87123),f196(f882(x87121,a870)))),f196(f882(x87121,a870)))+~P1(f333(f333(f335(x87121),x87123),x87122))+E(f333(f333(f246(x87121),x87123),f15(x87121,f333(f333(f22(f882(x87121,a870)),x87122),f333(f333(f311(x87121),x87123),f196(f882(x87121,a870)))))),f15(x87121,x87122)) % 183.90/184.45 [8769]~P106(x87691)+~P1(f333(f61(x87691),x87692))+E(f333(f333(f22(f882(x87691,a870)),x87692),f333(f333(f311(x87691),x87693),f196(f882(x87691,a870)))),f196(f882(x87691,a870)))+~P1(f333(f333(f335(x87691),x87693),x87692))+E(f333(f333(f245(x87691),x87693),f11(x87691,f245(x87691),f333(f333(f22(f882(x87691,a870)),x87692),f333(f333(f311(x87691),x87693),f196(f882(x87691,a870)))))),f11(x87691,f245(x87691),x87692)) % 183.90/184.45 [8770]~P106(x87701)+~P1(f333(f61(x87701),x87702))+E(f333(f333(f22(f882(x87701,a870)),x87702),f333(f333(f311(x87701),x87703),f196(f882(x87701,a870)))),f196(f882(x87701,a870)))+~P1(f333(f333(f335(x87701),x87703),x87702))+E(f333(f333(f246(x87701),x87703),f12(x87701,f246(x87701),f333(f333(f22(f882(x87701,a870)),x87702),f333(f333(f311(x87701),x87703),f196(f882(x87701,a870)))))),f12(x87701,f246(x87701),x87702)) % 183.90/184.45 [8784]~P62(x87841)+~P1(f333(f61(x87841),x87843))+~P1(f333(f61(x87841),x87842))+E(f333(f333(f104(f882(x87841,a870)),x87842),x87843),f196(f882(x87841,a870)))+E(f333(f333(f113(x87841),f13(x87841,f333(f333(f113(f882(x87841,a870)),x87842),x87843))),f13(x87841,f333(f333(f104(f882(x87841,a870)),x87842),x87843))),f333(f333(f113(x87841),f13(x87841,x87842)),f13(x87841,x87843))) % 183.90/184.45 [8785]~P62(x87851)+~P1(f333(f61(x87851),x87853))+~P1(f333(f61(x87851),x87852))+E(f333(f333(f104(f882(x87851,a870)),x87852),x87853),f196(f882(x87851,a870)))+E(f333(f333(f104(x87851),f10(x87851,f333(f333(f113(f882(x87851,a870)),x87852),x87853))),f10(x87851,f333(f333(f104(f882(x87851,a870)),x87852),x87853))),f333(f333(f104(x87851),f10(x87851,x87852)),f10(x87851,x87853))) % 183.90/184.45 [8786]~P106(x87861)+~P1(f333(f61(x87861),x87863))+~P1(f333(f61(x87861),x87862))+E(f333(f333(f104(f882(x87861,a870)),x87862),x87863),f196(f882(x87861,a870)))+E(f333(f333(f245(x87861),f14(x87861,f333(f333(f113(f882(x87861,a870)),x87862),x87863))),f14(x87861,f333(f333(f104(f882(x87861,a870)),x87862),x87863))),f333(f333(f245(x87861),f14(x87861,x87862)),f14(x87861,x87863))) % 183.90/184.45 [8787]~P106(x87871)+~P1(f333(f61(x87871),x87873))+~P1(f333(f61(x87871),x87872))+E(f333(f333(f104(f882(x87871,a870)),x87872),x87873),f196(f882(x87871,a870)))+E(f333(f333(f246(x87871),f15(x87871,f333(f333(f113(f882(x87871,a870)),x87872),x87873))),f15(x87871,f333(f333(f104(f882(x87871,a870)),x87872),x87873))),f333(f333(f246(x87871),f15(x87871,x87872)),f15(x87871,x87873))) % 183.90/184.45 [9011]~P106(x90111)+~P1(f333(f61(x90111),x90113))+~P1(f333(f61(x90111),x90112))+E(f333(f333(f104(f882(x90111,a870)),x90112),x90113),f196(f882(x90111,a870)))+E(f333(f333(f245(x90111),f11(x90111,f245(x90111),f333(f333(f113(f882(x90111,a870)),x90112),x90113))),f11(x90111,f245(x90111),f333(f333(f104(f882(x90111,a870)),x90112),x90113))),f333(f333(f245(x90111),f11(x90111,f245(x90111),x90112)),f11(x90111,f245(x90111),x90113))) % 183.90/184.45 [9012]~P106(x90121)+~P1(f333(f61(x90121),x90123))+~P1(f333(f61(x90121),x90122))+E(f333(f333(f104(f882(x90121,a870)),x90122),x90123),f196(f882(x90121,a870)))+E(f333(f333(f246(x90121),f12(x90121,f246(x90121),f333(f333(f113(f882(x90121,a870)),x90122),x90123))),f12(x90121,f246(x90121),f333(f333(f104(f882(x90121,a870)),x90122),x90123))),f333(f333(f246(x90121),f12(x90121,f246(x90121),x90122)),f12(x90121,f246(x90121),x90123))) % 183.90/184.45 [9803]~P120(x98033)+E(x98031,x98032)+~P1(f333(f333(f247(x98033),f2(x98033)),x98032))+~P1(f333(f333(f247(x98033),f2(x98033)),x98031))+~E(f333(f333(f258(x98033),x98031),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)))),f333(f333(f258(x98033),x98032),f333(f106(a875),f333(f333(f79(a1),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100)),f333(f333(f22(a1),f333(f333(f79(a1),a82),a82)),a100))))) % 183.90/184.45 [6321]E(f359(x63211,x63212,x63213),x63214)+E(f333(x63211,x63214),f2(a875))+~E(f333(f333(f6(x63213,a875),x63211),x63212),f77(a875))+~P1(f333(f61(x63213),x63212))+~P1(f333(f333(f335(x63213),x63214),x63212)) % 183.90/184.45 [6383]E(f361(x63831,x63832,x63833),x63834)+E(f333(x63831,x63834),f2(a875))+~E(f333(f333(f6(x63833,a875),x63831),x63832),f333(a115,f2(a875)))+~P1(f333(f61(x63833),x63832))+~P1(f333(f333(f335(x63833),x63834),x63832)) % 183.90/184.45 [6488]~P4(x64881)+~P106(x64881)+P1(f333(f333(f248(x64881),x64882),f39(x64881,x64883)))+~P1(f333(f333(f248(x64881),x64882),x64884))+~P1(f333(f333(f335(x64881),x64884),x64883)) % 183.90/184.45 [6661]~P4(x66611)+~P106(x66611)+~P1(f333(f333(f248(x66611),x66614),x66613))+P1(f333(f333(f248(x66611),f40(x66611,x66612)),x66613))+~P1(f333(f333(f335(x66611),x66614),x66612)) % 183.90/184.45 [6921]~P120(x69213)+E(x69211,x69212)+~E(f333(f333(f258(x69213),x69211),f333(a115,x69214)),f333(f333(f258(x69213),x69212),f333(a115,x69214)))+~P1(f333(f333(f247(x69213),f2(x69213)),x69212))+~P1(f333(f333(f247(x69213),f2(x69213)),x69211)) % 183.90/184.45 [7132]~E(f367(x71322,x71323,x71321,x71324),x71324)+~E(f333(x71322,x71324),f77(a875))+E(f333(f333(f6(x71321,a875),x71322),x71323),f77(a875))+~P1(f333(f61(x71321),x71323))+~P1(f333(f333(f335(x71321),x71324),x71323)) % 183.90/184.45 [7139]~P109(x71394)+~P129(x71394)+E(f333(x71391,f357(x71391,x71392,x71393,x71394)),f2(x71394))+~E(f333(f333(f9(x71393,x71394),x71391),x71392),f2(x71394))+~P1(f333(f61(x71393),x71392)) % 183.90/184.45 [7225]~E(f364(x72252,x72253,x72251,x72254),x72254)+~E(f333(x72252,x72254),f333(a115,f2(a875)))+E(f333(f333(f6(x72251,a875),x72252),x72253),f333(a115,f2(a875)))+~P1(f333(f61(x72251),x72253))+~P1(f333(f333(f335(x72251),x72254),x72253)) % 183.90/184.45 [7970]~E(f333(x79702,x79704),f77(a875))+~E(f333(x79702,f367(x79702,x79703,x79701,x79704)),f2(a875))+E(f333(f333(f6(x79701,a875),x79702),x79703),f77(a875))+~P1(f333(f61(x79701),x79703))+~P1(f333(f333(f335(x79701),x79704),x79703)) % 183.90/184.45 [8014]~E(f333(x80142,x80144),f333(a115,f2(a875)))+~E(f333(x80142,f364(x80142,x80143,x80141,x80144)),f2(a875))+E(f333(f333(f6(x80141,a875),x80142),x80143),f333(a115,f2(a875)))+~P1(f333(f61(x80141),x80143))+~P1(f333(f333(f335(x80141),x80144),x80143)) % 183.90/184.45 [8572]~P106(x85721)+~P14(x85721,x85724)+P14(x85721,x85722)+~E(x85722,f333(f333(f152(x85721),x85723),x85724))+~P1(f333(f333(f247(x85721),x85723),f763(x85722,x85721,x85724,x85723))) % 183.90/184.45 [8606]E(x86061,x86062)+E(f333(f333(f22(a1),f421(x86063,x86062,x86064,x86061)),f422(x86063,x86062,x86064,x86061)),x86061)+~E(f333(f333(f79(a1),x86061),x86064),x86062)+~P1(f333(f333(f248(a1),f2(a1)),x86064))+~P1(f333(f333(f335(a1),x86062),x86063)) % 183.90/184.45 [8607]E(x86071,x86072)+E(f333(f333(f79(a1),f428(x86073,x86072,x86074,x86071)),f429(x86073,x86072,x86074,x86071)),x86071)+~E(f333(f333(f22(a1),x86071),x86074),x86072)+~P1(f333(f333(f248(a1),f2(a1)),x86074))+~P1(f333(f333(f335(a1),x86072),x86073)) % 183.90/184.45 [8782]E(f333(x87821,f651(x87822,x87821,x87823,x87824)),x87822)+P1(f333(f333(f247(a875),x87824),f652(x87822,x87821,x87823,x87824)))+~P1(f333(f333(f247(a1),x87822),f333(x87821,x87823)))+~P1(f333(f333(f248(a875),x87824),x87823))+~P1(f333(f333(f247(a1),f333(x87821,x87824)),x87822)) % 183.90/184.45 [8783]~P106(x87831)+~P14(x87831,x87833)+P14(x87831,x87832)+~E(x87832,f333(f333(f152(x87831),x87834),x87833))+P1(f333(f333(f335(x87831),f763(x87832,x87831,x87833,x87834)),f333(f174(x87831),x87833))) % 183.90/184.45 [8801]~P109(x88014)+~P129(x88014)+~E(f333(f333(f9(x88011,x88014),x88012),x88013),f2(x88014))+~P1(f333(f61(x88011),x88013))+P1(f333(f333(f335(x88011),f357(x88012,x88013,x88011,x88014)),x88013)) % 183.90/184.45 [8836]~E(f333(x88362,x88364),f77(a875))+E(f333(f333(f6(x88361,a875),x88362),x88363),f77(a875))+~P1(f333(f61(x88361),x88363))+~P1(f333(f333(f335(x88361),x88364),x88363))+P1(f333(f333(f335(x88361),f367(x88362,x88363,x88361,x88364)),x88363)) % 183.90/184.45 [8845]E(x88451,x88452)+~E(f333(f333(f79(a1),x88452),x88454),x88451)+~P1(f333(f333(f248(a1),f2(a1)),x88454))+~P1(f333(f333(f335(a1),x88451),x88453))+P1(f333(f333(f335(a1),f421(x88453,x88451,x88454,x88452)),x88453)) % 183.90/184.45 [8846]E(x88461,x88462)+~E(f333(f333(f22(a1),x88462),x88464),x88461)+~P1(f333(f333(f248(a1),f2(a1)),x88464))+~P1(f333(f333(f335(a1),x88461),x88463))+P1(f333(f333(f335(a1),f428(x88463,x88461,x88464,x88462)),x88463)) % 183.90/184.45 [8848]~E(f333(x88482,x88484),f333(a115,f2(a875)))+E(f333(f333(f6(x88481,a875),x88482),x88483),f333(a115,f2(a875)))+~P1(f333(f61(x88481),x88483))+~P1(f333(f333(f335(x88481),x88484),x88483))+P1(f333(f333(f335(x88481),f364(x88482,x88483,x88481,x88484)),x88483)) % 183.90/184.45 [8853]P53(x88532,x88533,x88534,x88531)+E(x88531,f196(f882(x88532,a870)))+~P1(f333(f61(x88532),x88534))+~P1(f333(f61(x88532),x88531))+P1(f333(f333(f335(x88532),f560(x88531,x88534,x88533,x88532)),x88534)) % 183.90/184.45 [8938]E(x89381,x89382)+~E(f333(f333(f79(a1),x89382),x89384),x89381)+~P1(f333(f333(f248(a1),f2(a1)),x89384))+~P1(f333(f333(f335(a1),x89381),x89383))+P1(f333(f333(f335(a1),f422(x89383,x89381,x89384,x89382)),f304(a1,f77(a1),x89384))) % 183.90/184.45 [8939]E(x89391,x89392)+~E(f333(f333(f22(a1),x89392),x89394),x89391)+~P1(f333(f333(f248(a1),f2(a1)),x89394))+~P1(f333(f333(f335(a1),x89391),x89393))+P1(f333(f333(f335(a1),f429(x89393,x89391,x89394,x89392)),f304(a1,f77(a1),x89394))) % 183.90/184.45 [9017]P1(f333(f333(f247(a875),x90171),f651(x90172,x90173,x90174,x90171)))+~P1(f333(f333(f247(a1),x90172),f333(x90173,x90174)))+P1(f333(f333(f247(a875),x90171),f652(x90172,x90173,x90174,x90171)))+~P1(f333(f333(f248(a875),x90171),x90174))+~P1(f333(f333(f247(a1),f333(x90173,x90171)),x90172)) % 183.90/184.45 [9127]E(f333(x91271,f651(x91272,x91271,x91273,x91274)),x91272)+~P1(f333(f333(f247(a1),x91272),f333(x91271,x91273)))+P1(f333(f333(f248(a875),f652(x91272,x91271,x91273,x91274)),x91273))+~P1(f333(f333(f248(a875),x91274),x91273))+~P1(f333(f333(f247(a1),f333(x91271,x91274)),x91272)) % 183.90/184.45 [9258]~P1(f333(f333(f247(a1),x92582),f333(x92583,x92584)))+P1(f333(f333(f247(a875),x92581),f652(x92582,x92583,x92584,x92581)))+P1(f333(f333(f247(a875),f651(x92582,x92583,x92584,x92581)),x92584))+~P1(f333(f333(f248(a875),x92581),x92584))+~P1(f333(f333(f247(a1),f333(x92583,x92581)),x92582)) % 183.90/184.45 [9259]~P1(f333(f333(f247(a1),x92592),f333(x92593,x92594)))+P1(f333(f333(f247(a875),x92591),f651(x92592,x92593,x92594,x92591)))+P1(f333(f333(f248(a875),f652(x92592,x92593,x92594,x92591)),x92594))+~P1(f333(f333(f248(a875),x92591),x92594))+~P1(f333(f333(f247(a1),f333(x92593,x92591)),x92592)) % 183.90/184.45 [9366]~P1(f333(f333(f247(a1),x93661),f333(x93662,x93663)))+P1(f333(f333(f247(a875),f651(x93661,x93662,x93663,x93664)),x93663))+~P1(f333(f333(f248(a875),x93664),x93663))+~P1(f333(f333(f247(a1),f333(x93662,x93664)),x93661))+P1(f333(f333(f248(a875),f652(x93661,x93662,x93663,x93664)),x93663)) % 183.90/184.45 [9444]E(x94441,f196(f882(x94442,a870)))+~P1(f333(f61(x94442),x94444))+~P1(f333(f61(x94442),x94441))+P1(f333(f333(f335(f881(f882(x94442,a870),f882(x94442,a870))),f333(f333(f268(f882(x94442,a870),f882(x94442,a870)),x94444),x94441)),f325(x94442,x94443)))+P1(f333(f333(f335(x94442),f568(x94443,x94441,x94444,x94442)),x94444)) % 183.90/184.45 [9445]E(x94451,f196(f882(x94452,a870)))+~P1(f333(f61(x94452),x94454))+~P1(f333(f61(x94452),x94451))+P1(f333(f333(f335(f881(f882(x94452,a870),f882(x94452,a870))),f333(f333(f268(f882(x94452,a870),f882(x94452,a870)),x94454),x94451)),f325(x94452,x94453)))+P1(f333(f333(f335(x94452),f621(x94453,x94451,x94454,x94452)),x94454)) % 183.90/184.45 [10106]E(f333(x101061,f651(x101062,x101061,x101063,x101064)),x101062)+~P1(f333(f333(f247(a1),x101062),f333(x101061,x101063)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x101061,f333(f333(f79(a875),f652(x101062,x101061,x101063,x101064)),f77(a875)))),f333(x101061,f652(x101062,x101061,x101063,x101064))))),f77(a1)))+~P1(f333(f333(f248(a875),x101064),x101063))+~P1(f333(f333(f247(a1),f333(x101061,x101064)),x101062)) % 183.90/184.45 [10107]~P1(f333(f333(f247(a1),x101072),f333(x101073,x101074)))+P1(f333(f333(f247(a875),x101071),f651(x101072,x101073,x101074,x101071)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x101073,f333(f333(f79(a875),f652(x101072,x101073,x101074,x101071)),f77(a875)))),f333(x101073,f652(x101072,x101073,x101074,x101071))))),f77(a1)))+~P1(f333(f333(f248(a875),x101071),x101074))+~P1(f333(f333(f247(a1),f333(x101073,x101071)),x101072)) % 183.90/184.45 [10108]~P1(f333(f333(f247(a1),x101081),f333(x101082,x101083)))+~P1(f333(f333(f247(a1),f333(f74(a1),f333(f333(f22(a1),f333(x101082,f333(f333(f79(a875),f652(x101081,x101082,x101083,x101084)),f77(a875)))),f333(x101082,f652(x101081,x101082,x101083,x101084))))),f77(a1)))+~P1(f333(f333(f248(a875),x101084),x101083))+~P1(f333(f333(f247(a1),f333(x101082,x101084)),x101081))+P1(f333(f333(f247(a875),f651(x101081,x101082,x101083,x101084)),x101083)) % 183.90/184.45 [7192]~P60(x71921)+P1(f333(f333(f248(x71921),x71922),f2(x71921)))+~P1(f333(f333(f248(x71921),x71923),f2(x71921)))+P1(f333(f333(f248(x71921),f2(x71921)),x71922))+P1(f333(f333(f248(x71921),x71923),f333(f333(f291(x71921),x71924),x71922))) % 183.90/184.45 [7193]~P60(x71931)+P1(f333(f333(f248(x71931),x71932),f2(x71931)))+~P1(f333(f333(f247(x71931),x71933),f2(x71931)))+P1(f333(f333(f248(x71931),f2(x71931)),x71932))+P1(f333(f333(f247(x71931),x71933),f333(f333(f291(x71931),x71934),x71932))) % 183.90/184.45 [7442]~P60(x74421)+P1(f333(f333(f248(x74421),x74422),f2(x74421)))+P1(f333(f333(f248(x74421),x74423),f2(x74421)))+P1(f333(f333(f248(x74421),f2(x74421)),x74423))+~P1(f333(f333(f248(x74421),x74422),f333(f333(f291(x74421),x74424),x74423))) % 183.90/184.45 [7443]~P60(x74431)+P1(f333(f333(f248(x74431),x74432),f2(x74431)))+P1(f333(f333(f247(x74431),x74433),f2(x74431)))+P1(f333(f333(f248(x74431),f2(x74431)),x74432))+~P1(f333(f333(f247(x74431),x74433),f333(f333(f291(x74431),x74434),x74432))) % 183.90/184.45 [7562]E(x75621,x75622)+~E(f333(f333(f166(x75623),x75624),x75621),f333(f333(f166(x75623),x75624),x75622))+~P1(f333(f138(x75623),x75624))+~P1(f333(f333(f248(a875),x75622),f333(f197(f876(x75623)),x75624)))+~P1(f333(f333(f248(a875),x75621),f333(f197(f876(x75623)),x75624))) % 183.90/184.45 [7931]~P60(x79311)+~P1(f333(f333(f248(x79311),x79313),f2(x79311)))+P1(f333(f333(f248(x79311),f2(x79311)),x79312))+~P1(f333(f333(f248(x79311),x79314),f333(f333(f80(x79311),x79313),x79312)))+P1(f333(f333(f248(x79311),x79313),f333(f333(f291(x79311),x79314),x79312))) % 183.90/184.45 [7932]~P60(x79321)+~P1(f333(f333(f247(x79321),x79323),f2(x79321)))+P1(f333(f333(f248(x79321),f2(x79321)),x79322))+~P1(f333(f333(f247(x79321),x79324),f333(f333(f80(x79321),x79323),x79322)))+P1(f333(f333(f247(x79321),x79323),f333(f333(f291(x79321),x79324),x79322))) % 183.90/184.45 [7933]~P60(x79331)+~P1(f333(f333(f248(x79331),x79332),f2(x79331)))+P1(f333(f333(f248(x79331),f2(x79331)),x79332))+~P1(f333(f333(f248(x79331),x79334),f333(f333(f80(x79331),x79333),x79332)))+P1(f333(f333(f248(x79331),x79333),f333(f333(f291(x79331),x79334),x79332))) % 183.90/184.45 [7934]~P60(x79341)+~P1(f333(f333(f248(x79341),x79342),f2(x79341)))+P1(f333(f333(f248(x79341),f2(x79341)),x79342))+~P1(f333(f333(f248(x79341),x79344),f333(f333(f291(x79341),x79343),x79342)))+P1(f333(f333(f248(x79341),x79343),f333(f333(f80(x79341),x79344),x79342))) % 183.90/184.45 [7935]~P60(x79351)+~P1(f333(f333(f248(x79351),x79352),f2(x79351)))+P1(f333(f333(f248(x79351),f2(x79351)),x79352))+~P1(f333(f333(f247(x79351),x79354),f333(f333(f80(x79351),x79353),x79352)))+P1(f333(f333(f247(x79351),x79353),f333(f333(f291(x79351),x79354),x79352))) % 183.90/184.45 [7936]~P60(x79361)+~P1(f333(f333(f248(x79361),x79362),f2(x79361)))+P1(f333(f333(f248(x79361),f2(x79361)),x79362))+~P1(f333(f333(f247(x79361),x79364),f333(f333(f291(x79361),x79363),x79362)))+P1(f333(f333(f247(x79361),x79363),f333(f333(f80(x79361),x79364),x79362))) % 183.90/184.45 [8082]~P106(x80821)+~P14(x80821,x80822)+~P1(f333(f333(f247(a875),x80823),x80824))+P1(f333(f333(f247(x80821),f333(f333(f166(x80821),x80822),x80823)),f333(f333(f166(x80821),x80822),x80824)))+~P1(f333(f333(f248(a875),x80824),f333(f197(f876(x80821)),x80822))) % 183.90/184.45 [8133]~P120(x81331)+~P1(f333(f333(f248(x81331),x81332),f77(x81331)))+~P1(f333(f333(f248(x81331),f2(x81331)),x81332))+~P1(f333(f333(f248(a875),x81334),x81333))+P1(f333(f333(f248(x81331),f333(f333(f258(x81331),x81332),x81333)),f333(f333(f258(x81331),x81332),x81334))) % 183.90/184.45 [8134]~P120(x81341)+~P1(f333(f333(f247(x81341),x81342),f77(x81341)))+~P1(f333(f333(f247(x81341),f2(x81341)),x81342))+~P1(f333(f333(f247(a875),x81344),x81343))+P1(f333(f333(f247(x81341),f333(f333(f258(x81341),x81342),x81343)),f333(f333(f258(x81341),x81342),x81344))) % 183.90/184.45 [8135]~P120(x81351)+~P1(f333(f333(f247(x81351),f2(x81351)),x81352))+~P1(f333(f333(f248(a875),f2(a875)),x81353))+~P1(f333(f333(f248(x81351),x81352),x81354))+P1(f333(f333(f248(x81351),f333(f333(f258(x81351),x81352),x81353)),f333(f333(f258(x81351),x81354),x81353))) % 183.90/184.45 [8156]~P106(x81561)+~P14(x81561,f333(f170(x81561),x81562))+~P1(f333(f333(f247(a875),x81564),x81563))+P1(f333(f333(f247(x81561),f333(f333(f166(x81561),x81562),x81563)),f333(f333(f166(x81561),x81562),x81564)))+~P1(f333(f333(f248(a875),x81563),f333(f197(f876(x81561)),x81562))) % 183.90/184.45 [8404]~P61(x84041)+~P1(f333(f333(f248(x84041),x84042),f2(x84041)))+~P1(f333(f333(f248(x84041),x84043),x84044))+~P1(f333(f333(f248(x84041),f2(x84041)),f333(f333(f80(x84041),x84043),x84044)))+P1(f333(f333(f248(x84041),f333(f333(f291(x84041),x84042),x84043)),f333(f333(f291(x84041),x84042),x84044))) % 183.90/184.45 [8405]~P60(x84051)+~P1(f333(f333(f247(x84051),x84052),f2(x84051)))+~P1(f333(f333(f247(x84051),x84053),x84054))+~P1(f333(f333(f248(x84051),f2(x84051)),f333(f333(f80(x84051),x84053),x84054)))+P1(f333(f333(f247(x84051),f333(f333(f291(x84051),x84052),x84053)),f333(f333(f291(x84051),x84052),x84054))) % 183.90/184.45 [8415]~P61(x84151)+~P1(f333(f333(f248(x84151),x84154),x84153))+~P1(f333(f333(f248(x84151),f2(x84151)),x84152))+~P1(f333(f333(f248(x84151),f2(x84151)),f333(f333(f80(x84151),x84153),x84154)))+P1(f333(f333(f248(x84151),f333(f333(f291(x84151),x84152),x84153)),f333(f333(f291(x84151),x84152),x84154))) % 183.90/184.45 [8416]~P61(x84161)+~P1(f333(f333(f247(x84161),x84164),x84163))+~P1(f333(f333(f247(x84161),f2(x84161)),x84162))+~P1(f333(f333(f248(x84161),f2(x84161)),f333(f333(f80(x84161),x84163),x84164)))+P1(f333(f333(f247(x84161),f333(f333(f291(x84161),x84162),x84163)),f333(f333(f291(x84161),x84162),x84164))) % 183.90/184.45 [8523]P1(f333(x85231,x85232))+~P1(f333(f61(x85234),x85232))+P1(f333(x85231,f456(x85231,x85233,x85232,x85234)))+~P1(f333(x85231,f196(f882(x85234,a870))))+~P1(f333(f333(f247(f882(x85234,a870)),x85232),x85233)) % 183.90/184.45 [8531]P1(f333(x85311,x85312))+P1(f333(f61(x85313),f456(x85311,x85314,x85312,x85313)))+~P1(f333(f61(x85313),x85312))+~P1(f333(x85311,f196(f882(x85313,a870))))+~P1(f333(f333(f247(f882(x85313,a870)),x85312),x85314)) % 183.90/184.45 [8777]E(f333(f333(f79(a1),f430(x87771,x87772,x87773,x87774)),f431(x87771,x87772,x87773,x87774)),x87774)+~P1(f333(f333(f248(a1),f2(a1)),x87773))+~P1(f333(f333(f248(a1),x87772),x87774))+~P1(f333(f333(f335(a1),x87772),x87771))+P1(f333(f333(f248(a1),x87772),f333(f333(f22(a1),x87774),x87773))) % 183.90/184.45 [8998]~P1(f333(f333(f248(a1),f2(a1)),x89983))+~P1(f333(f333(f248(a1),x89982),x89984))+~P1(f333(f333(f335(a1),x89982),x89981))+P1(f333(f333(f335(a1),f430(x89981,x89982,x89983,x89984)),x89981))+P1(f333(f333(f248(a1),x89982),f333(f333(f22(a1),x89984),x89983))) % 183.90/184.45 [9010]P1(f333(x90101,x90102))+~P1(f333(f61(x90103),x90102))+P1(f333(f333(f335(x90103),f457(x90101,x90104,x90102,x90103)),x90104))+~P1(f333(x90101,f196(f882(x90103,a870))))+~P1(f333(f333(f247(f882(x90103,a870)),x90102),x90104)) % 183.90/184.45 [9027]E(f333(f333(f79(a1),f423(x90271,x90272,x90273,x90274)),f424(x90271,x90272,x90273,x90274)),x90274)+~P1(f333(f333(f248(a1),f2(a1)),x90273))+~P1(f333(f333(f247(a1),x90272),x90274))+P1(f333(f333(f247(a1),x90272),f333(f333(f22(a1),x90274),x90273)))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x90272),f77(a1))),x90271)) % 183.90/184.45 [9079]~P1(f333(f333(f248(a1),f2(a1)),x90793))+~P1(f333(f333(f248(a1),x90791),x90792))+~P1(f333(f333(f335(a1),x90791),x90794))+P1(f333(f333(f335(a1),f431(x90794,x90791,x90793,x90792)),f304(a1,f77(a1),x90793)))+P1(f333(f333(f248(a1),x90791),f333(f333(f22(a1),x90792),x90793))) % 183.90/184.45 [9174]~P1(f333(f333(f248(a1),f2(a1)),x91743))+~P1(f333(f333(f247(a1),x91742),x91744))+P1(f333(f333(f335(a1),f423(x91741,x91742,x91743,x91744)),x91741))+P1(f333(f333(f247(a1),x91742),f333(f333(f22(a1),x91744),x91743)))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x91742),f77(a1))),x91741)) % 183.90/184.45 [9214]~P1(f333(f333(f248(a1),f2(a1)),x92143))+~P1(f333(f333(f247(a1),x92141),x92142))+P1(f333(f333(f335(a1),f424(x92144,x92141,x92143,x92142)),f304(a1,f77(a1),x92143)))+P1(f333(f333(f247(a1),x92141),f333(f333(f22(a1),x92142),x92143)))+~P1(f333(f333(f335(a1),f333(f333(f22(a1),x92141),f77(a1))),x92144)) % 183.90/184.45 [9447]P1(f333(x94471,x94472))+~P1(f333(f333(f335(x94473),f457(x94471,x94474,x94472,x94473)),f456(x94471,x94474,x94472,x94473)))+~P1(f333(f61(x94473),x94472))+~P1(f333(x94471,f196(f882(x94473,a870))))+~P1(f333(f333(f247(f882(x94473,a870)),x94472),x94474)) % 183.90/184.45 [9663]P1(f333(x96631,x96632))+~P1(f333(f61(x96633),x96632))+~P1(f333(x96631,f333(f333(f311(x96633),f457(x96631,x96634,x96632,x96633)),f456(x96631,x96634,x96632,x96633))))+~P1(f333(x96631,f196(f882(x96633,a870))))+~P1(f333(f333(f247(f882(x96633,a870)),x96632),x96634)) % 183.90/184.45 [7700]~P60(x77001)+P1(f333(f333(f248(x77001),x77002),f2(x77001)))+P1(f333(f333(f248(x77001),f2(x77001)),x77002))+~P1(f333(f333(f248(x77001),f2(x77001)),x77004))+P1(f333(f333(f248(x77001),f333(f333(f291(x77001),x77003),x77002)),x77004)) % 183.90/184.45 [7701]~P60(x77011)+P1(f333(f333(f248(x77011),x77012),f2(x77011)))+~P1(f333(f333(f247(x77011),f2(x77011)),x77014))+P1(f333(f333(f248(x77011),f2(x77011)),x77012))+P1(f333(f333(f247(x77011),f333(f333(f291(x77011),x77013),x77012)),x77014)) % 183.90/184.45 [7986]~P1(f333(f333(f247(a1),x79864),f2(a1)))+~E(x79862,f333(f333(f79(a1),f333(f333(f80(a1),x79861),x79863)),x79864))+P1(f333(f333(f248(a1),f2(a1)),x79861))+~P1(f333(f333(f248(a1),x79861),x79864))+P1(f333(f48(x79862,x79861),f333(f333(f268(a1,a1),x79863),x79864))) % 183.90/184.45 [8025]~P1(f333(x80251,x80254))+P1(f333(x80251,f414(x80252,x80251,x80253)))+~P1(f333(f333(f248(a1),f2(a1)),x80253))+~P1(f333(f333(f247(a1),f2(a1)),x80252))+P1(f333(x80251,f333(f333(f22(a1),x80254),f333(f333(f80(a1),x80252),x80253)))) % 183.90/184.45 [8026]~P1(f333(x80261,x80264))+P1(f333(x80261,f417(x80262,x80261,x80263)))+~P1(f333(f333(f248(a1),f2(a1)),x80263))+~P1(f333(f333(f247(a1),f2(a1)),x80262))+P1(f333(x80261,f333(f333(f79(a1),x80264),f333(f333(f80(a1),x80262),x80263)))) % 183.90/184.45 [8027]~P60(x80271)+P1(f333(f333(f248(x80271),x80272),f2(x80271)))+P1(f333(f333(f248(x80271),f2(x80271)),x80272))+P1(f333(f333(f248(x80271),f2(x80271)),x80273))+~P1(f333(f333(f248(x80271),f333(f333(f291(x80271),x80274),x80272)),x80273)) % 183.90/184.45 [8028]~P60(x80281)+P1(f333(f333(f248(x80281),x80282),f2(x80281)))+P1(f333(f333(f248(x80281),f2(x80281)),x80282))+P1(f333(f333(f247(x80281),f2(x80281)),x80283))+~P1(f333(f333(f247(x80281),f333(f333(f291(x80281),x80284),x80282)),x80283)) % 183.90/184.45 [8076]~E(x80761,f333(f333(f79(a1),f333(f333(f80(a1),x80762),x80763)),x80764))+~P1(f333(f333(f248(a1),f2(a1)),x80762))+~P1(f333(f333(f247(a1),f2(a1)),x80764))+~P1(f333(f333(f248(a1),x80764),x80762))+P1(f333(f48(x80761,x80762),f333(f333(f268(a1,a1),x80763),x80764))) % 183.90/184.45 [8200]~P60(x82001)+P1(f333(f333(f248(x82001),x82002),f2(x82001)))+~P1(f333(f333(f248(x82001),f2(x82001)),x82004))+~P1(f333(f333(f248(x82001),x82003),f333(f333(f80(x82001),x82004),x82002)))+P1(f333(f333(f248(x82001),f333(f333(f291(x82001),x82003),x82002)),x82004)) % 183.90/184.45 [8201]~P60(x82011)+P1(f333(f333(f248(x82011),x82012),f2(x82011)))+~P1(f333(f333(f247(x82011),f2(x82011)),x82014))+~P1(f333(f333(f247(x82011),x82013),f333(f333(f80(x82011),x82014),x82012)))+P1(f333(f333(f247(x82011),f333(f333(f291(x82011),x82013),x82012)),x82014)) % 183.90/184.45 [8282]~P60(x82821)+P1(f333(f333(f248(x82821),x82822),f2(x82821)))+~P1(f333(f333(f248(x82821),x82823),f2(x82821)))+P1(f333(f333(f248(x82821),x82823),f333(f333(f291(x82821),x82824),x82822)))+~P1(f333(f333(f248(x82821),f333(f333(f80(x82821),x82823),x82822)),x82824)) % 183.90/184.45 [8283]~P60(x82831)+P1(f333(f333(f248(x82831),x82832),f2(x82831)))+~P1(f333(f333(f247(x82831),x82833),f2(x82831)))+P1(f333(f333(f247(x82831),x82833),f333(f333(f291(x82831),x82834),x82832)))+~P1(f333(f333(f247(x82831),f333(f333(f80(x82831),x82833),x82832)),x82834)) % 183.90/184.45 [8442]~P60(x84421)+~P1(f333(f333(f248(x84421),x84422),f2(x84421)))+P1(f333(f333(f248(x84421),f2(x84421)),x84422))+~P1(f333(f333(f248(x84421),f333(f333(f291(x84421),x84424),x84422)),x84423))+P1(f333(f333(f248(x84421),f333(f333(f80(x84421),x84423),x84422)),x84424)) % 183.90/184.45 [8443]~P60(x84431)+~P1(f333(f333(f248(x84431),x84432),f2(x84431)))+P1(f333(f333(f248(x84431),f2(x84431)),x84432))+~P1(f333(f333(f248(x84431),f333(f333(f80(x84431),x84434),x84432)),x84433))+P1(f333(f333(f248(x84431),f333(f333(f291(x84431),x84433),x84432)),x84434)) % 183.90/184.45 [8444]~P60(x84441)+~P1(f333(f333(f248(x84441),x84442),f2(x84441)))+P1(f333(f333(f248(x84441),f2(x84441)),x84442))+~P1(f333(f333(f247(x84441),f333(f333(f291(x84441),x84444),x84442)),x84443))+P1(f333(f333(f247(x84441),f333(f333(f80(x84441),x84443),x84442)),x84444)) % 183.90/184.45 [8445]~P60(x84451)+~P1(f333(f333(f248(x84451),x84452),f2(x84451)))+P1(f333(f333(f248(x84451),f2(x84451)),x84452))+~P1(f333(f333(f247(x84451),f333(f333(f80(x84451),x84454),x84452)),x84453))+P1(f333(f333(f247(x84451),f333(f333(f291(x84451),x84453),x84452)),x84454)) % 183.90/184.45 [8466]~P60(x84661)+~P1(f333(f333(f248(x84661),f2(x84661)),x84664))+P1(f333(f333(f248(x84661),f2(x84661)),x84662))+~P1(f333(f333(f248(x84661),f333(f333(f80(x84661),x84664),x84662)),x84663))+P1(f333(f333(f248(x84661),f333(f333(f291(x84661),x84663),x84662)),x84664)) % 183.90/184.45 [8467]~P60(x84671)+~P1(f333(f333(f247(x84671),f2(x84671)),x84674))+P1(f333(f333(f248(x84671),f2(x84671)),x84672))+~P1(f333(f333(f247(x84671),f333(f333(f80(x84671),x84674),x84672)),x84673))+P1(f333(f333(f247(x84671),f333(f333(f291(x84671),x84673),x84672)),x84674)) % 183.90/184.45 [8539]~P60(x85391)+~P1(f333(f333(f248(x85391),x85394),f2(x85391)))+~P1(f333(f333(f248(x85391),x85393),f333(f333(f80(x85391),x85392),x85394)))+P1(f333(f333(f248(x85391),x85392),f333(f333(f291(x85391),x85393),x85394)))+~P1(f333(f333(f248(x85391),f333(f333(f80(x85391),x85392),x85394)),x85393)) % 183.90/184.45 [8540]~P60(x85401)+~P1(f333(f333(f248(x85401),x85402),f2(x85401)))+~P1(f333(f333(f248(x85401),x85403),f333(f333(f80(x85401),x85402),x85404)))+P1(f333(f333(f248(x85401),x85402),f333(f333(f291(x85401),x85403),x85404)))+~P1(f333(f333(f248(x85401),f333(f333(f80(x85401),x85402),x85404)),x85403)) % 183.90/184.45 [8541]~P60(x85411)+~P1(f333(f333(f248(x85411),x85414),f2(x85411)))+~P1(f333(f333(f247(x85411),x85413),f333(f333(f80(x85411),x85412),x85414)))+P1(f333(f333(f247(x85411),x85412),f333(f333(f291(x85411),x85413),x85414)))+~P1(f333(f333(f247(x85411),f333(f333(f80(x85411),x85412),x85414)),x85413)) % 183.90/184.45 [8542]~P60(x85421)+~P1(f333(f333(f247(x85421),x85422),f2(x85421)))+~P1(f333(f333(f247(x85421),x85423),f333(f333(f80(x85421),x85422),x85424)))+P1(f333(f333(f247(x85421),x85422),f333(f333(f291(x85421),x85423),x85424)))+~P1(f333(f333(f247(x85421),f333(f333(f80(x85421),x85422),x85424)),x85423)) % 183.90/184.45 [8654]~P60(x86541)+~P1(f333(f333(f248(x86541),x86543),f2(x86541)))+~P1(f333(f333(f248(x86541),x86542),f333(f333(f80(x86541),x86544),x86543)))+~P1(f333(f333(f248(x86541),f333(f333(f80(x86541),x86544),x86543)),x86542))+P1(f333(f333(f248(x86541),f333(f333(f291(x86541),x86542),x86543)),x86544)) % 183.90/184.45 [8655]~P60(x86551)+~P1(f333(f333(f248(x86551),x86553),f2(x86551)))+~P1(f333(f333(f247(x86551),x86552),f333(f333(f80(x86551),x86554),x86553)))+~P1(f333(f333(f247(x86551),f333(f333(f80(x86551),x86554),x86553)),x86552))+P1(f333(f333(f247(x86551),f333(f333(f291(x86551),x86552),x86553)),x86554)) % 183.90/184.45 [8670]~P60(x86701)+~P1(f333(f333(f248(x86701),f2(x86701)),x86704))+~P1(f333(f333(f248(x86701),x86702),f333(f333(f80(x86701),x86704),x86703)))+~P1(f333(f333(f248(x86701),f333(f333(f80(x86701),x86704),x86703)),x86702))+P1(f333(f333(f248(x86701),f333(f333(f291(x86701),x86702),x86703)),x86704)) % 183.90/184.45 [8671]~P60(x86711)+~P1(f333(f333(f247(x86711),f2(x86711)),x86714))+~P1(f333(f333(f247(x86711),x86712),f333(f333(f80(x86711),x86714),x86713)))+~P1(f333(f333(f247(x86711),f333(f333(f80(x86711),x86714),x86713)),x86712))+P1(f333(f333(f247(x86711),f333(f333(f291(x86711),x86712),x86713)),x86714)) % 183.90/184.45 [8838]E(f333(f333(f22(a1),f439(x88381,x88382,x88383,x88384)),f440(x88381,x88382,x88383,x88384)),x88384)+~P1(f333(f333(f248(a1),f2(a1)),x88383))+~P1(f333(f333(f335(a1),x88382),x88381))+~P1(f333(f333(f248(a1),x88384),x88382))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x88384),x88383)),x88382)) % 183.90/184.45 [8919]~P1(f333(x89191,x89192))+~P1(f333(f333(f248(a1),f2(a1)),x89194))+~P1(f333(f333(f247(a1),f2(a1)),x89193))+~P1(f333(x89191,f333(f333(f22(a1),f414(x89193,x89191,x89194)),x89194)))+P1(f333(x89191,f333(f333(f22(a1),x89192),f333(f333(f80(a1),x89193),x89194)))) % 183.90/184.45 [8920]~P1(f333(x89201,x89202))+~P1(f333(f333(f248(a1),f2(a1)),x89204))+~P1(f333(f333(f247(a1),f2(a1)),x89203))+~P1(f333(x89201,f333(f333(f79(a1),f417(x89203,x89201,x89204)),x89204)))+P1(f333(x89201,f333(f333(f79(a1),x89202),f333(f333(f80(a1),x89203),x89204)))) % 183.90/184.45 [9073]~P1(f333(f333(f248(a1),f2(a1)),x90733))+~P1(f333(f333(f335(a1),x90732),x90731))+~P1(f333(f333(f248(a1),x90734),x90732))+P1(f333(f333(f335(a1),f439(x90731,x90732,x90733,x90734)),x90731))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x90734),x90733)),x90732)) % 183.90/184.45 [9093]E(f333(f333(f22(a1),f425(x90931,x90932,x90933,x90934)),f426(x90931,x90932,x90933,x90934)),x90934)+~P1(f333(f333(f248(a1),f2(a1)),x90933))+~P1(f333(f333(f247(a1),x90934),x90932))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x90932),f77(a1))),x90931))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x90934),x90933)),x90932)) % 183.90/184.45 [9119]~P1(f333(f333(f248(a1),f2(a1)),x91192))+~P1(f333(f333(f335(a1),x91193),x91194))+~P1(f333(f333(f248(a1),x91191),x91193))+P1(f333(f333(f335(a1),f440(x91194,x91193,x91192,x91191)),f304(a1,f77(a1),x91192)))+P1(f333(f333(f248(a1),f333(f333(f79(a1),x91191),x91192)),x91193)) % 183.90/184.45 [9209]~P1(f333(f333(f248(a1),f2(a1)),x92093))+~P1(f333(f333(f247(a1),x92094),x92092))+P1(f333(f333(f335(a1),f425(x92091,x92092,x92093,x92094)),x92091))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x92092),f77(a1))),x92091))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x92094),x92093)),x92092)) % 183.90/184.45 [9254]~P1(f333(f333(f248(a1),f2(a1)),x92542))+~P1(f333(f333(f247(a1),x92541),x92543))+P1(f333(f333(f335(a1),f426(x92544,x92543,x92542,x92541)),f304(a1,f77(a1),x92542)))+~P1(f333(f333(f335(a1),f333(f333(f79(a1),x92543),f77(a1))),x92544))+P1(f333(f333(f247(a1),f333(f333(f79(a1),x92541),x92542)),x92543)) % 183.90/184.45 [9539]~P37(x95391,x95393)+~P26(x95391,x95394)+P37(x95391,f333(f333(f113(f882(f881(x95391,x95391),a870)),x95392),x95393))+~P1(f333(f333(f247(f882(f881(x95391,x95391),a870)),x95392),f333(f267(f882(f881(x95391,x95391),a870),f882(f881(x95391,x95391),a870)),x95394)))+~P1(f333(f333(f247(f882(f881(x95391,x95391),a870)),x95393),f333(f271(f882(f881(x95391,x95391),a870),f882(f881(x95391,x95391),a870)),x95394))) % 183.90/184.45 [9831]~E(f333(f734(x98311,x98314,x98313,x98312),f736(x98311,x98314,x98313,x98312)),f209(f876(a329)))+P1(f333(f333(f248(a1),f735(x98311,x98314,x98313,x98312)),f736(x98311,x98314,x98313,x98312)))+P1(f333(f333(f333(x98311,x98312),x98313),x98314))+P1(f333(f333(f333(x98311,f734(x98311,x98314,x98313,x98312)),f735(x98311,x98314,x98313,x98312)),f333(f333(f79(a1),f736(x98311,x98314,x98313,x98312)),f77(a1))))+~P1(f333(f321(f881(f882(a1,f879(f876(a329))),f881(a1,a1)),a319),f333(f333(f268(f882(a1,f879(f876(a329))),f881(a1,a1)),x98312),f333(f333(f268(a1,a1),x98313),x98314)))) % 183.90/184.45 [9932]~P18(x99322,x99324,x99323)+E(x99321,f196(f882(x99322,a870)))+~P1(f333(f61(x99322),x99321))+P1(f333(f333(f335(x99322),f333(x99323,x99321)),x99321))+~P1(f333(f333(f335(x99322),f333(f333(x99324,f531(x99321,x99323,x99324,x99322)),f541(x99321,x99323,x99324,x99322))),f333(f333(f311(x99322),f531(x99321,x99323,x99324,x99322)),f333(f333(f311(x99322),f541(x99321,x99323,x99324,x99322)),f196(f882(x99322,a870)))))) % 183.90/184.45 [9863]~P108(x98632)+~P57(x98631)+~P1(f333(f333(f247(f882(x98631,x98632)),x98633),x98634))+P1(f333(f333(f248(f882(x98631,x98632)),x98633),x98634))+~P1(f333(f57(x98631),f333(f333(f8(a870,a870,x98631),a328),f333(f333(f18(x98631,x98632,a870),f333(f333(f8(x98632,f882(x98632,a870),x98631),a330),x98633)),x98634)))) % 183.90/184.45 [9455]~P49(x94551,x94551,x94554)+P1(f333(f333(f335(f881(x94551,x94551)),f333(f333(f268(x94551,x94551),x94552),x94553)),f309(x94551,x94554)))+P1(f333(f333(f335(f881(x94551,x94551)),f333(f333(f268(x94551,x94551),x94553),x94552)),f309(x94551,x94554)))+~P1(f333(f333(f335(f881(x94551,x94551)),f333(f333(f268(x94551,x94551),x94555),x94552)),f309(x94551,x94554)))+~P1(f333(f333(f335(f881(x94551,x94551)),f333(f333(f268(x94551,x94551),x94555),x94553)),f309(x94551,x94554))) % 183.90/184.45 [5612]E(x56121,f2(a875))+~E(f333(f37(x56122),x56125),x56121)+E(f333(f37(x56122),x56123),f333(a115,x56121))+~E(x56123,f333(f333(f311(x56122),x56124),x56125))+P1(f333(f333(f335(x56122),x56124),x56125)) % 183.90/184.45 [5736]~P59(x57362)+E(x57361,f2(x57362))+E(x57363,f2(x57362))+~E(f333(f333(f291(x57362),x57364),x57363),f333(f333(f291(x57362),x57365),x57361))+E(f333(f333(f80(x57362),x57364),x57361),f333(f333(f80(x57362),x57365),x57363)) % 183.90/184.45 [5737]~P59(x57372)+E(x57371,f2(x57372))+E(x57373,f2(x57372))+~E(f333(f333(f80(x57372),x57374),x57373),f333(f333(f80(x57372),x57375),x57371))+E(f333(f333(f291(x57372),x57374),x57371),f333(f333(f291(x57372),x57375),x57373)) % 183.90/184.45 [5803]~E(f333(f37(x58031),x58035),x58033)+~E(x58035,f196(f882(x58031,a870)))+E(f333(f37(x58031),x58032),f333(a115,x58033))+~E(x58032,f333(f333(f311(x58031),x58034),x58035))+P1(f333(f333(f335(x58031),x58034),x58035)) % 183.90/184.45 [6029]~P109(x60292)+~E(f333(x60293,x60295),f2(x60292))+E(f333(f333(f9(x60291,x60292),x60293),x60294),f2(x60292))+~P1(f333(f61(x60291),x60294))+~P1(f333(f333(f335(x60291),x60295),x60294)) % 183.90/184.45 [6396]~P106(x63963)+E(x63961,x63962)+~E(f333(f303(x63963,x63964),x63961),f333(f303(x63963,x63965),x63962))+~P1(f333(f333(f248(x63963),x63965),x63962))+~P1(f333(f333(f248(x63963),x63964),x63961)) % 183.90/184.45 [6397]~P106(x63973)+E(x63971,x63972)+~E(f333(f303(x63973,x63971),x63974),f333(f303(x63973,x63972),x63975))+~P1(f333(f333(f248(x63973),x63972),x63975))+~P1(f333(f333(f248(x63973),x63971),x63974)) % 183.90/184.45 [7459]~P106(x74591)+~P14(x74591,f333(f333(f135(x74591),x74594),x74595))+~P1(f333(f333(f335(x74591),x74593),f333(f174(x74591),x74595)))+~P1(f333(f333(f335(x74591),x74592),f333(f174(x74591),x74594)))+P1(f333(f333(f247(x74591),x74592),x74593)) % 183.90/184.45 [8574]~P108(x85741)+~P1(f333(f333(f248(f882(x85741,a870)),f304(x85741,x85745,x85742)),f304(x85741,x85744,x85743)))+~P1(f333(f333(f247(x85741),x85745),x85742))+P1(f333(f333(f248(x85741),x85742),x85743))+P1(f333(f333(f248(x85741),x85744),x85745)) % 183.90/184.45 [9975]~P17(x99752,x99755,x99753)+E(x99751,f196(f882(x99752,a870)))+~E(f333(f333(x99755,f333(x99754,f484(x99751,x99754,x99753,x99755,x99752))),f333(x99754,f498(x99751,x99754,x99753,x99755,x99752))),f333(x99754,f333(f333(x99755,f484(x99751,x99754,x99753,x99755,x99752)),f498(x99751,x99754,x99753,x99755,x99752))))+E(f333(x99753,f333(f312(x99752,x99752,x99754),x99751)),f333(x99754,f333(x99753,x99751)))+~P1(f333(f61(x99752),x99751)) % 183.90/184.45 [6393]~P18(x63932,x63935,x63933)+E(x63931,f196(f882(x63932,a870)))+~P1(f333(f61(x63932),x63931))+E(f333(x63933,f333(f333(f311(x63932),x63934),x63931)),f333(f333(x63935,x63934),f333(x63933,x63931)))+P1(f333(f333(f335(x63932),x63934),x63931)) % 183.90/184.45 [7216]~P17(x72162,x72163,x72164)+E(f333(f333(x72163,f333(x72164,x72161)),f333(x72164,x72165)),f333(x72164,x72165))+E(x72161,f196(f882(x72162,a870)))+~P1(f333(f61(x72162),x72165))+~P1(f333(f333(f247(f882(x72162,a870)),x72161),x72165)) % 183.90/184.45 [7435]~P57(x74354)+~P92(x74355)+E(f333(x74351,x74352),f333(x74353,x74352))+~P1(f333(f333(f335(x74354),x74352),f333(f174(x74354),f55(x74354))))+~P1(f333(f333(f90(f882(x74354,x74355)),x74351),x74353)) % 183.90/184.45 [7595]~P18(x75954,x75955,x75951)+E(f333(x75951,x75952),x75953)+~P1(f333(f61(x75954),x75952))+~E(f333(f333(f22(f882(x75954,a870)),x75952),f333(f333(f311(x75954),x75953),f196(f882(x75954,a870)))),f196(f882(x75954,a870)))+~P1(f333(f333(f335(x75954),x75953),x75952)) % 183.90/184.45 [7682]E(x76821,x76822)+~E(f333(f197(f876(x76823)),x76822),f333(f197(f876(x76824)),x76825))+~E(f333(f197(f876(x76823)),x76821),f333(f197(f876(x76824)),x76825))+~E(f333(f180(x76824,x76823),f333(f333(f184(x76824,x76823),x76825),x76821)),f333(f180(x76824,x76823),f333(f333(f184(x76824,x76823),x76825),x76822)))+~P1(f333(f138(x76824),x76825)) % 183.90/184.45 [8546]E(x85461,x85462)+~P7(x85463,x85464,x85465)+E(f333(f333(f104(f882(x85463,a870)),x85461),x85462),f196(f882(x85463,a870)))+~P1(f333(f333(f335(f882(x85463,a870)),x85462),f333(f333(f60(x85463),x85464),x85465)))+~P1(f333(f333(f335(f882(x85463,a870)),x85461),f333(f333(f60(x85463),x85464),x85465))) % 183.90/184.45 [9336]~P66(x93362)+~E(f333(x93363,f458(x93363,x93364,x93365,x93361,x93362)),f2(x93362))+E(f333(f333(f6(x93361,x93362),x93363),x93364),f333(f333(f6(x93361,x93362),x93363),x93365))+~P1(f333(f61(x93361),x93365))+~P1(f333(f333(f247(f882(x93361,a870)),x93364),x93365)) % 183.90/184.45 [9337]~P66(x93372)+~E(f333(x93373,f459(x93373,x93374,x93375,x93371,x93372)),f2(x93372))+E(f333(f333(f6(x93371,x93372),x93373),x93374),f333(f333(f6(x93371,x93372),x93373),x93375))+~P1(f333(f61(x93371),x93375))+~P1(f333(f333(f247(f882(x93371,a870)),x93374),x93375)) % 183.90/184.45 [9338]~P73(x93382)+~E(f333(x93383,f449(x93383,x93384,x93385,x93381,x93382)),f77(x93382))+E(f333(f333(f9(x93381,x93382),x93383),x93384),f333(f333(f9(x93381,x93382),x93383),x93385))+~P1(f333(f61(x93381),x93385))+~P1(f333(f333(f247(f882(x93381,a870)),x93384),x93385)) % 183.90/184.45 [9339]~P73(x93392)+~E(f333(x93393,f450(x93393,x93394,x93395,x93391,x93392)),f77(x93392))+E(f333(f333(f9(x93391,x93392),x93393),x93394),f333(f333(f9(x93391,x93392),x93393),x93395))+~P1(f333(f61(x93391),x93395))+~P1(f333(f333(f247(f882(x93391,a870)),x93394),x93395)) % 183.90/184.45 [9811]~P85(x98111)+~P1(f333(f61(x98112),x98115))+~P1(f333(f333(f247(x98111),f2(x98111)),f333(x98113,f371(x98113,x98114,x98115,x98112,x98111))))+P1(f333(f333(f247(x98111),f333(f333(f6(x98112,x98111),x98113),x98114)),f333(f333(f6(x98112,x98111),x98113),x98115)))+~P1(f333(f333(f247(f882(x98112,a870)),x98114),x98115)) % 183.90/184.45 [7456]E(x74561,f2(a875))+P1(f333(x74562,x74563))+~E(x74564,f333(f333(f79(a875),f333(f333(f80(a875),x74561),x74563)),x74565))+~P1(f333(f333(f248(a875),x74565),x74561))+~P1(f333(x74562,f333(f333(f38(a875),x74564),x74561))) % 183.90/184.45 [7536]E(x75361,f2(a875))+P1(f333(x75362,x75363))+~P1(f333(x75362,f44(a875,x75364,x75361)))+~E(x75364,f333(f333(f79(a875),f333(f333(f80(a875),x75361),x75365)),x75363))+~P1(f333(f333(f248(a875),x75363),x75361)) % 183.90/184.45 [7832]~P59(x78323)+E(f333(x78321,x78322),f2(x78323))+~P1(f333(f61(x78324),x78325))+E(f333(f333(f9(x78324,x78323),x78321),f333(f333(f22(f882(x78324,a870)),x78325),f333(f333(f311(x78324),x78322),f196(f882(x78324,a870))))),f333(f333(f9(x78324,x78323),x78321),x78325))+P1(f333(f333(f335(x78324),x78322),x78325)) % 183.90/184.45 [8241]~P66(x82411)+~P1(f333(f61(x82412),x82415))+~P1(f333(f61(x82412),x82414))+~E(f333(f333(f104(f882(x82412,a870)),x82414),x82415),f196(f882(x82412,a870)))+E(f333(f333(f79(x82411),f333(f333(f6(x82412,x82411),x82413),x82414)),f333(f333(f6(x82412,x82411),x82413),x82415)),f333(f333(f6(x82412,x82411),x82413),f333(f333(f113(f882(x82412,a870)),x82414),x82415))) % 183.90/184.45 [8243]~P73(x82431)+~P1(f333(f61(x82432),x82435))+~P1(f333(f61(x82432),x82434))+~E(f333(f333(f104(f882(x82432,a870)),x82434),x82435),f196(f882(x82432,a870)))+E(f333(f333(f80(x82431),f333(f333(f9(x82432,x82431),x82433),x82434)),f333(f333(f9(x82432,x82431),x82433),x82435)),f333(f333(f9(x82432,x82431),x82433),f333(f333(f113(f882(x82432,a870)),x82434),x82435))) % 183.90/184.45 [8336]~P59(x83363)+E(f333(x83361,x83362),f2(x83363))+~P1(f333(f61(x83364),x83365))+E(f333(f333(f9(x83364,x83363),x83361),f333(f333(f22(f882(x83364,a870)),x83365),f333(f333(f311(x83364),x83362),f196(f882(x83364,a870))))),f333(f333(f291(x83363),f333(f333(f9(x83364,x83363),x83361),x83365)),f333(x83361,x83362)))+~P1(f333(f333(f335(x83364),x83362),x83365)) % 183.90/184.45 [9052]~P7(x90521,x90525,x90524)+~E(f333(f333(f60(x90521),f333(f333(f311(x90521),x90522),f196(f882(x90521,a870)))),x90524),f333(f333(f60(x90521),f333(f333(f311(x90521),x90523),f196(f882(x90521,a870)))),x90524))+~P1(f333(f333(f335(x90521),x90523),x90525))+~P1(f333(f333(f335(x90521),x90522),x90525))+P1(f333(f333(f335(f881(x90521,x90521)),f333(f333(f268(x90521,x90521),x90522),x90523)),x90524)) % 183.90/184.45 [9072]~P7(x90721,x90725,x90723)+E(f333(f333(f60(x90721),f333(f333(f311(x90721),x90722),f196(f882(x90721,a870)))),x90723),f333(f333(f60(x90721),f333(f333(f311(x90721),x90724),f196(f882(x90721,a870)))),x90723))+~P1(f333(f333(f335(x90721),x90724),x90725))+~P1(f333(f333(f335(x90721),x90722),x90725))+~P1(f333(f333(f335(f881(x90721,x90721)),f333(f333(f268(x90721,x90721),x90722),x90724)),x90723)) % 183.90/184.45 [9365]~P73(x93651)+~P1(f333(f61(x93652),x93655))+~P1(f333(f61(x93652),x93654))+~E(f333(f333(f104(f882(x93652,a870)),x93654),x93655),f196(f882(x93652,a870)))+E(f333(f333(f80(x93651),f333(f333(f333(f65(x93651,x93652,f80(x93651)),x93653),f77(x93651)),x93654)),f333(f333(f333(f65(x93651,x93652,f80(x93651)),x93653),f77(x93651)),x93655)),f333(f333(f333(f65(x93651,x93652,f80(x93651)),x93653),f77(x93651)),f333(f333(f113(f882(x93652,a870)),x93654),x93655))) % 183.90/184.45 [9374]~P66(x93741)+~E(f333(x93743,f370(x93743,x93745,x93744,x93742,x93741)),f2(x93741))+~P1(f333(f61(x93742),x93744))+~P1(f333(f61(x93742),x93745))+E(f333(f333(f79(x93741),f333(f333(f6(x93742,x93741),x93743),x93744)),f333(f333(f6(x93742,x93741),x93743),x93745)),f333(f333(f6(x93742,x93741),x93743),f333(f333(f113(f882(x93742,a870)),x93744),x93745))) % 183.90/184.45 [9375]~P66(x93751)+~E(f333(x93753,f372(x93753,x93755,x93754,x93752,x93751)),f2(x93751))+~P1(f333(f61(x93752),x93754))+~P1(f333(f61(x93752),x93755))+E(f333(f333(f79(x93751),f333(f333(f6(x93752,x93751),x93753),x93754)),f333(f333(f6(x93752,x93751),x93753),x93755)),f333(f333(f6(x93752,x93751),x93753),f333(f333(f113(f882(x93752,a870)),x93754),x93755))) % 183.90/184.45 [9376]~P73(x93761)+~E(f333(x93763,f852(x93763,x93765,x93764,x93762,x93761)),f77(x93761))+~P1(f333(f61(x93762),x93764))+~P1(f333(f61(x93762),x93765))+E(f333(f333(f80(x93761),f333(f333(f9(x93762,x93761),x93763),x93764)),f333(f333(f9(x93762,x93761),x93763),x93765)),f333(f333(f9(x93762,x93761),x93763),f333(f333(f113(f882(x93762,a870)),x93764),x93765))) % 183.90/184.45 [9377]~P73(x93771)+~E(f333(x93773,f857(x93773,x93775,x93774,x93772,x93771)),f77(x93771))+~P1(f333(f61(x93772),x93774))+~P1(f333(f61(x93772),x93775))+E(f333(f333(f80(x93771),f333(f333(f9(x93772,x93771),x93773),x93774)),f333(f333(f9(x93772,x93771),x93773),x93775)),f333(f333(f9(x93772,x93771),x93773),f333(f333(f113(f882(x93772,a870)),x93774),x93775))) % 183.90/184.45 [9583]~P73(x95831)+~E(f333(x95833,f854(x95833,x95835,x95834,x95832,x95831)),f77(x95831))+~P1(f333(f61(x95832),x95834))+~P1(f333(f61(x95832),x95835))+E(f333(f333(f80(x95831),f333(f333(f333(f65(x95831,x95832,f80(x95831)),x95833),f77(x95831)),x95834)),f333(f333(f333(f65(x95831,x95832,f80(x95831)),x95833),f77(x95831)),x95835)),f333(f333(f333(f65(x95831,x95832,f80(x95831)),x95833),f77(x95831)),f333(f333(f113(f882(x95832,a870)),x95834),x95835))) % 183.90/184.45 [9690]~P66(x96902)+E(f333(f333(f6(x96901,x96902),x96903),x96904),f333(f333(f6(x96901,x96902),x96903),x96905))+~P1(f333(f61(x96901),x96905))+~P1(f333(f333(f247(f882(x96901,a870)),x96904),x96905))+P1(f333(f333(f335(x96901),f458(x96903,x96904,x96905,x96901,x96902)),f333(f333(f22(f882(x96901,a870)),x96905),x96904))) % 183.90/184.45 [9691]~P66(x96912)+E(f333(f333(f6(x96911,x96912),x96913),x96914),f333(f333(f6(x96911,x96912),x96913),x96915))+~P1(f333(f61(x96911),x96915))+~P1(f333(f333(f247(f882(x96911,a870)),x96914),x96915))+P1(f333(f333(f335(x96911),f459(x96913,x96914,x96915,x96911,x96912)),f333(f333(f22(f882(x96911,a870)),x96915),x96914))) % 183.90/184.45 [9692]~P73(x96922)+E(f333(f333(f9(x96921,x96922),x96923),x96924),f333(f333(f9(x96921,x96922),x96923),x96925))+~P1(f333(f61(x96921),x96925))+~P1(f333(f333(f247(f882(x96921,a870)),x96924),x96925))+P1(f333(f333(f335(x96921),f449(x96923,x96924,x96925,x96921,x96922)),f333(f333(f22(f882(x96921,a870)),x96925),x96924))) % 183.90/184.45 [9693]~P73(x96932)+E(f333(f333(f9(x96931,x96932),x96933),x96934),f333(f333(f9(x96931,x96932),x96933),x96935))+~P1(f333(f61(x96931),x96935))+~P1(f333(f333(f247(f882(x96931,a870)),x96934),x96935))+P1(f333(f333(f335(x96931),f450(x96933,x96934,x96935,x96931,x96932)),f333(f333(f22(f882(x96931,a870)),x96935),x96934))) % 183.90/184.45 [9710]~P66(x97101)+~P1(f333(f61(x97102),x97104))+~P1(f333(f61(x97102),x97105))+E(f333(f333(f79(x97101),f333(f333(f6(x97102,x97101),x97103),x97104)),f333(f333(f6(x97102,x97101),x97103),x97105)),f333(f333(f6(x97102,x97101),x97103),f333(f333(f113(f882(x97102,a870)),x97104),x97105)))+P1(f333(f333(f335(x97102),f370(x97103,x97105,x97104,x97102,x97101)),f333(f333(f104(f882(x97102,a870)),x97104),x97105))) % 183.90/184.45 [9711]~P66(x97111)+~P1(f333(f61(x97112),x97114))+~P1(f333(f61(x97112),x97115))+E(f333(f333(f79(x97111),f333(f333(f6(x97112,x97111),x97113),x97114)),f333(f333(f6(x97112,x97111),x97113),x97115)),f333(f333(f6(x97112,x97111),x97113),f333(f333(f113(f882(x97112,a870)),x97114),x97115)))+P1(f333(f333(f335(x97112),f372(x97113,x97115,x97114,x97112,x97111)),f333(f333(f104(f882(x97112,a870)),x97114),x97115))) % 183.90/184.45 [9712]~P73(x97121)+~P1(f333(f61(x97122),x97124))+~P1(f333(f61(x97122),x97125))+E(f333(f333(f80(x97121),f333(f333(f9(x97122,x97121),x97123),x97124)),f333(f333(f9(x97122,x97121),x97123),x97125)),f333(f333(f9(x97122,x97121),x97123),f333(f333(f113(f882(x97122,a870)),x97124),x97125)))+P1(f333(f333(f335(x97122),f852(x97123,x97125,x97124,x97122,x97121)),f333(f333(f104(f882(x97122,a870)),x97124),x97125))) % 183.90/184.45 [9713]~P73(x97131)+~P1(f333(f61(x97132),x97134))+~P1(f333(f61(x97132),x97135))+E(f333(f333(f80(x97131),f333(f333(f9(x97132,x97131),x97133),x97134)),f333(f333(f9(x97132,x97131),x97133),x97135)),f333(f333(f9(x97132,x97131),x97133),f333(f333(f113(f882(x97132,a870)),x97134),x97135)))+P1(f333(f333(f335(x97132),f857(x97133,x97135,x97134,x97132,x97131)),f333(f333(f104(f882(x97132,a870)),x97134),x97135))) % 183.90/184.45 [9720]~P85(x97205)+~P1(f333(f61(x97201),x97204))+P1(f333(f333(f247(x97205),f333(f333(f6(x97201,x97205),x97202),x97203)),f333(f333(f6(x97201,x97205),x97202),x97204)))+~P1(f333(f333(f247(f882(x97201,a870)),x97203),x97204))+P1(f333(f333(f335(x97201),f371(x97202,x97203,x97204,x97201,x97205)),f333(f333(f22(f882(x97201,a870)),x97204),x97203))) % 183.90/184.45 [9774]~P73(x97741)+~P1(f333(f61(x97742),x97744))+~P1(f333(f61(x97742),x97745))+E(f333(f333(f80(x97741),f333(f333(f333(f65(x97741,x97742,f80(x97741)),x97743),f77(x97741)),x97744)),f333(f333(f333(f65(x97741,x97742,f80(x97741)),x97743),f77(x97741)),x97745)),f333(f333(f333(f65(x97741,x97742,f80(x97741)),x97743),f77(x97741)),f333(f333(f113(f882(x97742,a870)),x97744),x97745)))+P1(f333(f333(f335(x97742),f854(x97743,x97745,x97744,x97742,x97741)),f333(f333(f104(f882(x97742,a870)),x97744),x97745))) % 183.90/184.45 [8738]~P18(x87381,x87384,x87385)+~P1(f333(f61(x87381),x87382))+E(f333(f333(f22(f882(x87381,a870)),x87382),f333(f333(f311(x87381),x87383),f196(f882(x87381,a870)))),f196(f882(x87381,a870)))+~P1(f333(f333(f335(x87381),x87383),x87382))+E(f333(f333(x87384,x87383),f333(x87385,f333(f333(f22(f882(x87381,a870)),x87382),f333(f333(f311(x87381),x87383),f196(f882(x87381,a870)))))),f333(x87385,x87382)) % 183.90/184.45 [8812]~P18(x88121,x88124,x88125)+~P1(f333(f61(x88121),x88123))+~P1(f333(f61(x88121),x88122))+E(f333(f333(f104(f882(x88121,a870)),x88122),x88123),f196(f882(x88121,a870)))+E(f333(f333(x88124,f333(x88125,f333(f333(f113(f882(x88121,a870)),x88122),x88123))),f333(x88125,f333(f333(f104(f882(x88121,a870)),x88122),x88123))),f333(f333(x88124,f333(x88125,x88122)),f333(x88125,x88123))) % 183.90/184.45 [9379]~P1(f333(f333(f247(a1),x93794),f2(a1)))+~P1(f333(f333(f248(a1),x93793),x93795))+P1(f333(f333(f247(a1),x93791),x93792))+~P1(f333(f333(f248(a1),x93793),x93794))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),f333(f333(f80(a1),x93793),x93792)),x93795)),f333(f333(f79(a1),f333(f333(f80(a1),x93793),x93791)),x93794))) % 183.90/184.45 [9381]~P1(f333(f333(f247(a1),f2(a1)),x93815))+P1(f333(f333(f247(a1),x93811),x93812))+~P1(f333(f333(f248(a1),x93813),x93814))+~P1(f333(f333(f248(a1),x93815),x93814))+~P1(f333(f333(f247(a1),f333(f333(f79(a1),f333(f333(f80(a1),x93814),x93811)),x93815)),f333(f333(f79(a1),f333(f333(f80(a1),x93814),x93812)),x93813))) % 183.90/184.45 [9492]~P59(x94925)+E(f333(x94921,f398(x94921,x94922,x94923,x94924,x94925)),f2(x94925))+~P1(f333(f61(x94924),x94923))+~P1(f333(f61(x94924),x94922))+E(f333(f333(f291(x94925),f333(f333(f80(x94925),f333(f333(f9(x94924,x94925),x94921),x94923)),f333(f333(f9(x94924,x94925),x94921),x94922))),f333(f333(f9(x94924,x94925),x94921),f333(f333(f104(f882(x94924,a870)),x94923),x94922))),f333(f333(f9(x94924,x94925),x94921),f333(f333(f113(f882(x94924,a870)),x94923),x94922))) % 183.90/184.45 [9766]~P59(x97661)+~P1(f333(f61(x97662),x97664))+~P1(f333(f61(x97662),x97665))+E(f333(f333(f291(x97661),f333(f333(f80(x97661),f333(f333(f9(x97662,x97661),x97663),x97664)),f333(f333(f9(x97662,x97661),x97663),x97665))),f333(f333(f9(x97662,x97661),x97663),f333(f333(f104(f882(x97662,a870)),x97664),x97665))),f333(f333(f9(x97662,x97661),x97663),f333(f333(f113(f882(x97662,a870)),x97664),x97665)))+P1(f333(f333(f335(x97662),f398(x97663,x97665,x97664,x97662,x97661)),f333(f333(f104(f882(x97662,a870)),x97664),x97665))) % 183.90/184.45 [9092]E(f333(f333(f135(x90921),x90922),x90923),f333(f333(f135(x90921),x90924),x90925))+~E(f333(f333(f177(x90921),f333(f197(f876(x90921)),x90924)),x90922),x90924)+~E(f333(f333(f177(x90921),f333(f197(f876(x90921)),x90922)),x90924),x90922)+~E(x90925,f333(f333(f135(x90921),f333(f333(f139(x90921),f333(f197(f876(x90921)),x90924)),x90922)),x90923))+~E(f333(f333(f135(x90921),f333(f333(f139(x90921),f333(f197(f876(x90921)),x90922)),x90924)),x90925),x90923) % 183.90/184.45 [9490]~P106(x94902)+E(f333(f333(f149(x94901,x94902,x94903),x94904),f172(x94901,x94904,x94905)),x94905)+~P14(x94902,f333(f333(f155(x94901,x94902),x94903),x94905))+~P1(f333(f333(f335(x94901),x94904),f333(f174(x94901),x94905)))+~E(f333(f142(x94901),f333(f137(x94901,f333(f333(f8(x94902,a870,x94901),f333(a330,f333(x94903,x94904))),x94903)),x94905)),x94904) % 183.90/184.45 [9828]~P67(x98281)+~P1(f333(f66(x98281,x98281,f80(x98281),x98282,x98283),x98285))+~P1(f333(f333(f335(x98281),x98284),x98283))+P1(f333(f333(f335(x98281),x98282),x98283))+P1(f333(f66(x98281,x98281,f80(x98281),x98284,f333(f333(f311(x98281),x98282),f333(f333(f22(f882(x98281,a870)),x98283),f333(f333(f311(x98281),x98284),f196(f882(x98281,a870)))))),x98285)) % 183.90/184.45 [7224]E(x72241,x72242)+~P25(x72244,x72245,x72243,x72246)+~E(f333(x72243,x72241),f333(x72243,x72242))+~P1(f333(f333(f335(x72244),x72242),x72246))+~P1(f333(f333(f335(x72244),x72241),x72246)) % 183.90/184.45 [6483]~P139(x64834)+E(x64831,x64832)+~E(x64835,x64836)+E(x64833,f2(x64834))+~E(f333(f333(f79(x64834),x64835),f333(f333(f80(x64834),x64833),x64831)),f333(f333(f79(x64834),x64836),f333(f333(f80(x64834),x64833),x64832))) % 183.90/184.45 [7516]~P4(x75161)+~P106(x75161)+~P1(f333(f333(f248(x75161),x75162),f333(x75165,x75166)))+~P1(f333(f333(f335(x75163),x75166),x75164))+P1(f333(f333(f248(x75161),x75162),f333(f333(f41(x75163,x75161),x75164),x75165))) % 183.90/184.45 [8211]~P4(x82111)+~P106(x82111)+~P1(f333(f333(f248(x82111),f333(x82114,x82116)),x82115))+~P1(f333(f333(f335(x82112),x82116),x82113))+P1(f333(f333(f248(x82111),f333(f333(f42(x82112,x82111),x82113),x82114)),x82115)) % 183.90/184.45 [8473]~P19(x84732,x84735,x84736,x84731)+~P1(f333(f61(x84732),x84734))+~P1(f333(f61(x84732),x84733))+~E(f333(f333(f104(f882(x84732,a870)),x84733),x84734),f196(f882(x84732,a870)))+E(f333(x84731,f333(f333(f113(f882(x84732,a870)),x84733),x84734)),f333(f72(x84735,x84735,x84735,f333(x84731,x84733)),f333(x84731,x84734))) % 183.90/184.45 [8781]E(x87811,x87812)+~P51(x87814,x87815,x87816,x87813,x87817)+~E(f333(x87813,x87811),f333(x87813,x87812))+~P1(f333(f333(f335(x87815),x87812),x87817))+~P1(f333(f333(f335(x87815),x87811),x87817)) % 183.90/184.45 [10074]~P1(f333(x100742,x100744))+~E(x100745,f333(f137(x100741,x100742),x100747))+E(f333(f137(x100741,x100742),x100743),f333(f333(f152(x100741),x100744),x100745))+~E(x100743,f333(f333(f135(x100741),x100746),f333(f333(f152(x100741),x100744),x100747)))+P1(f333(x100742,f789(x100745,x100744,x100743,x100742,x100741,x100746,x100747))) % 183.90/184.45 [10075]~P1(f333(x100754,x100752))+~E(x100753,f333(f137(x100751,x100754),x100757))+E(f333(f333(f152(x100751),x100752),x100753),f333(f137(x100751,x100754),x100755))+~E(x100755,f333(f333(f135(x100751),x100756),f333(f333(f152(x100751),x100752),x100757)))+P1(f333(x100754,f788(x100755,x100754,x100753,x100752,x100751,x100756,x100757))) % 183.90/184.45 [10109]~P1(f333(x101092,x101094))+~E(x101095,f333(f137(x101091,x101092),x101097))+E(f333(f137(x101091,x101092),x101093),f333(f333(f152(x101091),x101094),x101095))+~E(x101093,f333(f333(f135(x101091),x101096),f333(f333(f152(x101091),x101094),x101097)))+P1(f333(f333(f335(x101091),f789(x101095,x101094,x101093,x101092,x101091,x101096,x101097)),f333(f174(x101091),x101096))) % 183.90/184.45 [10110]~P1(f333(x101104,x101102))+~E(x101103,f333(f137(x101101,x101104),x101107))+E(f333(f333(f152(x101101),x101102),x101103),f333(f137(x101101,x101104),x101105))+~E(x101105,f333(f333(f135(x101101),x101106),f333(f333(f152(x101101),x101102),x101107)))+P1(f333(f333(f335(x101101),f788(x101105,x101104,x101103,x101102,x101101,x101106,x101107)),f333(f174(x101101),x101106))) % 183.90/184.45 [10113]~P7(x101131,x101137,x101136)+~P12(x101131,f882(x101135,a870),x101136,x101134)+P1(f333(f333(f335(x101131),f533(x101132,x101133,x101134,x101135,x101136,x101137,x101131)),x101137))+~P1(f333(f333(f335(f882(x101131,a870)),x101133),f333(f333(f60(x101131),x101137),x101136)))+P1(f333(f333(f335(f882(x101135,a870)),f333(f333(f41(x101131,f882(x101135,a870)),x101133),x101134)),x101132)) % 183.90/184.45 [10158]~P7(x101582,x101586,x101587)+~P12(x101582,f882(x101581,a870),x101587,x101584)+~P1(f333(f333(f335(f882(x101582,a870)),x101583),f333(f333(f60(x101582),x101586),x101587)))+~P1(f333(f333(f335(f882(x101581,a870)),f333(x101584,f533(x101585,x101583,x101584,x101581,x101587,x101586,x101582))),x101585))+P1(f333(f333(f335(f882(x101581,a870)),f333(f333(f41(x101582,f882(x101581,a870)),x101583),x101584)),x101585)) % 183.90/184.45 [8380]~P73(x83802)+~P25(x83801,x83805,x83808,x83804)+~E(x83803,f333(f72(x83805,x83802,x83801,x83806),x83808))+~E(x83807,f333(f312(x83801,x83805,x83808),x83804))+E(f333(f333(f9(x83801,x83802),x83803),x83804),f333(f333(f9(x83805,x83802),x83806),x83807)) % 183.90/184.45 [10162]~P73(x101622)+~P25(x101625,x101621,x101628,x101627)+~E(f333(x101626,f859(x101623,x101626,x101624,x101627,x101628,x101621,x101625,x101622)),f333(f333(f72(x101621,x101622,x101625,x101623),x101628),f859(x101623,x101626,x101624,x101627,x101628,x101621,x101625,x101622)))+~E(x101624,f333(f312(x101625,x101621,x101628),x101627))+E(f333(f333(f9(x101621,x101622),x101623),x101624),f333(f333(f9(x101625,x101622),x101626),x101627)) % 183.90/184.45 [10164]~P66(x101642)+~P25(x101641,x101645,x101648,x101644)+~E(x101647,f333(f312(x101641,x101645,x101648),x101644))+E(f333(f333(f6(x101641,x101642),x101643),x101644),f333(f333(f6(x101645,x101642),x101646),x101647))+P1(f333(f333(f335(x101641),f833(x101646,x101643,x101647,x101644,x101648,x101645,x101641,x101642)),x101644)) % 183.90/184.45 [10165]~P73(x101652)+~P25(x101651,x101655,x101658,x101654)+~E(x101657,f333(f312(x101651,x101655,x101658),x101654))+E(f333(f333(f9(x101651,x101652),x101653),x101654),f333(f333(f9(x101655,x101652),x101656),x101657))+P1(f333(f333(f335(x101651),f859(x101656,x101653,x101657,x101654,x101658,x101655,x101651,x101652)),x101654)) % 183.90/184.45 [10171]~P66(x101712)+~P25(x101715,x101711,x101718,x101717)+~E(x101714,f333(f312(x101715,x101711,x101718),x101717))+~E(f333(x101716,f833(x101713,x101716,x101714,x101717,x101718,x101711,x101715,x101712)),f333(x101713,f333(x101718,f833(x101713,x101716,x101714,x101717,x101718,x101711,x101715,x101712))))+E(f333(f333(f6(x101711,x101712),x101713),x101714),f333(f333(f6(x101715,x101712),x101716),x101717)) % 183.90/184.45 [9545]~E(f333(f197(f876(x95452)),x95455),f333(f197(f876(x95451)),x95453))+~E(f333(f197(f876(x95452)),x95454),f333(f197(f876(x95451)),x95453))+~E(f333(f333(f333(f71(x95451,f879(x95452)),f333(f180(x95451,x95452),f333(f333(f184(x95451,x95452),x95453),x95454))),x95456),f333(f240(x95452),x95457)),f333(f333(f333(f71(x95451,f879(x95452)),f333(f180(x95451,x95452),f333(f333(f184(x95451,x95452),x95453),x95455))),x95456),f333(f240(x95452),x95458)))+E(f333(f180(x95451,x95452),f333(f333(f184(x95451,x95452),x95453),x95454)),f333(f180(x95451,x95452),f333(f333(f184(x95451,x95452),x95453),x95455)))+P1(f333(f333(f335(x95451),x95456),f333(f174(x95451),x95453))) % 183.90/184.45 [9658]~P23(x96586,x96582,x96585,x96587,x96588,x96581)+~P1(f333(f61(x96582),x96584))+~P1(f333(f61(x96582),x96583))+~E(f333(f333(f104(f882(x96582,a870)),x96583),x96584),f196(f882(x96582,a870)))+E(f333(x96581,f333(f333(f113(f882(x96582,a870)),x96583),x96584)),f333(f333(x96585,f333(x96581,x96583)),f333(x96581,x96584))) % 183.90/184.45 [10061]~P23(x100618,x100612,x100615,x100617,x100616,x100611)+~E(f333(x100616,f641(x100614,x100613,x100611,x100616,x100617,x100615,x100612)),x100617)+~P1(f333(f61(x100612),x100613))+~P1(f333(f61(x100612),x100614))+E(f333(x100611,f333(f333(f113(f882(x100612,a870)),x100613),x100614)),f333(f333(x100615,f333(x100611,x100613)),f333(x100611,x100614))) % 183.90/184.45 [10118]~P23(x101188,x101182,x101185,x101187,x101186,x101181)+~P1(f333(f61(x101182),x101183))+~P1(f333(f61(x101182),x101184))+E(f333(x101181,f333(f333(f113(f882(x101182,a870)),x101183),x101184)),f333(f333(x101185,f333(x101181,x101183)),f333(x101181,x101184)))+P1(f333(f333(f335(x101182),f641(x101184,x101183,x101181,x101186,x101187,x101185,x101182)),f333(f333(f104(f882(x101182,a870)),x101183),x101184))) % 183.90/184.45 [9816]~P7(x98164,x98168,x98165)+~P7(x98161,x98169,x98163)+~P13(x98161,x98164,f882(x98162,a870),x98163,x98165,x98167)+P12(x98161,f882(x98162,a870),x98163,f333(f333(f8(f882(x98164,f882(x98162,a870)),f882(x98162,a870),x98161),f333(f41(x98164,f882(x98162,a870)),f333(f287(x98164,x98164,x98165),f333(f333(f311(x98164),x98166),f196(f882(x98164,a870)))))),x98167))+~P1(f333(f333(f335(x98164),x98166),x98168)) % 183.90/184.45 [5417]~P106(x54173)+~P14(x54173,x54171)+E(x54171,f760(x54172,x54173))+~E(f333(f174(x54173),x54171),x54172)+~P1(f333(f61(x54173),x54172))+~P1(f333(f138(x54173),x54171)) % 183.90/184.45 [5045]~P111(x50452)+~P124(x50452)+~P129(x50452)+~P140(x50452)+E(x50451,f2(x50452))+~E(f333(f333(f258(x50452),x50451),x50453),f2(x50452)) % 183.90/184.45 [5046]~P111(x50462)+~P124(x50462)+~P129(x50462)+~P140(x50462)+~E(x50461,f2(a875))+~E(f333(f333(f258(x50462),x50463),x50461),f2(x50462)) % 183.90/184.45 [6465]~P85(x64651)+~E(x64653,f2(x64651))+~E(x64652,f2(x64651))+E(f333(f333(f79(x64651),x64652),x64653),f2(x64651))+~P1(f333(f333(f247(x64651),f2(x64651)),x64653))+~P1(f333(f333(f247(x64651),f2(x64651)),x64652)) % 183.90/184.45 [8843]~E(f333(f267(a875,a875),x88433),f2(a875))+~E(x88431,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x88433)),x88432)),f333(f271(a875,a875),x88433)))+P1(f333(f47(x88431,x88432),x88433))+~P1(f333(f333(f247(a875),f333(f271(a875,a875),x88433)),f2(a875)))+P1(f333(f333(f248(a875),f2(a875)),x88432))+~P1(f333(f333(f248(a875),x88432),f333(f271(a875,a875),x88433))) % 183.90/184.45 [8851]E(x88511,f2(a875))+~E(x88512,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x88513)),x88511)),f333(f271(a875,a875),x88513)))+P1(f333(f47(x88512,x88511),x88513))+~P1(f333(f333(f248(a875),f2(a875)),x88511))+~P1(f333(f333(f247(a875),f2(a875)),f333(f271(a875,a875),x88513)))+~P1(f333(f333(f248(a875),f333(f271(a875,a875),x88513)),x88511)) % 183.90/184.45 [8869]~E(f333(f267(a875,a875),x88693),f2(a875))+~E(x88691,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x88693)),x88692)),f333(f271(a875,a875),x88693)))+P1(f333(f47(x88691,x88692),x88693))+~P1(f333(f333(f248(a875),f2(a875)),x88692))+~P1(f333(f333(f247(a875),f2(a875)),f333(f271(a875,a875),x88693)))+~P1(f333(f333(f248(a875),f333(f271(a875,a875),x88693)),x88692)) % 183.90/184.45 [6847]~P62(x68472)+E(x68471,f196(f882(x68472,a870)))+E(x68473,f196(f882(x68472,a870)))+~P1(f333(f61(x68472),x68471))+~P1(f333(f61(x68472),x68473))+E(f13(x68472,f333(f333(f113(f882(x68472,a870)),x68473),x68471)),f333(f333(f113(x68472),f13(x68472,x68473)),f13(x68472,x68471))) % 183.90/184.45 [6848]~P62(x68482)+E(x68481,f196(f882(x68482,a870)))+E(x68483,f196(f882(x68482,a870)))+~P1(f333(f61(x68482),x68481))+~P1(f333(f61(x68482),x68483))+E(f10(x68482,f333(f333(f113(f882(x68482,a870)),x68483),x68481)),f333(f333(f104(x68482),f10(x68482,x68483)),f10(x68482,x68481))) % 183.90/184.45 [6849]~P106(x68492)+E(x68491,f196(f882(x68492,a870)))+E(x68493,f196(f882(x68492,a870)))+~P1(f333(f61(x68492),x68491))+~P1(f333(f61(x68492),x68493))+E(f14(x68492,f333(f333(f113(f882(x68492,a870)),x68493),x68491)),f333(f333(f245(x68492),f14(x68492,x68493)),f14(x68492,x68491))) % 183.90/184.45 [6850]~P106(x68502)+E(x68501,f196(f882(x68502,a870)))+E(x68503,f196(f882(x68502,a870)))+~P1(f333(f61(x68502),x68501))+~P1(f333(f61(x68502),x68503))+E(f15(x68502,f333(f333(f113(f882(x68502,a870)),x68503),x68501)),f333(f333(f246(x68502),f15(x68502,x68503)),f15(x68502,x68501))) % 183.90/184.45 [7491]~P94(x74912)+E(x74911,f196(f882(x74912,a870)))+E(x74913,f196(f882(x74912,a870)))+~P1(f333(f61(x74912),x74911))+~P1(f333(f61(x74912),x74913))+E(f333(f333(f80(x74912),f333(f63(x74912,f80(x74912)),x74913)),f333(f63(x74912,f80(x74912)),x74911)),f333(f63(x74912,f80(x74912)),f333(f333(f113(f882(x74912,a870)),x74913),x74911))) % 183.90/184.45 [7649]~P106(x76492)+E(x76491,f196(f882(x76492,a870)))+E(x76493,f196(f882(x76492,a870)))+~P1(f333(f61(x76492),x76491))+~P1(f333(f61(x76492),x76493))+E(f333(f333(f245(x76492),f11(x76492,f245(x76492),x76493)),f11(x76492,f245(x76492),x76491)),f11(x76492,f245(x76492),f333(f333(f113(f882(x76492,a870)),x76493),x76491))) % 183.90/184.45 [7650]~P106(x76502)+E(x76501,f196(f882(x76502,a870)))+E(x76503,f196(f882(x76502,a870)))+~P1(f333(f61(x76502),x76501))+~P1(f333(f61(x76502),x76503))+E(f333(f333(f246(x76502),f12(x76502,f246(x76502),x76503)),f12(x76502,f246(x76502),x76501)),f12(x76502,f246(x76502),f333(f333(f113(f882(x76502,a870)),x76503),x76501))) % 183.90/184.45 [8691]~P1(f333(x86911,x86913))+P1(f333(x86911,f444(x86911,x86912)))+P1(f333(x86911,f434(x86911,x86912)))+~P1(f333(f333(f248(a1),f2(a1)),x86912))+~P1(f333(f333(f335(a1),x86913),f304(a1,f77(a1),x86912)))+P1(f333(x86911,f333(f333(f22(a1),f434(x86911,x86912)),f333(f333(f80(a1),f442(x86911,x86912)),x86912)))) % 183.90/184.45 [8991]~P1(f333(x89911,x89913))+~P1(f333(x89911,f434(x89911,x89912)))+P1(f333(x89911,f444(x89911,x89912)))+~P1(f333(f333(f248(a1),f2(a1)),x89912))+~P1(f333(f333(f335(a1),x89913),f304(a1,f77(a1),x89912)))+~P1(f333(x89911,f333(f333(f22(a1),f434(x89911,x89912)),f333(f333(f80(a1),f442(x89911,x89912)),x89912)))) % 183.90/184.45 [10196]~P96(x101962)+E(x101961,f196(f882(x101962,a870)))+E(x101963,f196(f882(x101962,a870)))+~P1(f333(f61(x101962),x101961))+~P1(f333(f61(x101962),x101963))+E(f10(x101962,f333(f253(x101962),f333(f333(f8(f882(x101962,a870),a870,x101962),f86(x101962)),f333(f333(f8(f882(x101962,f882(x101962,a870)),f882(x101962,a870),x101962),f333(f8(f882(x101962,a870),a870,x101962),f86(x101962))),f333(f333(f7(x101962,f882(x101962,f882(x101962,a870)),f882(x101962,f882(x101962,a870))),f333(f333(f8(f882(x101962,f882(f882(x101962,a870),f882(x101962,a870))),f882(f882(x101962,f882(x101962,a870)),f882(x101962,f882(x101962,a870))),x101962),f18(x101962,f882(x101962,a870),f882(x101962,a870))),f333(f333(f8(f882(x101962,f882(x101962,f882(a870,a870))),f882(x101962,f882(f882(x101962,a870),f882(x101962,a870))),x101962),f333(f8(f882(x101962,f882(a870,a870)),f882(f882(x101962,a870),f882(x101962,a870)),x101962),f18(x101962,a870,a870))),f333(f333(f8(f882(x101962,f882(x101962,a870)),f882(x101962,f882(x101962,f882(a870,a870))),x101962),f333(f8(f882(x101962,a870),f882(x101962,f882(a870,a870)),x101962),f333(f8(a870,f882(a870,a870),x101962),a331))),f333(f333(f7(x101962,f882(x101962,f882(x101962,x101962)),f882(x101962,f882(x101962,a870))),f333(f333(f8(f882(f882(x101962,x101962),f882(x101962,a870)),f882(f882(x101962,f882(x101962,x101962)),f882(x101962,f882(x101962,a870))),x101962),f8(f882(x101962,x101962),f882(x101962,a870),x101962)),f333(f333(f8(f882(x101962,a870),f882(f882(x101962,x101962),f882(x101962,a870)),x101962),f8(x101962,a870,x101962)),a330))),f113(x101962)))))),f333(f333(f7(x101962,f882(x101962,a870),f882(x101962,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x101962,a870),f882(x101962,a870)),x101962),f8(a870,a870,x101962)),f333(f333(f8(a870,f882(a870,a870),x101962),a331),f333(f333(f7(x101962,f882(x101962,a870),a870),f335(x101962)),x101963)))),f333(f333(f7(x101962,f882(x101962,a870),a870),f335(x101962)),x101961))))))),f333(f333(f113(x101962),f10(x101962,x101963)),f10(x101962,x101961))) % 183.90/184.45 [10197]~P96(x101972)+E(x101971,f196(f882(x101972,a870)))+E(x101973,f196(f882(x101972,a870)))+~P1(f333(f61(x101972),x101971))+~P1(f333(f61(x101972),x101973))+E(f13(x101972,f333(f253(x101972),f333(f333(f8(f882(x101972,a870),a870,x101972),f86(x101972)),f333(f333(f8(f882(x101972,f882(x101972,a870)),f882(x101972,a870),x101972),f333(f8(f882(x101972,a870),a870,x101972),f86(x101972))),f333(f333(f7(x101972,f882(x101972,f882(x101972,a870)),f882(x101972,f882(x101972,a870))),f333(f333(f8(f882(x101972,f882(f882(x101972,a870),f882(x101972,a870))),f882(f882(x101972,f882(x101972,a870)),f882(x101972,f882(x101972,a870))),x101972),f18(x101972,f882(x101972,a870),f882(x101972,a870))),f333(f333(f8(f882(x101972,f882(x101972,f882(a870,a870))),f882(x101972,f882(f882(x101972,a870),f882(x101972,a870))),x101972),f333(f8(f882(x101972,f882(a870,a870)),f882(f882(x101972,a870),f882(x101972,a870)),x101972),f18(x101972,a870,a870))),f333(f333(f8(f882(x101972,f882(x101972,a870)),f882(x101972,f882(x101972,f882(a870,a870))),x101972),f333(f8(f882(x101972,a870),f882(x101972,f882(a870,a870)),x101972),f333(f8(a870,f882(a870,a870),x101972),a331))),f333(f333(f7(x101972,f882(x101972,f882(x101972,x101972)),f882(x101972,f882(x101972,a870))),f333(f333(f8(f882(f882(x101972,x101972),f882(x101972,a870)),f882(f882(x101972,f882(x101972,x101972)),f882(x101972,f882(x101972,a870))),x101972),f8(f882(x101972,x101972),f882(x101972,a870),x101972)),f333(f333(f8(f882(x101972,a870),f882(f882(x101972,x101972),f882(x101972,a870)),x101972),f8(x101972,a870,x101972)),a330))),f104(x101972)))))),f333(f333(f7(x101972,f882(x101972,a870),f882(x101972,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x101972,a870),f882(x101972,a870)),x101972),f8(a870,a870,x101972)),f333(f333(f8(a870,f882(a870,a870),x101972),a331),f333(f333(f7(x101972,f882(x101972,a870),a870),f335(x101972)),x101973)))),f333(f333(f7(x101972,f882(x101972,a870),a870),f335(x101972)),x101971))))))),f333(f333(f104(x101972),f13(x101972,x101973)),f13(x101972,x101971))) % 183.90/184.45 [10198]~P106(x101982)+E(x101981,f196(f882(x101982,a870)))+E(x101983,f196(f882(x101982,a870)))+~P1(f333(f61(x101982),x101981))+~P1(f333(f61(x101982),x101983))+E(f12(x101982,f246(x101982),f333(f253(x101982),f333(f333(f8(f882(x101982,a870),a870,x101982),f86(x101982)),f333(f333(f8(f882(x101982,f882(x101982,a870)),f882(x101982,a870),x101982),f333(f8(f882(x101982,a870),a870,x101982),f86(x101982))),f333(f333(f7(x101982,f882(x101982,f882(x101982,a870)),f882(x101982,f882(x101982,a870))),f333(f333(f8(f882(x101982,f882(f882(x101982,a870),f882(x101982,a870))),f882(f882(x101982,f882(x101982,a870)),f882(x101982,f882(x101982,a870))),x101982),f18(x101982,f882(x101982,a870),f882(x101982,a870))),f333(f333(f8(f882(x101982,f882(x101982,f882(a870,a870))),f882(x101982,f882(f882(x101982,a870),f882(x101982,a870))),x101982),f333(f8(f882(x101982,f882(a870,a870)),f882(f882(x101982,a870),f882(x101982,a870)),x101982),f18(x101982,a870,a870))),f333(f333(f8(f882(x101982,f882(x101982,a870)),f882(x101982,f882(x101982,f882(a870,a870))),x101982),f333(f8(f882(x101982,a870),f882(x101982,f882(a870,a870)),x101982),f333(f8(a870,f882(a870,a870),x101982),a331))),f333(f333(f7(x101982,f882(x101982,f882(x101982,x101982)),f882(x101982,f882(x101982,a870))),f333(f333(f8(f882(f882(x101982,x101982),f882(x101982,a870)),f882(f882(x101982,f882(x101982,x101982)),f882(x101982,f882(x101982,a870))),x101982),f8(f882(x101982,x101982),f882(x101982,a870),x101982)),f333(f333(f8(f882(x101982,a870),f882(f882(x101982,x101982),f882(x101982,a870)),x101982),f8(x101982,a870,x101982)),a330))),f245(x101982)))))),f333(f333(f7(x101982,f882(x101982,a870),f882(x101982,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x101982,a870),f882(x101982,a870)),x101982),f8(a870,a870,x101982)),f333(f333(f8(a870,f882(a870,a870),x101982),a331),f333(f333(f7(x101982,f882(x101982,a870),a870),f335(x101982)),x101983)))),f333(f333(f7(x101982,f882(x101982,a870),a870),f335(x101982)),x101981))))))),f333(f333(f245(x101982),f12(x101982,f246(x101982),x101983)),f12(x101982,f246(x101982),x101981))) % 183.90/184.45 [10199]~P106(x101992)+E(x101991,f196(f882(x101992,a870)))+E(x101993,f196(f882(x101992,a870)))+~P1(f333(f61(x101992),x101991))+~P1(f333(f61(x101992),x101993))+E(f11(x101992,f245(x101992),f333(f253(x101992),f333(f333(f8(f882(x101992,a870),a870,x101992),f86(x101992)),f333(f333(f8(f882(x101992,f882(x101992,a870)),f882(x101992,a870),x101992),f333(f8(f882(x101992,a870),a870,x101992),f86(x101992))),f333(f333(f7(x101992,f882(x101992,f882(x101992,a870)),f882(x101992,f882(x101992,a870))),f333(f333(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))),f333(f333(f8(f882(x101992,f882(x101992,f882(a870,a870))),f882(x101992,f882(f882(x101992,a870),f882(x101992,a870))),x101992),f333(f8(f882(x101992,f882(a870,a870)),f882(f882(x101992,a870),f882(x101992,a870)),x101992),f18(x101992,a870,a870))),f333(f333(f8(f882(x101992,f882(x101992,a870)),f882(x101992,f882(x101992,f882(a870,a870))),x101992),f333(f8(f882(x101992,a870),f882(x101992,f882(a870,a870)),x101992),f333(f8(a870,f882(a870,a870),x101992),a331))),f333(f333(f7(x101992,f882(x101992,f882(x101992,x101992)),f882(x101992,f882(x101992,a870))),f333(f333(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)),f333(f333(f8(f882(x101992,a870),f882(f882(x101992,x101992),f882(x101992,a870)),x101992),f8(x101992,a870,x101992)),a330))),f246(x101992)))))),f333(f333(f7(x101992,f882(x101992,a870),f882(x101992,a870)),f333(f333(f8(f882(a870,a870),f882(f882(x101992,a870),f882(x101992,a870)),x101992),f8(a870,a870,x101992)),f333(f333(f8(a870,f882(a870,a870),x101992),a331),f333(f333(f7(x101992,f882(x101992,a870),a870),f335(x101992)),x101993)))),f333(f333(f7(x101992,f882(x101992,a870),a870),f335(x101992)),x101991))))))),f333(f333(f246(x101992),f11(x101992,f245(x101992),x101993)),f11(x101992,f245(x101992),x101991))) % 183.90/184.45 [7175]~P120(x71753)+E(x71751,x71752)+~E(f333(f333(f258(x71753),x71751),x71754),f333(f333(f258(x71753),x71752),x71754))+~P1(f333(f333(f247(x71753),f2(x71753)),x71752))+~P1(f333(f333(f247(x71753),f2(x71753)),x71751))+~P1(f333(f333(f248(a875),f2(a875)),x71754)) % 183.90/184.45 [7448]~P106(x74482)+E(x74481,f196(f882(x74482,a870)))+~P1(f333(f61(x74482),x74481))+~P1(f333(f333(f335(x74482),x74484),x74481))+P1(f333(f333(f248(x74482),x74483),x74484))+~P1(f333(f333(f248(x74482),x74483),f333(f63(x74482,f245(x74482)),x74481))) % 183.90/184.45 [7449]~P99(x74492)+E(x74491,f196(f882(x74492,a870)))+~P1(f333(f61(x74492),x74491))+~P1(f333(f333(f335(x74492),x74494),x74491))+P1(f333(f333(f247(x74492),x74493),x74494))+~P1(f333(f333(f247(x74492),x74493),f333(f63(x74492,f104(x74492)),x74491))) % 183.90/184.45 [7450]~P106(x74502)+E(x74501,f196(f882(x74502,a870)))+~P1(f333(f61(x74502),x74501))+~P1(f333(f333(f335(x74502),x74504),x74501))+P1(f333(f333(f247(x74502),x74503),x74504))+~P1(f333(f333(f247(x74502),x74503),f333(f63(x74502,f245(x74502)),x74501))) % 183.90/184.45 [7349]E(x73491,f2(a1))+E(f333(f333(f38(a1),x73492),x73491),x73493)+~P1(f333(f333(f247(a1),x73494),f2(a1)))+~E(x73492,f333(f333(f79(a1),f333(f333(f80(a1),x73491),x73493)),x73494))+P1(f333(f333(f248(a1),f2(a1)),x73491))+~P1(f333(f333(f248(a1),x73491),x73494)) % 183.90/184.45 [7364]E(f44(a1,x73642,x73641),x73643)+E(x73641,f2(a1))+~P1(f333(f333(f247(a1),x73643),f2(a1)))+~E(x73642,f333(f333(f79(a1),f333(f333(f80(a1),x73641),x73644)),x73643))+P1(f333(f333(f248(a1),f2(a1)),x73641))+~P1(f333(f333(f248(a1),x73641),x73643)) % 183.90/184.45 [7490]E(x74901,f2(a1))+E(f333(f333(f38(a1),x74902),x74901),x74903)+~E(x74902,f333(f333(f79(a1),f333(f333(f80(a1),x74901),x74903)),x74904))+~P1(f333(f333(f248(a1),f2(a1)),x74901))+~P1(f333(f333(f247(a1),f2(a1)),x74904))+~P1(f333(f333(f248(a1),x74904),x74901)) % 183.90/184.45 [7512]E(f44(a1,x75122,x75121),x75123)+E(x75121,f2(a1))+~E(x75122,f333(f333(f79(a1),f333(f333(f80(a1),x75121),x75124)),x75123))+~P1(f333(f333(f248(a1),f2(a1)),x75121))+~P1(f333(f333(f247(a1),f2(a1)),x75123))+~P1(f333(f333(f248(a1),x75123),x75121)) % 183.90/184.45 [7653]~P106(x76532)+E(x76531,f196(f882(x76532,a870)))+~P1(f333(f61(x76532),x76531))+~P1(f333(f333(f248(x76532),x76534),x76533))+~P1(f333(f333(f335(x76532),x76534),x76531))+P1(f333(f333(f248(x76532),f333(f63(x76532,f245(x76532)),x76531)),x76533)) % 183.90/184.45 [7654]~P106(x76542)+E(x76541,f196(f882(x76542,a870)))+~P1(f333(f61(x76542),x76541))+~P1(f333(f333(f247(x76542),x76544),x76543))+~P1(f333(f333(f335(x76542),x76544),x76541))+P1(f333(f333(f247(x76542),f333(f63(x76542,f245(x76542)),x76541)),x76543)) % 183.90/184.45 [8236]~P1(f333(f333(f247(a1),x82364),f2(a1)))+~E(x82361,f333(f333(f79(a1),f333(f333(f80(a1),x82362),x82363)),x82364))+~P1(f333(f333(f247(a1),f2(a1)),x82364))+~P1(f333(f333(f248(a1),x82364),x82362))+~P1(f333(f333(f248(a1),x82362),x82364))+P1(f333(f48(x82361,x82362),f333(f333(f268(a1,a1),x82363),x82364))) % 183.90/184.45 [9184]~P57(x91843)+~P57(x91844)+E(x91841,x91842)+~E(f333(f197(f876(x91843)),x91842),f333(f197(f876(x91844)),f55(x91844)))+~E(f333(f197(f876(x91843)),x91841),f333(f197(f876(x91844)),f55(x91844)))+~E(f333(f72(f879(x91843),x91843,x91844,f244(x91843)),f333(f180(x91844,x91843),f333(f333(f184(x91844,x91843),f55(x91844)),x91841))),f333(f72(f879(x91843),x91843,x91844,f244(x91843)),f333(f180(x91844,x91843),f333(f333(f184(x91844,x91843),f55(x91844)),x91842)))) % 183.90/184.45 [8401]~P108(x84011)+P1(f333(f333(f248(f882(x84011,a870)),f304(x84011,x84012,x84013)),f304(x84011,x84014,x84015)))+~P1(f333(f333(f248(x84011),x84013),x84015))+~P1(f333(f333(f247(x84011),x84014),x84012))+~P1(f333(f333(f247(x84011),x84014),x84015))+~P1(f333(f333(f247(x84011),x84013),x84015)) % 183.90/184.45 [8402]~P108(x84021)+P1(f333(f333(f248(f882(x84021,a870)),f304(x84021,x84022,x84023)),f304(x84021,x84024,x84025)))+~P1(f333(f333(f248(x84021),x84024),x84022))+~P1(f333(f333(f247(x84021),x84023),x84025))+~P1(f333(f333(f247(x84021),x84024),x84025))+~P1(f333(f333(f247(x84021),x84024),x84022)) % 183.90/184.45 [9249]P53(x92492,x92493,x92494,x92491)+E(x92491,f196(f882(x92492,a870)))+~P1(f333(f61(x92492),x92494))+~P1(f333(f61(x92492),x92491))+~P1(f333(f333(x92493,f560(x92491,x92494,x92493,x92492)),x92495))+~P1(f333(f333(f335(x92492),x92495),x92491)) % 183.90/184.45 [9398]~E(x93983,x93985)+~P66(x93981)+~P73(x93981)+~P38(x93983)+E(f333(f333(f6(a1,x93981),x93982),x93983),f333(f333(f6(a1,x93981),x93984),x93985))+P1(f333(f333(f247(a1),f2(a1)),f467(x93982,x93984,x93983,x93985,x93981))) % 183.90/184.45 [9399]~E(x93993,x93995)+~P66(x93991)+~P73(x93991)+~P38(x93993)+E(f333(f333(f9(a1,x93991),x93992),x93993),f333(f333(f9(a1,x93991),x93994),x93995))+P1(f333(f333(f247(a1),f2(a1)),f463(x93992,x93994,x93993,x93995,x93991))) % 183.90/184.45 [9566]~E(x95665,x95663)+~P66(x95661)+~P73(x95661)+~P38(x95665)+~E(f333(x95662,f467(x95664,x95662,x95665,x95663,x95661)),f333(x95664,f467(x95664,x95662,x95665,x95663,x95661)))+E(f333(f333(f6(a1,x95661),x95662),x95663),f333(f333(f6(a1,x95661),x95664),x95665)) % 183.90/184.45 [9567]~E(x95675,x95673)+~P66(x95671)+~P73(x95671)+~P38(x95675)+~E(f333(x95672,f463(x95674,x95672,x95675,x95673,x95671)),f333(x95674,f463(x95674,x95672,x95675,x95673,x95671)))+E(f333(f333(f9(a1,x95671),x95672),x95673),f333(f333(f9(a1,x95671),x95674),x95675)) % 183.90/184.45 [9655]~P82(x96553)+E(f333(x96551,x96552),f2(x96553))+~E(f333(f333(f6(x96554,x96553),x96551),x96555),f2(x96553))+~P1(f333(f61(x96554),x96555))+P1(f333(f333(f335(x96554),f399(x96552,x96551,x96555,x96554,x96553)),x96555))+~P1(f333(f333(f335(x96554),x96552),x96555)) % 183.90/184.45 [9790]~P82(x97903)+E(f333(x97901,x97902),f2(x97903))+~E(f333(f333(f6(x97904,x97903),x97901),x97905),f2(x97903))+~P1(f333(f61(x97904),x97905))+~P1(f333(f333(f335(x97904),x97902),x97905))+~P1(f333(f333(f247(x97903),f2(x97903)),f333(x97901,f399(x97902,x97901,x97905,x97904,x97903)))) % 183.90/184.45 [8317]~P125(x83171)+~P1(f333(f333(f247(x83171),f2(x83171)),x83173))+~P1(f333(f333(f248(x83171),x83173),x83175))+~P1(f333(f333(f248(x83171),x83172),x83174))+~P1(f333(f333(f248(x83171),f2(x83171)),x83174))+P1(f333(f333(f248(x83171),f333(f333(f80(x83171),x83172),x83173)),f333(f333(f80(x83171),x83174),x83175))) % 183.90/184.45 [8318]~P125(x83181)+~P1(f333(f333(f247(x83181),f2(x83181)),x83183))+~P1(f333(f333(f247(x83181),f2(x83181)),x83182))+~P1(f333(f333(f248(x83181),x83183),x83185))+~P1(f333(f333(f248(x83181),x83182),x83184))+P1(f333(f333(f248(x83181),f333(f333(f80(x83181),x83182),x83183)),f333(f333(f80(x83181),x83184),x83185))) % 183.90/184.45 [8319]~P125(x83191)+~P1(f333(f333(f247(x83191),x83192),x83194))+~P1(f333(f333(f247(x83191),f2(x83191)),x83193))+~P1(f333(f333(f248(x83191),x83193),x83195))+~P1(f333(f333(f248(x83191),f2(x83191)),x83192))+P1(f333(f333(f248(x83191),f333(f333(f80(x83191),x83192),x83193)),f333(f333(f80(x83191),x83194),x83195))) % 183.90/184.45 [8320]~P125(x83201)+~P1(f333(f333(f247(x83201),x83203),x83205))+~P1(f333(f333(f247(x83201),f2(x83201)),x83202))+~P1(f333(f333(f248(x83201),x83202),x83204))+~P1(f333(f333(f248(x83201),f2(x83201)),x83203))+P1(f333(f333(f248(x83201),f333(f333(f80(x83201),x83202),x83203)),f333(f333(f80(x83201),x83204),x83205))) % 183.90/184.45 [8321]~P61(x83211)+~P1(f333(f333(f247(x83211),x83212),x83214))+~P1(f333(f333(f248(x83211),x83215),x83213))+~P1(f333(f333(f248(x83211),f2(x83211)),x83215))+~P1(f333(f333(f248(x83211),f2(x83211)),x83212))+P1(f333(f333(f248(x83211),f333(f333(f291(x83211),x83212),x83213)),f333(f333(f291(x83211),x83214),x83215))) % 183.90/184.45 [8322]~P61(x83221)+~P1(f333(f333(f247(x83221),x83225),x83223))+~P1(f333(f333(f247(x83221),f2(x83221)),x83222))+~P1(f333(f333(f248(x83221),x83222),x83224))+~P1(f333(f333(f248(x83221),f2(x83221)),x83225))+P1(f333(f333(f248(x83221),f333(f333(f291(x83221),x83222),x83223)),f333(f333(f291(x83221),x83224),x83225))) % 183.90/184.45 [8323]~P132(x83231)+~P1(f333(f333(f247(x83231),x83233),x83235))+~P1(f333(f333(f247(x83231),x83232),x83234))+~P1(f333(f333(f247(x83231),f2(x83231)),x83233))+~P1(f333(f333(f247(x83231),f2(x83231)),x83234))+P1(f333(f333(f247(x83231),f333(f333(f80(x83231),x83232),x83233)),f333(f333(f80(x83231),x83234),x83235))) % 183.90/184.45 [8324]~P132(x83241)+~P1(f333(f333(f247(x83241),x83243),x83245))+~P1(f333(f333(f247(x83241),x83242),x83244))+~P1(f333(f333(f247(x83241),f2(x83241)),x83243))+~P1(f333(f333(f247(x83241),f2(x83241)),x83242))+P1(f333(f333(f247(x83241),f333(f333(f80(x83241),x83242),x83243)),f333(f333(f80(x83241),x83244),x83245))) % 183.90/184.45 [8325]~P61(x83251)+~P1(f333(f333(f248(x83251),f2(x83251)),x83255))+~P1(f333(f333(f247(x83251),x83255),x83253))+~P1(f333(f333(f247(x83251),x83252),x83254))+~P1(f333(f333(f247(x83251),f2(x83251)),x83252))+P1(f333(f333(f247(x83251),f333(f333(f291(x83251),x83252),x83253)),f333(f333(f291(x83251),x83254),x83255))) % 183.90/184.45 [9694]~P66(x96945)+~P79(x96945)+E(x96941,f196(f882(x96942,a870)))+~P1(f333(f61(x96942),x96941))+P1(f333(f333(f335(x96942),f460(x96943,x96944,x96941,x96942,x96945)),x96941))+P1(f333(f333(f248(x96945),f333(f333(f6(x96942,x96945),x96944),x96941)),f333(f333(f6(x96942,x96945),x96943),x96941))) % 183.90/184.45 [9812]~P66(x98121)+~P81(x98121)+~P1(f333(f61(x98122),x98125))+~P1(f333(f333(f247(x98121),f2(x98121)),f333(x98123,f379(x98123,x98124,x98125,x98122,x98121))))+P1(f333(f333(f247(x98121),f333(f333(f6(x98122,x98121),x98123),x98124)),f333(f333(f6(x98122,x98121),x98123),x98125)))+~P1(f333(f333(f247(f882(x98122,a870)),x98124),x98125)) % 183.90/184.45 [9980]~P66(x99803)+~P79(x99803)+E(x99801,f196(f882(x99802,a870)))+~P1(f333(f61(x99802),x99801))+~P1(f333(f333(f248(x99803),f333(x99804,f460(x99805,x99804,x99801,x99802,x99803))),f333(x99805,f460(x99805,x99804,x99801,x99802,x99803))))+P1(f333(f333(f248(x99803),f333(f333(f6(x99802,x99803),x99804),x99801)),f333(f333(f6(x99802,x99803),x99805),x99801))) % 183.90/184.45 [7034]~P17(x70342,x70345,x70344)+E(x70341,f196(f882(x70342,a870)))+E(x70343,f196(f882(x70342,a870)))+~P1(f333(f61(x70342),x70341))+~P1(f333(f61(x70342),x70343))+E(f333(x70344,f333(f333(f113(f882(x70342,a870)),x70343),x70341)),f333(f333(x70345,f333(x70344,x70343)),f333(x70344,x70341))) % 183.90/184.45 [7619]~P144(x76191,x76194,x76193)+P1(f333(x76191,x76192))+~P1(f333(f333(f248(a1),x76194),f2(a1)))+~P1(f333(f333(f247(a1),x76195),f2(a1)))+~E(x76193,f333(f333(f79(a1),f333(f333(f80(a1),x76194),x76192)),x76195))+~P1(f333(f333(f248(a1),x76194),x76195)) % 183.90/184.45 [7620]~P143(x76201,x76204,x76203)+P1(f333(x76201,x76202))+~P1(f333(f333(f248(a1),x76204),f2(a1)))+~P1(f333(f333(f247(a1),x76202),f2(a1)))+~E(x76203,f333(f333(f79(a1),f333(f333(f80(a1),x76204),x76205)),x76202))+~P1(f333(f333(f248(a1),x76204),x76202)) % 183.90/184.45 [7662]~P144(x76621,x76624,x76623)+P1(f333(x76621,x76622))+~E(x76623,f333(f333(f79(a1),f333(f333(f80(a1),x76624),x76622)),x76625))+~P1(f333(f333(f248(a1),f2(a1)),x76624))+~P1(f333(f333(f247(a1),f2(a1)),x76625))+~P1(f333(f333(f248(a1),x76625),x76624)) % 183.90/184.45 [7663]~P143(x76631,x76634,x76633)+P1(f333(x76631,x76632))+~E(x76633,f333(f333(f79(a1),f333(f333(f80(a1),x76634),x76635)),x76632))+~P1(f333(f333(f248(a1),f2(a1)),x76634))+~P1(f333(f333(f247(a1),f2(a1)),x76632))+~P1(f333(f333(f248(a1),x76632),x76634)) % 183.90/184.45 [8613]P1(f333(f333(x86131,x86132),x86133))+~P1(f333(f333(x86131,f333(f333(f38(a1),x86134),x86135)),f44(a1,x86134,x86135)))+~P1(f333(f333(f248(a1),x86135),f2(a1)))+~P1(f333(f333(f247(a1),x86133),f2(a1)))+~E(x86134,f333(f333(f79(a1),f333(f333(f80(a1),x86135),x86132)),x86133))+~P1(f333(f333(f248(a1),x86135),x86133)) % 183.90/184.45 [8622]P1(f333(f333(x86221,x86222),x86223))+~P1(f333(f333(x86221,f333(f333(f38(a1),x86224),x86225)),f44(a1,x86224,x86225)))+~E(x86224,f333(f333(f79(a1),f333(f333(f80(a1),x86225),x86222)),x86223))+~P1(f333(f333(f248(a1),f2(a1)),x86225))+~P1(f333(f333(f247(a1),f2(a1)),x86223))+~P1(f333(f333(f248(a1),x86223),x86225)) % 183.90/184.45 [8857]E(x88571,x88572)+~P50(x88573,x88575,x88574)+~P1(f333(f333(f335(x88573),x88572),x88575))+~P1(f333(f333(f335(x88573),x88571),x88575))+P1(f333(f333(f335(f881(x88573,x88573)),f333(f333(f268(x88573,x88573),x88571),x88572)),x88574))+P1(f333(f333(f335(f881(x88573,x88573)),f333(f333(f268(x88573,x88573),x88572),x88571)),x88574)) % 183.90/184.45 [9721]~P66(x97215)+~P81(x97215)+~P1(f333(f61(x97211),x97214))+P1(f333(f333(f247(x97215),f333(f333(f6(x97211,x97215),x97212),x97213)),f333(f333(f6(x97211,x97215),x97212),x97214)))+~P1(f333(f333(f247(f882(x97211,a870)),x97213),x97214))+P1(f333(f333(f335(x97211),f379(x97212,x97213,x97214,x97211,x97215)),f333(f333(f22(f882(x97211,a870)),x97214),x97213))) % 183.90/184.45 [9820]E(x98201,f196(f882(x98202,a870)))+~P1(f333(f61(x98202),x98203))+~P1(f333(f61(x98202),x98201))+P1(f333(f333(f335(f881(f882(x98202,a870),f882(x98202,a870))),f333(f333(f268(f882(x98202,a870),f882(x98202,a870)),x98203),x98201)),f325(x98202,x98204)))+~P1(f333(f333(f335(x98202),x98205),x98201))+~P1(f333(f333(f335(f881(x98202,x98202)),f333(f333(f268(x98202,x98202),f568(x98204,x98201,x98203,x98202)),x98205)),x98204)) % 183.90/184.45 [9821]E(x98211,f196(f882(x98212,a870)))+~P1(f333(f61(x98212),x98213))+~P1(f333(f61(x98212),x98211))+P1(f333(f333(f335(f881(f882(x98212,a870),f882(x98212,a870))),f333(f333(f268(f882(x98212,a870),f882(x98212,a870)),x98213),x98211)),f325(x98212,x98214)))+~P1(f333(f333(f335(x98212),x98215),x98211))+~P1(f333(f333(f335(f881(x98212,x98212)),f333(f333(f268(x98212,x98212),f621(x98214,x98211,x98213,x98212)),x98215)),x98214)) % 183.90/184.45 [9984]~P82(x99841)+~E(f333(f333(f6(x99845,x99841),x99842),x99846),x99844)+~P1(f333(f61(x99845),x99846))+P1(f333(f333(f335(x99845),f400(x99843,x99844,x99842,x99846,x99845,x99841)),x99846))+P1(f333(f333(f247(x99841),f333(x99842,x99843)),x99844))+~P1(f333(f333(f335(x99845),x99843),x99846)) % 183.90/184.45 [10031]~P82(x100311)+~E(f333(f333(f6(x100315,x100311),x100312),x100316),x100314)+~P1(f333(f61(x100315),x100316))+~P1(f333(f333(f335(x100315),x100313),x100316))+~P1(f333(f333(f247(x100311),f2(x100311)),f333(x100312,f400(x100313,x100314,x100312,x100316,x100315,x100311))))+P1(f333(f333(f247(x100311),f333(x100312,x100313)),x100314)) % 183.90/184.45 [10144]~E(x101445,x101448)+~E(x101444,x101447)+~P66(x101442)+~P107(x101441)+E(f333(f333(f6(x101441,x101442),x101443),f333(f303(x101441,x101444),x101445)),f333(f333(f6(x101441,x101442),x101446),f333(f303(x101441,x101447),x101448)))+P1(f333(f333(f247(x101441),x101444),f624(x101443,x101446,x101445,x101448,x101444,x101447,x101441,x101442))) % 183.90/184.45 [10161]~E(x101617,x101614)+~E(x101618,x101615)+~P66(x101612)+~P107(x101611)+~E(f333(x101613,f624(x101616,x101613,x101618,x101615,x101617,x101614,x101611,x101612)),f333(x101616,f624(x101616,x101613,x101618,x101615,x101617,x101614,x101611,x101612)))+E(f333(f333(f6(x101611,x101612),x101613),f333(f303(x101611,x101614),x101615)),f333(f333(f6(x101611,x101612),x101616),f333(f303(x101611,x101617),x101618))) % 183.90/184.45 [10163]~E(x101634,x101637)+~E(x101635,x101638)+~P66(x101632)+~P107(x101631)+E(f333(f333(f6(x101631,x101632),x101633),f333(f303(x101631,x101634),x101635)),f333(f333(f6(x101631,x101632),x101636),f333(f303(x101631,x101637),x101638)))+P1(f333(f333(f248(x101631),f624(x101633,x101636,x101635,x101638,x101634,x101637,x101631,x101632)),x101635)) % 183.90/184.45 [9826]~P7(x98265,x98269,x98266)+~P7(x98261,x982610,x98263)+~P13(x98261,x98265,f882(x98262,a870),x98263,x98266,x98268)+~P1(f333(f333(f335(x98265),x98267),x98269))+~P1(f333(f333(f335(x98261),x98264),x982610))+E(f333(f333(f41(x98261,f882(x98262,a870)),f333(f287(x98261,x98261,x98263),f333(f333(f311(x98261),x98264),f196(f882(x98261,a870))))),f333(f333(f8(f882(x98265,f882(x98262,a870)),f882(x98262,a870),x98261),f333(f41(x98265,f882(x98262,a870)),f333(f287(x98265,x98265,x98266),f333(f333(f311(x98265),x98267),f196(f882(x98265,a870)))))),x98268)),f333(f333(x98268,x98264),x98267)) % 183.90/184.45 [5585]~P106(x55853)+~P14(x55853,x55852)+~P14(x55853,x55851)+E(x55851,x55852)+~E(f333(f174(x55853),x55851),f333(f174(x55853),x55852))+~P1(f333(f138(x55853),x55852))+~P1(f333(f138(x55853),x55851)) % 183.90/184.45 [4930]~P111(x49302)+~P124(x49302)+~P129(x49302)+~P140(x49302)+~E(x49303,f2(x49302))+E(x49301,f2(a875))+E(f333(f333(f258(x49302),x49303),x49301),f2(x49302)) % 183.90/184.45 [9125]E(x91251,f2(a875))+~E(x91252,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x91253)),x91251)),f333(f271(a875,a875),x91253)))+P1(f333(f47(x91252,x91251),x91253))+~P1(f333(f333(f247(a875),f333(f271(a875,a875),x91253)),f2(a875)))+~P1(f333(f333(f247(a875),f2(a875)),f333(f271(a875,a875),x91253)))+~P1(f333(f333(f248(a875),x91251),f333(f271(a875,a875),x91253)))+~P1(f333(f333(f248(a875),f333(f271(a875,a875),x91253)),x91251)) % 183.90/184.45 [9134]~E(f333(f267(a875,a875),x91343),f2(a875))+~E(x91341,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),x91343)),x91342)),f333(f271(a875,a875),x91343)))+P1(f333(f47(x91341,x91342),x91343))+~P1(f333(f333(f247(a875),f333(f271(a875,a875),x91343)),f2(a875)))+~P1(f333(f333(f247(a875),f2(a875)),f333(f271(a875,a875),x91343)))+~P1(f333(f333(f248(a875),x91342),f333(f271(a875,a875),x91343)))+~P1(f333(f333(f248(a875),f333(f271(a875,a875),x91343)),x91342)) % 183.90/184.45 [7982]~P67(x79822)+E(x79821,f196(f882(x79822,a870)))+E(x79823,f196(f882(x79822,a870)))+~P1(f333(f61(x79822),x79821))+~P1(f333(f61(x79822),x79823))+~E(f333(f333(f104(f882(x79822,a870)),x79823),x79821),f196(f882(x79822,a870)))+E(f333(f333(f80(x79822),f333(f63(x79822,f80(x79822)),x79823)),f333(f63(x79822,f80(x79822)),x79821)),f333(f63(x79822,f80(x79822)),f333(f333(f113(f882(x79822,a870)),x79823),x79821))) % 183.90/184.45 [7762]E(x77621,f2(a1))+E(f333(f333(f38(a1),x77622),x77621),x77623)+~P1(f333(f333(f247(a1),x77624),f2(a1)))+~E(x77622,f333(f333(f79(a1),f333(f333(f80(a1),x77621),x77623)),x77624))+~P1(f333(f333(f247(a1),f2(a1)),x77624))+~P1(f333(f333(f248(a1),x77624),x77621))+~P1(f333(f333(f248(a1),x77621),x77624)) % 183.90/184.45 [7771]E(f44(a1,x77712,x77711),x77713)+E(x77711,f2(a1))+~P1(f333(f333(f247(a1),x77713),f2(a1)))+~E(x77712,f333(f333(f79(a1),f333(f333(f80(a1),x77711),x77714)),x77713))+~P1(f333(f333(f247(a1),f2(a1)),x77713))+~P1(f333(f333(f248(a1),x77713),x77711))+~P1(f333(f333(f248(a1),x77711),x77713)) % 183.90/184.45 [7671]~P18(x76712,x76715,x76714)+E(x76711,f196(f882(x76712,a870)))+E(x76713,f196(f882(x76712,a870)))+~P1(f333(f61(x76712),x76711))+~P1(f333(f61(x76712),x76713))+~E(f333(f333(f104(f882(x76712,a870)),x76713),x76711),f196(f882(x76712,a870)))+E(f333(x76714,f333(f333(f113(f882(x76712,a870)),x76713),x76711)),f333(f333(x76715,f333(x76714,x76713)),f333(x76714,x76711))) % 183.90/184.45 [9370]~P25(x93703,x93701,x93705,x93704)+~P25(x93701,x93703,x93706,x93702)+E(f333(f37(x93701),x93702),f333(f37(x93703),x93704))+~P1(f333(f61(x93703),x93704))+~P1(f333(f61(x93701),x93702))+~P1(f333(f333(f247(f882(x93703,a870)),f333(f312(x93701,x93703,x93706),x93702)),x93704))+~P1(f333(f333(f247(f882(x93701,a870)),f333(f312(x93703,x93701,x93705),x93704)),x93702)) % 183.90/184.45 [9314]~P1(f333(f333(f248(a1),f333(f333(f79(a1),f333(f333(f80(a1),x93145),x93141)),x93146)),f2(a1)))+~E(f333(f333(f79(a1),f333(f333(f80(a1),x93143),x93142)),x93144),f333(f333(f79(a1),f333(f333(f80(a1),x93145),x93141)),x93146))+~P1(f333(f333(f248(a1),f2(a1)),x93145))+~P1(f333(f333(f247(a1),f2(a1)),x93146))+~P1(f333(f333(f248(a1),x93144),x93143))+~P1(f333(f333(f247(a1),x93145),x93143))+P1(f333(f333(f247(a1),x93141),x93142)) % 183.90/184.45 [9078]~E(f333(f333(f79(a1),f333(f333(f80(a1),x90783),x90781)),x90784),f333(f333(f79(a1),f333(f333(f80(a1),x90785),x90782)),x90786))+~P1(f333(f333(f248(a1),f2(a1)),x90785))+~P1(f333(f333(f247(a1),f2(a1)),x90784))+~P1(f333(f333(f248(a1),x90786),x90785))+~P1(f333(f333(f247(a1),x90785),x90783))+P1(f333(f333(f247(a1),x90781),x90782))+~P1(f333(f333(f247(a1),f2(a1)),f333(f333(f79(a1),f333(f333(f80(a1),x90785),x90782)),x90786))) % 183.90/184.45 [9255]~P128(x92551)+~E(f333(f333(f79(x92551),x92552),x92554),f77(x92551))+~P1(f333(f333(f247(x92551),f2(x92551)),x92554))+~P1(f333(f333(f247(x92551),f2(x92551)),x92552))+~P1(f333(f333(f248(x92551),x92555),x92556))+~P1(f333(f333(f248(x92551),x92553),x92556))+P1(f333(f333(f248(x92551),f333(f333(f79(x92551),f333(f333(f80(x92551),x92552),x92553)),f333(f333(f80(x92551),x92554),x92555))),x92556)) % 183.90/184.45 [9256]~P127(x92561)+~E(f333(f333(f79(x92561),x92562),x92564),f77(x92561))+~P1(f333(f333(f247(x92561),x92565),x92566))+~P1(f333(f333(f247(x92561),x92563),x92566))+~P1(f333(f333(f247(x92561),f2(x92561)),x92564))+~P1(f333(f333(f247(x92561),f2(x92561)),x92562))+P1(f333(f333(f247(x92561),f333(f333(f79(x92561),f333(f333(f80(x92561),x92562),x92563)),f333(f333(f80(x92561),x92564),x92565))),x92566)) % 183.90/184.45 [10077]~P7(x100777,x100776,x100775)+E(x100771,x100772)+~P12(x100777,f882(x100774,a870),x100775,x100773)+E(f333(x100773,f543(x100771,x100772,x100773,x100774,x100775,x100776,x100777)),f333(x100773,f542(x100771,x100772,x100773,x100774,x100775,x100776,x100777)))+~E(f333(f333(f41(x100777,f882(x100774,a870)),x100771),x100773),f333(f333(f41(x100777,f882(x100774,a870)),x100772),x100773))+~P1(f333(f333(f335(f882(x100777,a870)),x100772),f333(f333(f60(x100777),x100776),x100775)))+~P1(f333(f333(f335(f882(x100777,a870)),x100771),f333(f333(f60(x100777),x100776),x100775))) % 183.90/184.45 [10111]~P7(x101113,x101117,x101116)+E(x101111,x101112)+~P12(x101113,f882(x101115,a870),x101116,x101114)+~E(f333(f333(f41(x101113,f882(x101115,a870)),x101111),x101114),f333(f333(f41(x101113,f882(x101115,a870)),x101112),x101114))+P1(f333(f333(f335(x101113),f542(x101111,x101112,x101114,x101115,x101116,x101117,x101113)),x101117))+~P1(f333(f333(f335(f882(x101113,a870)),x101112),f333(f333(f60(x101113),x101117),x101116)))+~P1(f333(f333(f335(f882(x101113,a870)),x101111),f333(f333(f60(x101113),x101117),x101116))) % 183.90/184.45 [10112]~P7(x101123,x101127,x101126)+E(x101121,x101122)+~P12(x101123,f882(x101125,a870),x101126,x101124)+~E(f333(f333(f41(x101123,f882(x101125,a870)),x101121),x101124),f333(f333(f41(x101123,f882(x101125,a870)),x101122),x101124))+P1(f333(f333(f335(x101123),f543(x101121,x101122,x101124,x101125,x101126,x101127,x101123)),x101127))+~P1(f333(f333(f335(f882(x101123,a870)),x101122),f333(f333(f60(x101123),x101127),x101126)))+~P1(f333(f333(f335(f882(x101123,a870)),x101121),f333(f333(f60(x101123),x101127),x101126))) % 183.90/184.45 [10180]E(x101801,x101802)+~P7(x101803,x101806,x101807)+~P12(x101803,f882(x101804,a870),x101807,x101805)+~E(f333(f333(f41(x101803,f882(x101804,a870)),x101801),x101805),f333(f333(f41(x101803,f882(x101804,a870)),x101802),x101805))+~P1(f333(f333(f335(f881(x101803,x101803)),f333(f333(f268(x101803,x101803),f542(x101801,x101802,x101805,x101804,x101807,x101806,x101803)),f543(x101801,x101802,x101805,x101804,x101807,x101806,x101803))),x101807))+~P1(f333(f333(f335(f882(x101803,a870)),x101802),f333(f333(f60(x101803),x101806),x101807)))+~P1(f333(f333(f335(f882(x101803,a870)),x101801),f333(f333(f60(x101803),x101806),x101807))) % 183.90/184.45 [9077]~P7(x90771,x90777,x90774)+~E(x90775,x90776)+~P1(f333(f333(f335(x90771),x90773),x90776))+~P1(f333(f333(f335(x90771),x90772),x90775))+~P1(f333(f333(f335(f882(x90771,a870)),x90776),f333(f333(f60(x90771),x90777),x90774)))+~P1(f333(f333(f335(f882(x90771,a870)),x90775),f333(f333(f60(x90771),x90777),x90774)))+P1(f333(f333(f335(f881(x90771,x90771)),f333(f333(f268(x90771,x90771),x90772),x90773)),x90774)) % 183.90/184.45 [9212]E(x92121,x92122)+~P7(x92123,x92124,x92125)+~P1(f333(f333(f335(x92123),x92126),x92122))+~P1(f333(f333(f335(x92123),x92127),x92121))+~P1(f333(f333(f335(f882(x92123,a870)),x92122),f333(f333(f60(x92123),x92124),x92125)))+~P1(f333(f333(f335(f882(x92123,a870)),x92121),f333(f333(f60(x92123),x92124),x92125)))+~P1(f333(f333(f335(f881(x92123,x92123)),f333(f333(f268(x92123,x92123),x92127),x92126)),x92125)) % 183.90/184.45 [10203]~P7(x102039,x102038,x102037)+~P7(x102031,x1020311,x1020310)+~P13(x102031,x102039,f882(x102036,a870),x1020310,x102037,x102035)+P1(f333(f333(f335(x102031),f534(x102032,x102033,x102034,x102035,x102036,x102037,x102038,x102039,x1020310,x1020311,x102031)),x1020311))+~P1(f333(f333(f335(f882(x102039,a870)),x102033),f333(f333(f60(x102039),x102038),x102037)))+~P1(f333(f333(f335(f882(x102031,a870)),x102034),f333(f333(f60(x102031),x1020311),x1020310)))+P1(f333(f333(f335(f882(x102036,a870)),f333(f333(f41(x102031,f882(x102036,a870)),x102034),f333(f333(f8(f882(x102039,f882(x102036,a870)),f882(x102036,a870),x102031),f333(f41(x102039,f882(x102036,a870)),x102033)),x102035))),x102032)) % 183.90/184.45 [10204]~P7(x1020411,x1020410,x102049)+~P7(x102041,x102048,x102047)+~P13(x1020411,x102041,f882(x102046,a870),x102049,x102047,x102045)+P1(f333(f333(f335(x102041),f535(x102042,x102043,x102044,x102045,x102046,x102047,x102048,x102041,x102049,x1020410,x1020411)),x102048))+~P1(f333(f333(f335(f882(x1020411,a870)),x102044),f333(f333(f60(x1020411),x1020410),x102049)))+~P1(f333(f333(f335(f882(x102041,a870)),x102043),f333(f333(f60(x102041),x102048),x102047)))+P1(f333(f333(f335(f882(x102046,a870)),f333(f333(f41(x1020411,f882(x102046,a870)),x102044),f333(f333(f8(f882(x102041,f882(x102046,a870)),f882(x102046,a870),x1020411),f333(f41(x102041,f882(x102046,a870)),x102043)),x102045))),x102042)) % 183.90/184.45 [10207]~P7(x102072,x102078,x102079)+~P7(x102074,x1020710,x1020711)+~P13(x102072,x102074,f882(x102071,a870),x102079,x1020711,x102076)+~P1(f333(f333(f335(f882(x102072,a870)),x102073),f333(f333(f60(x102072),x102078),x102079)))+~P1(f333(f333(f335(f882(x102074,a870)),x102075),f333(f333(f60(x102074),x1020710),x1020711)))+~P1(f333(f333(f335(f882(x102071,a870)),f333(f333(x102076,f534(x102077,x102075,x102073,x102076,x102071,x1020711,x1020710,x102074,x102079,x102078,x102072)),f535(x102077,x102075,x102073,x102076,x102071,x1020711,x1020710,x102074,x102079,x102078,x102072))),x102077))+P1(f333(f333(f335(f882(x102071,a870)),f333(f333(f41(x102072,f882(x102071,a870)),x102073),f333(f333(f8(f882(x102074,f882(x102071,a870)),f882(x102071,a870),x102072),f333(f41(x102074,f882(x102071,a870)),x102075)),x102076))),x102077)) % 183.90/184.45 [9112]E(x91121,x91122)+~P106(x91124)+~P25(x91123,x91124,x91125,f333(f333(f113(f882(x91123,a870)),f333(f174(x91123),x91121)),f333(f174(x91123),x91122)))+~E(f333(f174(x91123),x91121),f333(f174(x91123),x91122))+~P14(x91124,f333(f333(f155(x91123,x91124),x91125),x91122))+~P14(x91124,f333(f333(f155(x91123,x91124),x91125),x91121))+~P1(f333(f138(x91124),f333(f333(f155(x91123,x91124),x91125),x91122)))+~P1(f333(f138(x91124),f333(f333(f155(x91123,x91124),x91125),x91121))) % 183.90/184.45 %EqnAxiom % 183.90/184.45 [1]E(x11,x11) % 183.90/184.45 [2]E(x22,x21)+~E(x21,x22) % 183.90/184.45 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 183.90/184.45 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 183.90/184.45 [5]~E(x51,x52)+E(f103(x51),f103(x52)) % 183.90/184.45 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 183.90/184.45 [7]~E(x71,x72)+E(f196(x71),f196(x72)) % 183.90/184.45 [8]~E(x81,x82)+E(f333(x81,x83),f333(x82,x83)) % 183.90/184.45 [9]~E(x91,x92)+E(f333(x93,x91),f333(x93,x92)) % 183.90/184.45 [10]~E(x101,x102)+E(f30(x101),f30(x102)) % 183.90/184.45 [11]~E(x111,x112)+E(f7(x111,x113,x114),f7(x112,x113,x114)) % 183.90/184.45 [12]~E(x121,x122)+E(f7(x123,x121,x124),f7(x123,x122,x124)) % 183.90/184.45 [13]~E(x131,x132)+E(f7(x133,x134,x131),f7(x133,x134,x132)) % 183.90/184.45 [14]~E(x141,x142)+E(f104(x141),f104(x142)) % 183.90/184.45 [15]~E(x151,x152)+E(f245(x151),f245(x152)) % 183.90/184.45 [16]~E(x161,x162)+E(f113(x161),f113(x162)) % 183.90/184.45 [17]~E(x171,x172)+E(f246(x171),f246(x172)) % 183.90/184.45 [18]~E(x181,x182)+E(f105(x181),f105(x182)) % 183.90/184.45 [19]~E(x191,x192)+E(f33(x191),f33(x192)) % 183.90/184.45 [20]~E(x201,x202)+E(f83(x201),f83(x202)) % 183.90/184.45 [21]~E(x211,x212)+E(f876(x211),f876(x212)) % 183.90/184.45 [22]~E(x221,x222)+E(f31(x221,x223),f31(x222,x223)) % 183.90/184.45 [23]~E(x231,x232)+E(f31(x233,x231),f31(x233,x232)) % 183.90/184.45 [24]~E(x241,x242)+E(f535(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f535(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 183.90/184.45 [25]~E(x251,x252)+E(f535(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f535(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 183.90/184.45 [26]~E(x261,x262)+E(f535(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f535(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612)) % 183.90/184.45 [27]~E(x271,x272)+E(f535(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f535(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712)) % 183.90/184.45 [28]~E(x281,x282)+E(f535(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f535(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812)) % 183.90/184.45 [29]~E(x291,x292)+E(f535(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f535(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912)) % 183.90/184.45 [30]~E(x301,x302)+E(f535(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f535(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012)) % 183.90/184.45 [31]~E(x311,x312)+E(f535(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f535(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112)) % 183.90/184.45 [32]~E(x321,x322)+E(f535(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f535(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212)) % 183.90/184.45 [33]~E(x331,x332)+E(f535(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f535(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312)) % 183.90/184.45 [34]~E(x341,x342)+E(f535(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f535(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342)) % 183.90/184.45 [35]~E(x351,x352)+E(f77(x351),f77(x352)) % 183.90/184.45 [36]~E(x361,x362)+E(f202(x361),f202(x362)) % 183.90/184.45 [37]~E(x371,x372)+E(f534(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f534(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 183.90/184.45 [38]~E(x381,x382)+E(f534(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f534(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 183.90/184.45 [39]~E(x391,x392)+E(f534(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f534(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 183.90/184.45 [40]~E(x401,x402)+E(f534(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f534(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012)) % 183.90/184.45 [41]~E(x411,x412)+E(f534(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f534(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112)) % 183.90/184.45 [42]~E(x421,x422)+E(f534(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f534(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212)) % 183.90/184.45 [43]~E(x431,x432)+E(f534(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f534(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312)) % 183.90/184.45 [44]~E(x441,x442)+E(f534(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f534(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412)) % 183.90/184.45 [45]~E(x451,x452)+E(f534(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f534(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512)) % 183.90/184.45 [46]~E(x461,x462)+E(f534(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f534(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612)) % 183.90/184.45 [47]~E(x471,x472)+E(f534(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f534(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472)) % 183.90/184.45 [48]~E(x481,x482)+E(f4(x481),f4(x482)) % 183.90/184.45 [49]~E(x491,x492)+E(f335(x491),f335(x492)) % 183.90/184.45 [50]~E(x501,x502)+E(f882(x501,x503),f882(x502,x503)) % 183.90/184.45 [51]~E(x511,x512)+E(f882(x513,x511),f882(x513,x512)) % 183.90/184.45 [52]~E(x521,x522)+E(f114(x521),f114(x522)) % 183.90/184.45 [53]~E(x531,x532)+E(f248(x531),f248(x532)) % 183.90/184.45 [54]~E(x541,x542)+E(f874(x541),f874(x542)) % 183.90/184.45 [55]~E(x551,x552)+E(f879(x551),f879(x552)) % 183.90/184.45 [56]~E(x561,x562)+E(f304(x561,x563,x564),f304(x562,x563,x564)) % 183.90/184.45 [57]~E(x571,x572)+E(f304(x573,x571,x574),f304(x573,x572,x574)) % 183.90/184.45 [58]~E(x581,x582)+E(f304(x583,x584,x581),f304(x583,x584,x582)) % 183.90/184.45 [59]~E(x591,x592)+E(f877(x591),f877(x592)) % 183.90/184.45 [60]~E(x601,x602)+E(f508(x601,x603,x604),f508(x602,x603,x604)) % 183.90/184.45 [61]~E(x611,x612)+E(f508(x613,x611,x614),f508(x613,x612,x614)) % 183.90/184.45 [62]~E(x621,x622)+E(f508(x623,x624,x621),f508(x623,x624,x622)) % 183.90/184.45 [63]~E(x631,x632)+E(f80(x631),f80(x632)) % 183.90/184.45 [64]~E(x641,x642)+E(f287(x641,x643,x644),f287(x642,x643,x644)) % 183.90/184.45 [65]~E(x651,x652)+E(f287(x653,x651,x654),f287(x653,x652,x654)) % 183.90/184.45 [66]~E(x661,x662)+E(f287(x663,x664,x661),f287(x663,x664,x662)) % 183.90/184.45 [67]~E(x671,x672)+E(f311(x671),f311(x672)) % 183.90/184.45 [68]~E(x681,x682)+E(f78(x681),f78(x682)) % 183.90/184.45 [69]~E(x691,x692)+E(f61(x691),f61(x692)) % 183.90/184.45 [70]~E(x701,x702)+E(f197(x701),f197(x702)) % 183.90/184.45 [71]~E(x711,x712)+E(f184(x711,x713),f184(x712,x713)) % 183.90/184.45 [72]~E(x721,x722)+E(f184(x723,x721),f184(x723,x722)) % 183.90/184.45 [73]~E(x731,x732)+E(f106(x731),f106(x732)) % 183.90/184.45 [74]~E(x741,x742)+E(f16(x741,x743),f16(x742,x743)) % 183.90/184.45 [75]~E(x751,x752)+E(f16(x753,x751),f16(x753,x752)) % 183.90/184.45 [76]~E(x761,x762)+E(f247(x761),f247(x762)) % 183.90/184.45 [77]~E(x771,x772)+E(f166(x771),f166(x772)) % 183.90/184.45 [78]~E(x781,x782)+E(f313(x781,x783,x784),f313(x782,x783,x784)) % 183.90/184.45 [79]~E(x791,x792)+E(f313(x793,x791,x794),f313(x793,x792,x794)) % 183.90/184.45 [80]~E(x801,x802)+E(f313(x803,x804,x801),f313(x803,x804,x802)) % 183.90/184.45 [81]~E(x811,x812)+E(f57(x811),f57(x812)) % 183.90/184.45 [82]~E(x821,x822)+E(f309(x821,x823),f309(x822,x823)) % 183.90/184.45 [83]~E(x831,x832)+E(f309(x833,x831),f309(x833,x832)) % 183.90/184.45 [84]~E(x841,x842)+E(f63(x841,x843),f63(x842,x843)) % 183.90/184.45 [85]~E(x851,x852)+E(f63(x853,x851),f63(x853,x852)) % 183.90/184.45 [86]~E(x861,x862)+E(f48(x861,x863),f48(x862,x863)) % 183.90/184.45 [87]~E(x871,x872)+E(f48(x873,x871),f48(x873,x872)) % 183.90/184.45 [88]~E(x881,x882)+E(f881(x881,x883),f881(x882,x883)) % 183.90/184.45 [89]~E(x891,x892)+E(f881(x893,x891),f881(x893,x892)) % 183.90/184.45 [90]~E(x901,x902)+E(f291(x901),f291(x902)) % 183.90/184.45 [91]~E(x911,x912)+E(f116(x911),f116(x912)) % 183.90/184.45 [92]~E(x921,x922)+E(f135(x921),f135(x922)) % 183.90/184.45 [93]~E(x931,x932)+E(f60(x931),f60(x932)) % 183.90/184.45 [94]~E(x941,x942)+E(f8(x941,x943,x944),f8(x942,x943,x944)) % 183.90/184.45 [95]~E(x951,x952)+E(f8(x953,x951,x954),f8(x953,x952,x954)) % 183.90/184.45 [96]~E(x961,x962)+E(f8(x963,x964,x961),f8(x963,x964,x962)) % 183.90/184.45 [97]~E(x971,x972)+E(f155(x971,x973),f155(x972,x973)) % 183.90/184.45 [98]~E(x981,x982)+E(f155(x983,x981),f155(x983,x982)) % 183.90/184.45 [99]~E(x991,x992)+E(f15(x991,x993),f15(x992,x993)) % 183.90/184.45 [100]~E(x1001,x1002)+E(f15(x1003,x1001),f15(x1003,x1002)) % 183.90/184.45 [101]~E(x1011,x1012)+E(f268(x1011,x1013),f268(x1012,x1013)) % 183.90/184.45 [102]~E(x1021,x1022)+E(f268(x1023,x1021),f268(x1023,x1022)) % 183.90/184.45 [103]~E(x1031,x1032)+E(f271(x1031,x1033),f271(x1032,x1033)) % 183.90/184.45 [104]~E(x1041,x1042)+E(f271(x1043,x1041),f271(x1043,x1042)) % 183.90/184.45 [105]~E(x1051,x1052)+E(f79(x1051),f79(x1052)) % 183.90/184.45 [106]~E(x1061,x1062)+E(f74(x1061),f74(x1062)) % 183.90/184.45 [107]~E(x1071,x1072)+E(f170(x1071),f170(x1072)) % 183.90/184.45 [108]~E(x1081,x1082)+E(f152(x1081),f152(x1082)) % 183.90/184.45 [109]~E(x1091,x1092)+E(f290(x1091,x1093,x1094),f290(x1092,x1093,x1094)) % 183.90/184.45 [110]~E(x1101,x1102)+E(f290(x1103,x1101,x1104),f290(x1103,x1102,x1104)) % 183.90/184.45 [111]~E(x1111,x1112)+E(f290(x1113,x1114,x1111),f290(x1113,x1114,x1112)) % 183.90/184.45 [112]~E(x1121,x1122)+E(f342(x1121,x1123,x1124),f342(x1122,x1123,x1124)) % 183.90/184.45 [113]~E(x1131,x1132)+E(f342(x1133,x1131,x1134),f342(x1133,x1132,x1134)) % 183.90/184.45 [114]~E(x1141,x1142)+E(f342(x1143,x1144,x1141),f342(x1143,x1144,x1142)) % 183.90/184.45 [115]~E(x1151,x1152)+E(f143(x1151,x1153,x1154,x1155),f143(x1152,x1153,x1154,x1155)) % 183.90/184.45 [116]~E(x1161,x1162)+E(f143(x1163,x1161,x1164,x1165),f143(x1163,x1162,x1164,x1165)) % 183.90/184.45 [117]~E(x1171,x1172)+E(f143(x1173,x1174,x1171,x1175),f143(x1173,x1174,x1172,x1175)) % 183.90/184.45 [118]~E(x1181,x1182)+E(f143(x1183,x1184,x1185,x1181),f143(x1183,x1184,x1185,x1182)) % 183.90/184.45 [119]~E(x1191,x1192)+E(f6(x1191,x1193),f6(x1192,x1193)) % 183.90/184.45 [120]~E(x1201,x1202)+E(f6(x1203,x1201),f6(x1203,x1202)) % 183.90/184.45 [121]~E(x1211,x1212)+E(f138(x1211),f138(x1212)) % 183.90/184.45 [122]~E(x1221,x1222)+E(f37(x1221),f37(x1222)) % 183.90/184.45 [123]~E(x1231,x1232)+E(f817(x1231,x1233,x1234),f817(x1232,x1233,x1234)) % 183.90/184.45 [124]~E(x1241,x1242)+E(f817(x1243,x1241,x1244),f817(x1243,x1242,x1244)) % 183.90/184.45 [125]~E(x1251,x1252)+E(f817(x1253,x1254,x1251),f817(x1253,x1254,x1252)) % 183.90/184.45 [126]~E(x1261,x1262)+E(f732(x1261,x1263,x1264,x1265),f732(x1262,x1263,x1264,x1265)) % 183.90/184.45 [127]~E(x1271,x1272)+E(f732(x1273,x1271,x1274,x1275),f732(x1273,x1272,x1274,x1275)) % 183.90/184.45 [128]~E(x1281,x1282)+E(f732(x1283,x1284,x1281,x1285),f732(x1283,x1284,x1282,x1285)) % 183.90/184.45 [129]~E(x1291,x1292)+E(f732(x1293,x1294,x1295,x1291),f732(x1293,x1294,x1295,x1292)) % 183.90/184.45 [130]~E(x1301,x1302)+E(f174(x1301),f174(x1302)) % 183.90/184.45 [131]~E(x1311,x1312)+E(f41(x1311,x1313),f41(x1312,x1313)) % 183.90/184.45 [132]~E(x1321,x1322)+E(f41(x1323,x1321),f41(x1323,x1322)) % 183.90/184.45 [133]~E(x1331,x1332)+E(f267(x1331,x1333),f267(x1332,x1333)) % 183.90/184.45 [134]~E(x1341,x1342)+E(f267(x1343,x1341),f267(x1343,x1342)) % 183.90/184.45 [135]~E(x1351,x1352)+E(f86(x1351),f86(x1352)) % 183.90/184.45 [136]~E(x1361,x1362)+E(f253(x1361),f253(x1362)) % 183.90/184.45 [137]~E(x1371,x1372)+E(f179(x1371,x1373,x1374),f179(x1372,x1373,x1374)) % 183.90/184.45 [138]~E(x1381,x1382)+E(f179(x1383,x1381,x1384),f179(x1383,x1382,x1384)) % 183.90/184.45 [139]~E(x1391,x1392)+E(f179(x1393,x1394,x1391),f179(x1393,x1394,x1392)) % 183.90/184.45 [140]~E(x1401,x1402)+E(f44(x1401,x1403,x1404),f44(x1402,x1403,x1404)) % 183.90/184.45 [141]~E(x1411,x1412)+E(f44(x1413,x1411,x1414),f44(x1413,x1412,x1414)) % 183.90/184.45 [142]~E(x1421,x1422)+E(f44(x1423,x1424,x1421),f44(x1423,x1424,x1422)) % 183.90/184.45 [143]~E(x1431,x1432)+E(f72(x1431,x1433,x1434,x1435),f72(x1432,x1433,x1434,x1435)) % 183.90/184.45 [144]~E(x1441,x1442)+E(f72(x1443,x1441,x1444,x1445),f72(x1443,x1442,x1444,x1445)) % 183.90/184.45 [145]~E(x1451,x1452)+E(f72(x1453,x1454,x1451,x1455),f72(x1453,x1454,x1452,x1455)) % 183.90/184.45 [146]~E(x1461,x1462)+E(f72(x1463,x1464,x1465,x1461),f72(x1463,x1464,x1465,x1462)) % 183.90/184.45 [147]~E(x1471,x1472)+E(f307(x1471,x1473,x1474),f307(x1472,x1473,x1474)) % 183.90/184.45 [148]~E(x1481,x1482)+E(f307(x1483,x1481,x1484),f307(x1483,x1482,x1484)) % 183.90/184.45 [149]~E(x1491,x1492)+E(f307(x1493,x1494,x1491),f307(x1493,x1494,x1492)) % 183.90/184.45 [150]~E(x1501,x1502)+E(f42(x1501,x1503),f42(x1502,x1503)) % 183.90/184.45 [151]~E(x1511,x1512)+E(f42(x1513,x1511),f42(x1513,x1512)) % 183.90/184.45 [152]~E(x1521,x1522)+E(f108(x1521),f108(x1522)) % 183.90/184.45 [153]~E(x1531,x1532)+E(f110(x1531),f110(x1532)) % 183.90/184.45 [154]~E(x1541,x1542)+E(f334(x1541),f334(x1542)) % 183.90/184.45 [155]~E(x1551,x1552)+E(f401(x1551),f401(x1552)) % 183.90/184.45 [156]~E(x1561,x1562)+E(f366(x1561,x1563,x1564),f366(x1562,x1563,x1564)) % 183.90/184.45 [157]~E(x1571,x1572)+E(f366(x1573,x1571,x1574),f366(x1573,x1572,x1574)) % 183.90/184.45 [158]~E(x1581,x1582)+E(f366(x1583,x1584,x1581),f366(x1583,x1584,x1582)) % 183.90/184.45 [159]~E(x1591,x1592)+E(f71(x1591,x1593),f71(x1592,x1593)) % 183.90/184.45 [160]~E(x1601,x1602)+E(f71(x1603,x1601),f71(x1603,x1602)) % 183.90/184.45 [161]~E(x1611,x1612)+E(f697(x1611,x1613,x1614,x1615,x1616),f697(x1612,x1613,x1614,x1615,x1616)) % 183.90/184.45 [162]~E(x1621,x1622)+E(f697(x1623,x1621,x1624,x1625,x1626),f697(x1623,x1622,x1624,x1625,x1626)) % 183.90/184.45 [163]~E(x1631,x1632)+E(f697(x1633,x1634,x1631,x1635,x1636),f697(x1633,x1634,x1632,x1635,x1636)) % 183.90/184.45 [164]~E(x1641,x1642)+E(f697(x1643,x1644,x1645,x1641,x1646),f697(x1643,x1644,x1645,x1642,x1646)) % 183.90/184.45 [165]~E(x1651,x1652)+E(f697(x1653,x1654,x1655,x1656,x1651),f697(x1653,x1654,x1655,x1656,x1652)) % 183.90/184.45 [166]~E(x1661,x1662)+E(f5(x1661),f5(x1662)) % 183.90/184.45 [167]~E(x1671,x1672)+E(f517(x1671,x1673,x1674),f517(x1672,x1673,x1674)) % 183.90/184.45 [168]~E(x1681,x1682)+E(f517(x1683,x1681,x1684),f517(x1683,x1682,x1684)) % 183.90/184.45 [169]~E(x1691,x1692)+E(f517(x1693,x1694,x1691),f517(x1693,x1694,x1692)) % 183.90/184.45 [170]~E(x1701,x1702)+E(f862(x1701,x1703,x1704),f862(x1702,x1703,x1704)) % 183.90/184.45 [171]~E(x1711,x1712)+E(f862(x1713,x1711,x1714),f862(x1713,x1712,x1714)) % 183.90/184.45 [172]~E(x1721,x1722)+E(f862(x1723,x1724,x1721),f862(x1723,x1724,x1722)) % 183.90/184.45 [173]~E(x1731,x1732)+E(f157(x1731,x1733,x1734,x1735),f157(x1732,x1733,x1734,x1735)) % 183.90/184.45 [174]~E(x1741,x1742)+E(f157(x1743,x1741,x1744,x1745),f157(x1743,x1742,x1744,x1745)) % 183.90/184.45 [175]~E(x1751,x1752)+E(f157(x1753,x1754,x1751,x1755),f157(x1753,x1754,x1752,x1755)) % 183.90/184.45 [176]~E(x1761,x1762)+E(f157(x1763,x1764,x1765,x1761),f157(x1763,x1764,x1765,x1762)) % 183.90/184.45 [177]~E(x1771,x1772)+E(f312(x1771,x1773,x1774),f312(x1772,x1773,x1774)) % 183.90/184.45 [178]~E(x1781,x1782)+E(f312(x1783,x1781,x1784),f312(x1783,x1782,x1784)) % 183.90/184.45 [179]~E(x1791,x1792)+E(f312(x1793,x1794,x1791),f312(x1793,x1794,x1792)) % 183.90/184.45 [180]~E(x1801,x1802)+E(f10(x1801,x1803),f10(x1802,x1803)) % 183.90/184.45 [181]~E(x1811,x1812)+E(f10(x1813,x1811),f10(x1813,x1812)) % 183.90/184.45 [182]~E(x1821,x1822)+E(f815(x1821,x1823,x1824),f815(x1822,x1823,x1824)) % 183.90/184.45 [183]~E(x1831,x1832)+E(f815(x1833,x1831,x1834),f815(x1833,x1832,x1834)) % 183.90/184.45 [184]~E(x1841,x1842)+E(f815(x1843,x1844,x1841),f815(x1843,x1844,x1842)) % 183.90/184.45 [185]~E(x1851,x1852)+E(f28(x1851,x1853,x1854),f28(x1852,x1853,x1854)) % 183.90/184.45 [186]~E(x1861,x1862)+E(f28(x1863,x1861,x1864),f28(x1863,x1862,x1864)) % 183.90/184.45 [187]~E(x1871,x1872)+E(f28(x1873,x1874,x1871),f28(x1873,x1874,x1872)) % 183.90/184.45 [188]~E(x1881,x1882)+E(f55(x1881),f55(x1882)) % 183.90/184.45 [189]~E(x1891,x1892)+E(f272(x1891,x1893,x1894),f272(x1892,x1893,x1894)) % 183.90/184.45 [190]~E(x1901,x1902)+E(f272(x1903,x1901,x1904),f272(x1903,x1902,x1904)) % 183.90/184.45 [191]~E(x1911,x1912)+E(f272(x1913,x1914,x1911),f272(x1913,x1914,x1912)) % 183.90/184.45 [192]~E(x1921,x1922)+E(f177(x1921),f177(x1922)) % 183.90/184.45 [193]~E(x1931,x1932)+E(f258(x1931),f258(x1932)) % 183.90/184.45 [194]~E(x1941,x1942)+E(f13(x1941,x1943),f13(x1942,x1943)) % 183.90/184.45 [195]~E(x1951,x1952)+E(f13(x1953,x1951),f13(x1953,x1952)) % 183.90/184.45 [196]~E(x1961,x1962)+E(f310(x1961),f310(x1962)) % 183.90/184.45 [197]~E(x1971,x1972)+E(f787(x1971,x1973,x1974,x1975,x1976),f787(x1972,x1973,x1974,x1975,x1976)) % 183.90/184.45 [198]~E(x1981,x1982)+E(f787(x1983,x1981,x1984,x1985,x1986),f787(x1983,x1982,x1984,x1985,x1986)) % 183.90/184.45 [199]~E(x1991,x1992)+E(f787(x1993,x1994,x1991,x1995,x1996),f787(x1993,x1994,x1992,x1995,x1996)) % 183.90/184.45 [200]~E(x2001,x2002)+E(f787(x2003,x2004,x2005,x2001,x2006),f787(x2003,x2004,x2005,x2002,x2006)) % 183.90/184.45 [201]~E(x2011,x2012)+E(f787(x2013,x2014,x2015,x2016,x2011),f787(x2013,x2014,x2015,x2016,x2012)) % 183.90/184.45 [202]~E(x2021,x2022)+E(f14(x2021,x2023),f14(x2022,x2023)) % 183.90/184.45 [203]~E(x2031,x2032)+E(f14(x2033,x2031),f14(x2033,x2032)) % 183.90/184.45 [204]~E(x2041,x2042)+E(f137(x2041,x2043),f137(x2042,x2043)) % 183.90/184.45 [205]~E(x2051,x2052)+E(f137(x2053,x2051),f137(x2053,x2052)) % 183.90/184.45 [206]~E(x2061,x2062)+E(f117(x2061,x2063),f117(x2062,x2063)) % 183.90/184.45 [207]~E(x2071,x2072)+E(f117(x2073,x2071),f117(x2073,x2072)) % 183.90/184.45 [208]~E(x2081,x2082)+E(f45(x2081,x2083),f45(x2082,x2083)) % 183.90/184.45 [209]~E(x2091,x2092)+E(f45(x2093,x2091),f45(x2093,x2092)) % 183.90/184.45 [210]~E(x2101,x2102)+E(f321(x2101,x2103),f321(x2102,x2103)) % 183.90/184.45 [211]~E(x2111,x2112)+E(f321(x2113,x2111),f321(x2113,x2112)) % 183.90/184.45 [212]~E(x2121,x2122)+E(f273(x2121,x2123,x2124,x2125,x2126,x2127),f273(x2122,x2123,x2124,x2125,x2126,x2127)) % 183.90/184.45 [213]~E(x2131,x2132)+E(f273(x2133,x2131,x2134,x2135,x2136,x2137),f273(x2133,x2132,x2134,x2135,x2136,x2137)) % 183.90/184.45 [214]~E(x2141,x2142)+E(f273(x2143,x2144,x2141,x2145,x2146,x2147),f273(x2143,x2144,x2142,x2145,x2146,x2147)) % 183.90/184.45 [215]~E(x2151,x2152)+E(f273(x2153,x2154,x2155,x2151,x2156,x2157),f273(x2153,x2154,x2155,x2152,x2156,x2157)) % 183.90/184.45 [216]~E(x2161,x2162)+E(f273(x2163,x2164,x2165,x2166,x2161,x2167),f273(x2163,x2164,x2165,x2166,x2162,x2167)) % 183.90/184.45 [217]~E(x2171,x2172)+E(f273(x2173,x2174,x2175,x2176,x2177,x2171),f273(x2173,x2174,x2175,x2176,x2177,x2172)) % 183.90/184.45 [218]~E(x2181,x2182)+E(f338(x2181),f338(x2182)) % 183.90/184.45 [219]~E(x2191,x2192)+E(f279(x2191,x2193),f279(x2192,x2193)) % 183.90/184.45 [220]~E(x2201,x2202)+E(f279(x2203,x2201),f279(x2203,x2202)) % 183.90/184.45 [221]~E(x2211,x2212)+E(f91(x2211),f91(x2212)) % 183.90/184.45 [222]~E(x2221,x2222)+E(f352(x2221,x2223,x2224,x2225,x2226),f352(x2222,x2223,x2224,x2225,x2226)) % 183.90/184.45 [223]~E(x2231,x2232)+E(f352(x2233,x2231,x2234,x2235,x2236),f352(x2233,x2232,x2234,x2235,x2236)) % 183.90/184.45 [224]~E(x2241,x2242)+E(f352(x2243,x2244,x2241,x2245,x2246),f352(x2243,x2244,x2242,x2245,x2246)) % 183.90/184.45 [225]~E(x2251,x2252)+E(f352(x2253,x2254,x2255,x2251,x2256),f352(x2253,x2254,x2255,x2252,x2256)) % 183.90/184.45 [226]~E(x2261,x2262)+E(f352(x2263,x2264,x2265,x2266,x2261),f352(x2263,x2264,x2265,x2266,x2262)) % 183.90/184.45 [227]~E(x2271,x2272)+E(f270(x2271,x2273),f270(x2272,x2273)) % 183.90/184.45 [228]~E(x2281,x2282)+E(f270(x2283,x2281),f270(x2283,x2282)) % 183.90/184.45 [229]~E(x2291,x2292)+E(f39(x2291,x2293),f39(x2292,x2293)) % 183.90/184.45 [230]~E(x2301,x2302)+E(f39(x2303,x2301),f39(x2303,x2302)) % 183.90/184.45 [231]~E(x2311,x2312)+E(f256(x2311),f256(x2312)) % 183.90/184.45 [232]~E(x2321,x2322)+E(f29(x2321,x2323,x2324),f29(x2322,x2323,x2324)) % 183.90/184.45 [233]~E(x2331,x2332)+E(f29(x2333,x2331,x2334),f29(x2333,x2332,x2334)) % 183.90/184.45 [234]~E(x2341,x2342)+E(f29(x2343,x2344,x2341),f29(x2343,x2344,x2342)) % 183.90/184.45 [235]~E(x2351,x2352)+E(f47(x2351,x2353),f47(x2352,x2353)) % 183.90/184.45 [236]~E(x2361,x2362)+E(f47(x2363,x2361),f47(x2363,x2362)) % 183.90/184.45 [237]~E(x2371,x2372)+E(f191(x2371,x2373),f191(x2372,x2373)) % 183.90/184.45 [238]~E(x2381,x2382)+E(f191(x2383,x2381),f191(x2383,x2382)) % 183.90/184.45 [239]~E(x2391,x2392)+E(f602(x2391,x2393,x2394),f602(x2392,x2393,x2394)) % 183.90/184.45 [240]~E(x2401,x2402)+E(f602(x2403,x2401,x2404),f602(x2403,x2402,x2404)) % 183.90/184.45 [241]~E(x2411,x2412)+E(f602(x2413,x2414,x2411),f602(x2413,x2414,x2412)) % 183.90/184.45 [242]~E(x2421,x2422)+E(f809(x2421,x2423,x2424,x2425),f809(x2422,x2423,x2424,x2425)) % 183.90/184.45 [243]~E(x2431,x2432)+E(f809(x2433,x2431,x2434,x2435),f809(x2433,x2432,x2434,x2435)) % 183.90/184.45 [244]~E(x2441,x2442)+E(f809(x2443,x2444,x2441,x2445),f809(x2443,x2444,x2442,x2445)) % 183.90/184.45 [245]~E(x2451,x2452)+E(f809(x2453,x2454,x2455,x2451),f809(x2453,x2454,x2455,x2452)) % 183.90/184.45 [246]~E(x2461,x2462)+E(f52(x2461,x2463),f52(x2462,x2463)) % 183.90/184.45 [247]~E(x2471,x2472)+E(f52(x2473,x2471),f52(x2473,x2472)) % 183.90/184.45 [248]~E(x2481,x2482)+E(f595(x2481,x2483,x2484),f595(x2482,x2483,x2484)) % 183.90/184.45 [249]~E(x2491,x2492)+E(f595(x2493,x2491,x2494),f595(x2493,x2492,x2494)) % 183.90/184.45 [250]~E(x2501,x2502)+E(f595(x2503,x2504,x2501),f595(x2503,x2504,x2502)) % 183.90/184.45 [251]~E(x2511,x2512)+E(f413(x2511,x2513),f413(x2512,x2513)) % 183.90/184.45 [252]~E(x2521,x2522)+E(f413(x2523,x2521),f413(x2523,x2522)) % 183.90/184.45 [253]~E(x2531,x2532)+E(f203(x2531,x2533),f203(x2532,x2533)) % 183.90/184.45 [254]~E(x2541,x2542)+E(f203(x2543,x2541),f203(x2543,x2542)) % 183.90/184.45 [255]~E(x2551,x2552)+E(f49(x2551,x2553),f49(x2552,x2553)) % 183.90/184.45 [256]~E(x2561,x2562)+E(f49(x2563,x2561),f49(x2563,x2562)) % 183.90/184.45 [257]~E(x2571,x2572)+E(f40(x2571,x2573),f40(x2572,x2573)) % 183.90/184.45 [258]~E(x2581,x2582)+E(f40(x2583,x2581),f40(x2583,x2582)) % 183.90/184.45 [259]~E(x2591,x2592)+E(f720(x2591,x2593,x2594),f720(x2592,x2593,x2594)) % 183.90/184.45 [260]~E(x2601,x2602)+E(f720(x2603,x2601,x2604),f720(x2603,x2602,x2604)) % 183.90/184.45 [261]~E(x2611,x2612)+E(f720(x2613,x2614,x2611),f720(x2613,x2614,x2612)) % 183.90/184.45 [262]~E(x2621,x2622)+E(f153(x2621,x2623),f153(x2622,x2623)) % 183.90/184.45 [263]~E(x2631,x2632)+E(f153(x2633,x2631),f153(x2633,x2632)) % 183.90/184.45 [264]~E(x2641,x2642)+E(f148(x2641,x2643),f148(x2642,x2643)) % 183.90/184.45 [265]~E(x2651,x2652)+E(f148(x2653,x2651),f148(x2653,x2652)) % 183.90/184.45 [266]~E(x2661,x2662)+E(f199(x2661),f199(x2662)) % 183.90/184.45 [267]~E(x2671,x2672)+E(f303(x2671,x2673),f303(x2672,x2673)) % 183.90/184.45 [268]~E(x2681,x2682)+E(f303(x2683,x2681),f303(x2683,x2682)) % 183.90/184.45 [269]~E(x2691,x2692)+E(f118(x2691),f118(x2692)) % 183.90/184.45 [270]~E(x2701,x2702)+E(f187(x2701,x2703,x2704,x2705),f187(x2702,x2703,x2704,x2705)) % 183.90/184.45 [271]~E(x2711,x2712)+E(f187(x2713,x2711,x2714,x2715),f187(x2713,x2712,x2714,x2715)) % 183.90/184.45 [272]~E(x2721,x2722)+E(f187(x2723,x2724,x2721,x2725),f187(x2723,x2724,x2722,x2725)) % 183.90/184.45 [273]~E(x2731,x2732)+E(f187(x2733,x2734,x2735,x2731),f187(x2733,x2734,x2735,x2732)) % 183.90/184.45 [274]~E(x2741,x2742)+E(f178(x2741,x2743,x2744),f178(x2742,x2743,x2744)) % 183.90/184.45 [275]~E(x2751,x2752)+E(f178(x2753,x2751,x2754),f178(x2753,x2752,x2754)) % 183.90/184.45 [276]~E(x2761,x2762)+E(f178(x2763,x2764,x2761),f178(x2763,x2764,x2762)) % 183.90/184.45 [277]~E(x2771,x2772)+E(f160(x2771,x2773),f160(x2772,x2773)) % 183.90/184.45 [278]~E(x2781,x2782)+E(f160(x2783,x2781),f160(x2783,x2782)) % 183.90/184.45 [279]~E(x2791,x2792)+E(f880(x2791,x2793),f880(x2792,x2793)) % 183.90/184.45 [280]~E(x2801,x2802)+E(f880(x2803,x2801),f880(x2803,x2802)) % 183.90/184.45 [281]~E(x2811,x2812)+E(f302(x2811),f302(x2812)) % 183.90/184.45 [282]~E(x2821,x2822)+E(f169(x2821),f169(x2822)) % 183.90/184.45 [283]~E(x2831,x2832)+E(f306(x2831,x2833,x2834),f306(x2832,x2833,x2834)) % 183.90/184.45 [284]~E(x2841,x2842)+E(f306(x2843,x2841,x2844),f306(x2843,x2842,x2844)) % 183.90/184.45 [285]~E(x2851,x2852)+E(f306(x2853,x2854,x2851),f306(x2853,x2854,x2852)) % 183.90/184.45 [286]~E(x2861,x2862)+E(f397(x2861,x2863,x2864,x2865),f397(x2862,x2863,x2864,x2865)) % 183.90/184.45 [287]~E(x2871,x2872)+E(f397(x2873,x2871,x2874,x2875),f397(x2873,x2872,x2874,x2875)) % 183.90/184.45 [288]~E(x2881,x2882)+E(f397(x2883,x2884,x2881,x2885),f397(x2883,x2884,x2882,x2885)) % 183.90/184.45 [289]~E(x2891,x2892)+E(f397(x2893,x2894,x2895,x2891),f397(x2893,x2894,x2895,x2892)) % 183.90/184.45 [290]~E(x2901,x2902)+E(f774(x2901,x2903,x2904,x2905,x2906),f774(x2902,x2903,x2904,x2905,x2906)) % 183.90/184.45 [291]~E(x2911,x2912)+E(f774(x2913,x2911,x2914,x2915,x2916),f774(x2913,x2912,x2914,x2915,x2916)) % 183.90/184.45 [292]~E(x2921,x2922)+E(f774(x2923,x2924,x2921,x2925,x2926),f774(x2923,x2924,x2922,x2925,x2926)) % 183.90/184.45 [293]~E(x2931,x2932)+E(f774(x2933,x2934,x2935,x2931,x2936),f774(x2933,x2934,x2935,x2932,x2936)) % 183.90/184.45 [294]~E(x2941,x2942)+E(f774(x2943,x2944,x2945,x2946,x2941),f774(x2943,x2944,x2945,x2946,x2942)) % 183.90/184.45 [295]~E(x2951,x2952)+E(f180(x2951,x2953),f180(x2952,x2953)) % 183.90/184.45 [296]~E(x2961,x2962)+E(f180(x2963,x2961),f180(x2963,x2962)) % 183.90/184.45 [297]~E(x2971,x2972)+E(f38(x2971),f38(x2972)) % 183.90/184.45 [298]~E(x2981,x2982)+E(f173(x2981),f173(x2982)) % 183.90/184.45 [299]~E(x2991,x2992)+E(f326(x2991,x2993,x2994,x2995),f326(x2992,x2993,x2994,x2995)) % 183.90/184.45 [300]~E(x3001,x3002)+E(f326(x3003,x3001,x3004,x3005),f326(x3003,x3002,x3004,x3005)) % 183.90/184.45 [301]~E(x3011,x3012)+E(f326(x3013,x3014,x3011,x3015),f326(x3013,x3014,x3012,x3015)) % 183.90/184.45 [302]~E(x3021,x3022)+E(f326(x3023,x3024,x3025,x3021),f326(x3023,x3024,x3025,x3022)) % 183.90/184.45 [303]~E(x3031,x3032)+E(f344(x3031,x3033),f344(x3032,x3033)) % 183.90/184.45 [304]~E(x3041,x3042)+E(f344(x3043,x3041),f344(x3043,x3042)) % 183.90/184.45 [305]~E(x3051,x3052)+E(f240(x3051),f240(x3052)) % 183.90/184.45 [306]~E(x3061,x3062)+E(f99(x3061),f99(x3062)) % 183.90/184.45 [307]~E(x3071,x3072)+E(f18(x3071,x3073,x3074),f18(x3072,x3073,x3074)) % 183.90/184.45 [308]~E(x3081,x3082)+E(f18(x3083,x3081,x3084),f18(x3083,x3082,x3084)) % 183.90/184.45 [309]~E(x3091,x3092)+E(f18(x3093,x3094,x3091),f18(x3093,x3094,x3092)) % 183.90/184.45 [310]~E(x3101,x3102)+E(f142(x3101),f142(x3102)) % 183.90/184.45 [311]~E(x3111,x3112)+E(f90(x3111),f90(x3112)) % 183.90/184.45 [312]~E(x3121,x3122)+E(f305(x3121),f305(x3122)) % 183.90/184.45 [313]~E(x3131,x3132)+E(f64(x3131,x3133,x3134),f64(x3132,x3133,x3134)) % 183.90/184.45 [314]~E(x3141,x3142)+E(f64(x3143,x3141,x3144),f64(x3143,x3142,x3144)) % 183.90/184.45 [315]~E(x3151,x3152)+E(f64(x3153,x3154,x3151),f64(x3153,x3154,x3152)) % 183.90/184.45 [316]~E(x3161,x3162)+E(f32(x3161,x3163),f32(x3162,x3163)) % 183.90/184.45 [317]~E(x3171,x3172)+E(f32(x3173,x3171),f32(x3173,x3172)) % 183.90/184.45 [318]~E(x3181,x3182)+E(f380(x3181,x3183,x3184,x3185,x3186,x3187),f380(x3182,x3183,x3184,x3185,x3186,x3187)) % 183.90/184.45 [319]~E(x3191,x3192)+E(f380(x3193,x3191,x3194,x3195,x3196,x3197),f380(x3193,x3192,x3194,x3195,x3196,x3197)) % 183.90/184.45 [320]~E(x3201,x3202)+E(f380(x3203,x3204,x3201,x3205,x3206,x3207),f380(x3203,x3204,x3202,x3205,x3206,x3207)) % 183.90/184.45 [321]~E(x3211,x3212)+E(f380(x3213,x3214,x3215,x3211,x3216,x3217),f380(x3213,x3214,x3215,x3212,x3216,x3217)) % 183.90/184.45 [322]~E(x3221,x3222)+E(f380(x3223,x3224,x3225,x3226,x3221,x3227),f380(x3223,x3224,x3225,x3226,x3222,x3227)) % 183.90/184.45 [323]~E(x3231,x3232)+E(f380(x3233,x3234,x3235,x3236,x3237,x3231),f380(x3233,x3234,x3235,x3236,x3237,x3232)) % 183.90/184.45 [324]~E(x3241,x3242)+E(f159(x3241,x3243),f159(x3242,x3243)) % 183.90/184.45 [325]~E(x3251,x3252)+E(f159(x3253,x3251),f159(x3253,x3252)) % 183.90/184.45 [326]~E(x3261,x3262)+E(f452(x3261,x3263),f452(x3262,x3263)) % 183.90/184.45 [327]~E(x3271,x3272)+E(f452(x3273,x3271),f452(x3273,x3272)) % 183.90/184.45 [328]~E(x3281,x3282)+E(f264(x3281,x3283),f264(x3282,x3283)) % 183.90/184.45 [329]~E(x3291,x3292)+E(f264(x3293,x3291),f264(x3293,x3292)) % 183.90/184.45 [330]~E(x3301,x3302)+E(f324(x3301,x3303),f324(x3302,x3303)) % 183.90/184.45 [331]~E(x3311,x3312)+E(f324(x3313,x3311),f324(x3313,x3312)) % 183.90/184.45 [332]~E(x3321,x3322)+E(f277(x3321,x3323),f277(x3322,x3323)) % 183.90/184.45 [333]~E(x3331,x3332)+E(f277(x3333,x3331),f277(x3333,x3332)) % 183.90/184.45 [334]~E(x3341,x3342)+E(f325(x3341,x3343),f325(x3342,x3343)) % 183.90/184.45 [335]~E(x3351,x3352)+E(f325(x3353,x3351),f325(x3353,x3352)) % 183.90/184.45 [336]~E(x3361,x3362)+E(f190(x3361,x3363,x3364,x3365),f190(x3362,x3363,x3364,x3365)) % 183.90/184.45 [337]~E(x3371,x3372)+E(f190(x3373,x3371,x3374,x3375),f190(x3373,x3372,x3374,x3375)) % 183.90/184.45 [338]~E(x3381,x3382)+E(f190(x3383,x3384,x3381,x3385),f190(x3383,x3384,x3382,x3385)) % 183.90/184.45 [339]~E(x3391,x3392)+E(f190(x3393,x3394,x3395,x3391),f190(x3393,x3394,x3395,x3392)) % 183.90/184.45 [340]~E(x3401,x3402)+E(f757(x3401,x3403,x3404,x3405),f757(x3402,x3403,x3404,x3405)) % 183.90/184.45 [341]~E(x3411,x3412)+E(f757(x3413,x3411,x3414,x3415),f757(x3413,x3412,x3414,x3415)) % 183.90/184.45 [342]~E(x3421,x3422)+E(f757(x3423,x3424,x3421,x3425),f757(x3423,x3424,x3422,x3425)) % 183.90/184.45 [343]~E(x3431,x3432)+E(f757(x3433,x3434,x3435,x3431),f757(x3433,x3434,x3435,x3432)) % 183.90/184.45 [344]~E(x3441,x3442)+E(f235(x3441,x3443,x3444),f235(x3442,x3443,x3444)) % 183.90/184.45 [345]~E(x3451,x3452)+E(f235(x3453,x3451,x3454),f235(x3453,x3452,x3454)) % 183.90/184.45 [346]~E(x3461,x3462)+E(f235(x3463,x3464,x3461),f235(x3463,x3464,x3462)) % 183.90/184.45 [347]~E(x3471,x3472)+E(f824(x3471,x3473,x3474),f824(x3472,x3473,x3474)) % 183.90/184.45 [348]~E(x3481,x3482)+E(f824(x3483,x3481,x3484),f824(x3483,x3482,x3484)) % 183.90/184.45 [349]~E(x3491,x3492)+E(f824(x3493,x3494,x3491),f824(x3493,x3494,x3492)) % 183.90/184.45 [350]~E(x3501,x3502)+E(f473(x3501,x3503,x3504),f473(x3502,x3503,x3504)) % 183.90/184.45 [351]~E(x3511,x3512)+E(f473(x3513,x3511,x3514),f473(x3513,x3512,x3514)) % 183.90/184.45 [352]~E(x3521,x3522)+E(f473(x3523,x3524,x3521),f473(x3523,x3524,x3522)) % 183.90/184.45 [353]~E(x3531,x3532)+E(f171(x3531,x3533,x3534),f171(x3532,x3533,x3534)) % 183.90/184.45 [354]~E(x3541,x3542)+E(f171(x3543,x3541,x3544),f171(x3543,x3542,x3544)) % 183.90/184.45 [355]~E(x3551,x3552)+E(f171(x3553,x3554,x3551),f171(x3553,x3554,x3552)) % 183.90/184.45 [356]~E(x3561,x3562)+E(f495(x3561,x3563,x3564,x3565,x3566,x3567),f495(x3562,x3563,x3564,x3565,x3566,x3567)) % 183.90/184.45 [357]~E(x3571,x3572)+E(f495(x3573,x3571,x3574,x3575,x3576,x3577),f495(x3573,x3572,x3574,x3575,x3576,x3577)) % 183.90/184.45 [358]~E(x3581,x3582)+E(f495(x3583,x3584,x3581,x3585,x3586,x3587),f495(x3583,x3584,x3582,x3585,x3586,x3587)) % 183.90/184.45 [359]~E(x3591,x3592)+E(f495(x3593,x3594,x3595,x3591,x3596,x3597),f495(x3593,x3594,x3595,x3592,x3596,x3597)) % 183.90/184.45 [360]~E(x3601,x3602)+E(f495(x3603,x3604,x3605,x3606,x3601,x3607),f495(x3603,x3604,x3605,x3606,x3602,x3607)) % 183.90/184.45 [361]~E(x3611,x3612)+E(f495(x3613,x3614,x3615,x3616,x3617,x3611),f495(x3613,x3614,x3615,x3616,x3617,x3612)) % 183.90/184.45 [362]~E(x3621,x3622)+E(f140(x3621,x3623),f140(x3622,x3623)) % 183.90/184.45 [363]~E(x3631,x3632)+E(f140(x3633,x3631),f140(x3633,x3632)) % 183.90/184.45 [364]~E(x3641,x3642)+E(f209(x3641),f209(x3642)) % 183.90/184.45 [365]~E(x3651,x3652)+E(f753(x3651,x3653,x3654),f753(x3652,x3653,x3654)) % 183.90/184.45 [366]~E(x3661,x3662)+E(f753(x3663,x3661,x3664),f753(x3663,x3662,x3664)) % 183.90/184.45 [367]~E(x3671,x3672)+E(f753(x3673,x3674,x3671),f753(x3673,x3674,x3672)) % 183.90/184.45 [368]~E(x3681,x3682)+E(f652(x3681,x3683,x3684,x3685),f652(x3682,x3683,x3684,x3685)) % 183.90/184.45 [369]~E(x3691,x3692)+E(f652(x3693,x3691,x3694,x3695),f652(x3693,x3692,x3694,x3695)) % 183.90/184.45 [370]~E(x3701,x3702)+E(f652(x3703,x3704,x3701,x3705),f652(x3703,x3704,x3702,x3705)) % 183.90/184.45 [371]~E(x3711,x3712)+E(f652(x3713,x3714,x3715,x3711),f652(x3713,x3714,x3715,x3712)) % 183.90/184.45 [372]~E(x3721,x3722)+E(f431(x3721,x3723,x3724,x3725),f431(x3722,x3723,x3724,x3725)) % 183.90/184.45 [373]~E(x3731,x3732)+E(f431(x3733,x3731,x3734,x3735),f431(x3733,x3732,x3734,x3735)) % 183.90/184.45 [374]~E(x3741,x3742)+E(f431(x3743,x3744,x3741,x3745),f431(x3743,x3744,x3742,x3745)) % 183.90/184.45 [375]~E(x3751,x3752)+E(f431(x3753,x3754,x3755,x3751),f431(x3753,x3754,x3755,x3752)) % 183.90/184.45 [376]~E(x3761,x3762)+E(f743(x3761,x3763),f743(x3762,x3763)) % 183.90/184.45 [377]~E(x3771,x3772)+E(f743(x3773,x3771),f743(x3773,x3772)) % 183.90/184.45 [378]~E(x3781,x3782)+E(f75(x3781,x3783,x3784,x3785,x3786),f75(x3782,x3783,x3784,x3785,x3786)) % 183.90/184.45 [379]~E(x3791,x3792)+E(f75(x3793,x3791,x3794,x3795,x3796),f75(x3793,x3792,x3794,x3795,x3796)) % 183.90/184.45 [380]~E(x3801,x3802)+E(f75(x3803,x3804,x3801,x3805,x3806),f75(x3803,x3804,x3802,x3805,x3806)) % 183.90/184.45 [381]~E(x3811,x3812)+E(f75(x3813,x3814,x3815,x3811,x3816),f75(x3813,x3814,x3815,x3812,x3816)) % 183.90/184.45 [382]~E(x3821,x3822)+E(f75(x3823,x3824,x3825,x3826,x3821),f75(x3823,x3824,x3825,x3826,x3822)) % 183.90/184.45 [383]~E(x3831,x3832)+E(f386(x3831,x3833,x3834,x3835),f386(x3832,x3833,x3834,x3835)) % 183.90/184.45 [384]~E(x3841,x3842)+E(f386(x3843,x3841,x3844,x3845),f386(x3843,x3842,x3844,x3845)) % 183.90/184.45 [385]~E(x3851,x3852)+E(f386(x3853,x3854,x3851,x3855),f386(x3853,x3854,x3852,x3855)) % 183.90/184.45 [386]~E(x3861,x3862)+E(f386(x3863,x3864,x3865,x3861),f386(x3863,x3864,x3865,x3862)) % 183.90/184.45 [387]~E(x3871,x3872)+E(f84(x3871,x3873),f84(x3872,x3873)) % 183.90/184.45 [388]~E(x3881,x3882)+E(f84(x3883,x3881),f84(x3883,x3882)) % 183.90/184.45 [389]~E(x3891,x3892)+E(f744(x3891,x3893),f744(x3892,x3893)) % 183.90/184.45 [390]~E(x3901,x3902)+E(f744(x3903,x3901),f744(x3903,x3902)) % 183.90/184.45 [391]~E(x3911,x3912)+E(f139(x3911),f139(x3912)) % 183.90/184.45 [392]~E(x3921,x3922)+E(f89(x3921,x3923),f89(x3922,x3923)) % 183.90/184.45 [393]~E(x3931,x3932)+E(f89(x3933,x3931),f89(x3933,x3932)) % 183.90/184.45 [394]~E(x3941,x3942)+E(f181(x3941,x3943),f181(x3942,x3943)) % 183.90/184.45 [395]~E(x3951,x3952)+E(f181(x3953,x3951),f181(x3953,x3952)) % 183.90/184.45 [396]~E(x3961,x3962)+E(f154(x3961,x3963),f154(x3962,x3963)) % 183.90/184.45 [397]~E(x3971,x3972)+E(f154(x3973,x3971),f154(x3973,x3972)) % 183.90/184.45 [398]~E(x3981,x3982)+E(f442(x3981,x3983),f442(x3982,x3983)) % 183.90/184.45 [399]~E(x3991,x3992)+E(f442(x3993,x3991),f442(x3993,x3992)) % 183.90/184.45 [400]~E(x4001,x4002)+E(f763(x4001,x4003,x4004,x4005),f763(x4002,x4003,x4004,x4005)) % 183.90/184.45 [401]~E(x4011,x4012)+E(f763(x4013,x4011,x4014,x4015),f763(x4013,x4012,x4014,x4015)) % 183.90/184.45 [402]~E(x4021,x4022)+E(f763(x4023,x4024,x4021,x4025),f763(x4023,x4024,x4022,x4025)) % 183.90/184.45 [403]~E(x4031,x4032)+E(f763(x4033,x4034,x4035,x4031),f763(x4033,x4034,x4035,x4032)) % 183.90/184.45 [404]~E(x4041,x4042)+E(f244(x4041),f244(x4042)) % 183.90/184.45 [405]~E(x4051,x4052)+E(f158(x4051,x4053),f158(x4052,x4053)) % 183.90/184.45 [406]~E(x4061,x4062)+E(f158(x4063,x4061),f158(x4063,x4062)) % 183.90/184.45 [407]~E(x4071,x4072)+E(f213(x4071),f213(x4072)) % 183.90/184.45 [408]~E(x4081,x4082)+E(f683(x4081,x4083,x4084),f683(x4082,x4083,x4084)) % 183.90/184.45 [409]~E(x4091,x4092)+E(f683(x4093,x4091,x4094),f683(x4093,x4092,x4094)) % 183.90/184.45 [410]~E(x4101,x4102)+E(f683(x4103,x4104,x4101),f683(x4103,x4104,x4102)) % 183.90/184.45 [411]~E(x4111,x4112)+E(f9(x4111,x4113),f9(x4112,x4113)) % 183.90/184.45 [412]~E(x4121,x4122)+E(f9(x4123,x4121),f9(x4123,x4122)) % 183.90/184.45 [413]~E(x4131,x4132)+E(f604(x4131,x4133,x4134),f604(x4132,x4133,x4134)) % 183.90/184.45 [414]~E(x4141,x4142)+E(f604(x4143,x4141,x4144),f604(x4143,x4142,x4144)) % 183.90/184.45 [415]~E(x4151,x4152)+E(f604(x4153,x4154,x4151),f604(x4153,x4154,x4152)) % 183.90/184.45 [416]~E(x4161,x4162)+E(f189(x4161,x4163,x4164,x4165,x4166),f189(x4162,x4163,x4164,x4165,x4166)) % 183.90/184.45 [417]~E(x4171,x4172)+E(f189(x4173,x4171,x4174,x4175,x4176),f189(x4173,x4172,x4174,x4175,x4176)) % 183.90/184.45 [418]~E(x4181,x4182)+E(f189(x4183,x4184,x4181,x4185,x4186),f189(x4183,x4184,x4182,x4185,x4186)) % 183.90/184.45 [419]~E(x4191,x4192)+E(f189(x4193,x4194,x4195,x4191,x4196),f189(x4193,x4194,x4195,x4192,x4196)) % 183.90/184.45 [420]~E(x4201,x4202)+E(f189(x4203,x4204,x4205,x4206,x4201),f189(x4203,x4204,x4205,x4206,x4202)) % 183.90/184.45 [421]~E(x4211,x4212)+E(f12(x4211,x4213,x4214),f12(x4212,x4213,x4214)) % 183.90/184.45 [422]~E(x4221,x4222)+E(f12(x4223,x4221,x4224),f12(x4223,x4222,x4224)) % 183.90/184.45 [423]~E(x4231,x4232)+E(f12(x4233,x4234,x4231),f12(x4233,x4234,x4232)) % 183.90/184.45 [424]~E(x4241,x4242)+E(f628(x4241,x4243,x4244),f628(x4242,x4243,x4244)) % 183.90/184.45 [425]~E(x4251,x4252)+E(f628(x4253,x4251,x4254),f628(x4253,x4252,x4254)) % 183.90/184.45 [426]~E(x4261,x4262)+E(f628(x4263,x4264,x4261),f628(x4263,x4264,x4262)) % 183.90/184.45 [427]~E(x4271,x4272)+E(f66(x4271,x4273,x4274,x4275,x4276),f66(x4272,x4273,x4274,x4275,x4276)) % 183.90/184.45 [428]~E(x4281,x4282)+E(f66(x4283,x4281,x4284,x4285,x4286),f66(x4283,x4282,x4284,x4285,x4286)) % 183.90/184.45 [429]~E(x4291,x4292)+E(f66(x4293,x4294,x4291,x4295,x4296),f66(x4293,x4294,x4292,x4295,x4296)) % 183.90/184.45 [430]~E(x4301,x4302)+E(f66(x4303,x4304,x4305,x4301,x4306),f66(x4303,x4304,x4305,x4302,x4306)) % 183.90/184.45 [431]~E(x4311,x4312)+E(f66(x4313,x4314,x4315,x4316,x4311),f66(x4313,x4314,x4315,x4316,x4312)) % 183.90/184.45 [432]~E(x4321,x4322)+E(f151(x4321,x4323,x4324,x4325),f151(x4322,x4323,x4324,x4325)) % 183.90/184.45 [433]~E(x4331,x4332)+E(f151(x4333,x4331,x4334,x4335),f151(x4333,x4332,x4334,x4335)) % 183.90/184.45 [434]~E(x4341,x4342)+E(f151(x4343,x4344,x4341,x4345),f151(x4343,x4344,x4342,x4345)) % 183.90/184.45 [435]~E(x4351,x4352)+E(f151(x4353,x4354,x4355,x4351),f151(x4353,x4354,x4355,x4352)) % 183.90/184.45 [436]~E(x4361,x4362)+E(f651(x4361,x4363,x4364,x4365),f651(x4362,x4363,x4364,x4365)) % 183.90/184.45 [437]~E(x4371,x4372)+E(f651(x4373,x4371,x4374,x4375),f651(x4373,x4372,x4374,x4375)) % 183.90/184.45 [438]~E(x4381,x4382)+E(f651(x4383,x4384,x4381,x4385),f651(x4383,x4384,x4382,x4385)) % 183.90/184.45 [439]~E(x4391,x4392)+E(f651(x4393,x4394,x4395,x4391),f651(x4393,x4394,x4395,x4392)) % 183.90/184.45 [440]~E(x4401,x4402)+E(f94(x4401,x4403,x4404),f94(x4402,x4403,x4404)) % 183.90/184.45 [441]~E(x4411,x4412)+E(f94(x4413,x4411,x4414),f94(x4413,x4412,x4414)) % 183.90/184.45 [442]~E(x4421,x4422)+E(f94(x4423,x4424,x4421),f94(x4423,x4424,x4422)) % 183.90/184.45 [443]~E(x4431,x4432)+E(f812(x4431,x4433,x4434),f812(x4432,x4433,x4434)) % 183.90/184.45 [444]~E(x4441,x4442)+E(f812(x4443,x4441,x4444),f812(x4443,x4442,x4444)) % 183.90/184.45 [445]~E(x4451,x4452)+E(f812(x4453,x4454,x4451),f812(x4453,x4454,x4452)) % 183.90/184.45 [446]~E(x4461,x4462)+E(f657(x4461,x4463),f657(x4462,x4463)) % 183.90/184.45 [447]~E(x4471,x4472)+E(f657(x4473,x4471),f657(x4473,x4472)) % 183.90/184.45 [448]~E(x4481,x4482)+E(f288(x4481,x4483),f288(x4482,x4483)) % 183.90/184.45 [449]~E(x4491,x4492)+E(f288(x4493,x4491),f288(x4493,x4492)) % 183.90/184.45 [450]~E(x4501,x4502)+E(f112(x4501),f112(x4502)) % 183.90/184.45 [451]~E(x4511,x4512)+E(f668(x4511,x4513,x4514),f668(x4512,x4513,x4514)) % 183.90/184.45 [452]~E(x4521,x4522)+E(f668(x4523,x4521,x4524),f668(x4523,x4522,x4524)) % 183.90/184.45 [453]~E(x4531,x4532)+E(f668(x4533,x4534,x4531),f668(x4533,x4534,x4532)) % 183.90/184.45 [454]~E(x4541,x4542)+E(f418(x4541,x4543,x4544,x4545),f418(x4542,x4543,x4544,x4545)) % 183.90/184.45 [455]~E(x4551,x4552)+E(f418(x4553,x4551,x4554,x4555),f418(x4553,x4552,x4554,x4555)) % 183.90/184.45 [456]~E(x4561,x4562)+E(f418(x4563,x4564,x4561,x4565),f418(x4563,x4564,x4562,x4565)) % 183.90/184.45 [457]~E(x4571,x4572)+E(f418(x4573,x4574,x4575,x4571),f418(x4573,x4574,x4575,x4572)) % 183.90/184.45 [458]~E(x4581,x4582)+E(f182(x4581,x4583),f182(x4582,x4583)) % 183.90/184.45 [459]~E(x4591,x4592)+E(f182(x4593,x4591),f182(x4593,x4592)) % 183.90/184.45 [460]~E(x4601,x4602)+E(f254(x4601),f254(x4602)) % 183.90/184.45 [461]~E(x4611,x4612)+E(f167(x4611),f167(x4612)) % 183.90/184.45 [462]~E(x4621,x4622)+E(f186(x4621,x4623,x4624),f186(x4622,x4623,x4624)) % 183.90/184.45 [463]~E(x4631,x4632)+E(f186(x4633,x4631,x4634),f186(x4633,x4632,x4634)) % 183.90/184.45 [464]~E(x4641,x4642)+E(f186(x4643,x4644,x4641),f186(x4643,x4644,x4642)) % 183.90/184.45 [465]~E(x4651,x4652)+E(f372(x4651,x4653,x4654,x4655,x4656),f372(x4652,x4653,x4654,x4655,x4656)) % 183.90/184.45 [466]~E(x4661,x4662)+E(f372(x4663,x4661,x4664,x4665,x4666),f372(x4663,x4662,x4664,x4665,x4666)) % 183.90/184.45 [467]~E(x4671,x4672)+E(f372(x4673,x4674,x4671,x4675,x4676),f372(x4673,x4674,x4672,x4675,x4676)) % 183.90/184.45 [468]~E(x4681,x4682)+E(f372(x4683,x4684,x4685,x4681,x4686),f372(x4683,x4684,x4685,x4682,x4686)) % 183.90/184.45 [469]~E(x4691,x4692)+E(f372(x4693,x4694,x4695,x4696,x4691),f372(x4693,x4694,x4695,x4696,x4692)) % 183.90/184.45 [470]~E(x4701,x4702)+E(f462(x4701,x4703,x4704),f462(x4702,x4703,x4704)) % 183.90/184.45 [471]~E(x4711,x4712)+E(f462(x4713,x4711,x4714),f462(x4713,x4712,x4714)) % 183.90/184.45 [472]~E(x4721,x4722)+E(f462(x4723,x4724,x4721),f462(x4723,x4724,x4722)) % 183.90/184.45 [473]~E(x4731,x4732)+E(f793(x4731,x4733,x4734,x4735,x4736,x4737,x4738),f793(x4732,x4733,x4734,x4735,x4736,x4737,x4738)) % 183.90/184.45 [474]~E(x4741,x4742)+E(f793(x4743,x4741,x4744,x4745,x4746,x4747,x4748),f793(x4743,x4742,x4744,x4745,x4746,x4747,x4748)) % 183.90/184.45 [475]~E(x4751,x4752)+E(f793(x4753,x4754,x4751,x4755,x4756,x4757,x4758),f793(x4753,x4754,x4752,x4755,x4756,x4757,x4758)) % 183.90/184.45 [476]~E(x4761,x4762)+E(f793(x4763,x4764,x4765,x4761,x4766,x4767,x4768),f793(x4763,x4764,x4765,x4762,x4766,x4767,x4768)) % 183.90/184.45 [477]~E(x4771,x4772)+E(f793(x4773,x4774,x4775,x4776,x4771,x4777,x4778),f793(x4773,x4774,x4775,x4776,x4772,x4777,x4778)) % 183.90/184.45 [478]~E(x4781,x4782)+E(f793(x4783,x4784,x4785,x4786,x4787,x4781,x4788),f793(x4783,x4784,x4785,x4786,x4787,x4782,x4788)) % 183.90/184.45 [479]~E(x4791,x4792)+E(f793(x4793,x4794,x4795,x4796,x4797,x4798,x4791),f793(x4793,x4794,x4795,x4796,x4797,x4798,x4792)) % 183.90/184.45 [480]~E(x4801,x4802)+E(f553(x4801,x4803,x4804),f553(x4802,x4803,x4804)) % 183.90/184.45 [481]~E(x4811,x4812)+E(f553(x4813,x4811,x4814),f553(x4813,x4812,x4814)) % 183.90/184.45 [482]~E(x4821,x4822)+E(f553(x4823,x4824,x4821),f553(x4823,x4824,x4822)) % 183.90/184.45 [483]~E(x4831,x4832)+E(f308(x4831),f308(x4832)) % 183.90/184.45 [484]~E(x4841,x4842)+E(f355(x4841),f355(x4842)) % 183.90/184.45 [485]~E(x4851,x4852)+E(f320(x4851,x4853,x4854,x4855),f320(x4852,x4853,x4854,x4855)) % 183.90/184.45 [486]~E(x4861,x4862)+E(f320(x4863,x4861,x4864,x4865),f320(x4863,x4862,x4864,x4865)) % 183.90/184.45 [487]~E(x4871,x4872)+E(f320(x4873,x4874,x4871,x4875),f320(x4873,x4874,x4872,x4875)) % 183.90/184.45 [488]~E(x4881,x4882)+E(f320(x4883,x4884,x4885,x4881),f320(x4883,x4884,x4885,x4882)) % 183.90/184.45 [489]~E(x4891,x4892)+E(f415(x4891,x4893,x4894),f415(x4892,x4893,x4894)) % 183.90/184.45 [490]~E(x4901,x4902)+E(f415(x4903,x4901,x4904),f415(x4903,x4902,x4904)) % 183.90/184.45 [491]~E(x4911,x4912)+E(f415(x4913,x4914,x4911),f415(x4913,x4914,x4912)) % 183.90/184.45 [492]~E(x4921,x4922)+E(f375(x4921),f375(x4922)) % 183.90/184.45 [493]~E(x4931,x4932)+E(f792(x4931,x4933,x4934),f792(x4932,x4933,x4934)) % 183.90/184.45 [494]~E(x4941,x4942)+E(f792(x4943,x4941,x4944),f792(x4943,x4942,x4944)) % 183.90/184.45 [495]~E(x4951,x4952)+E(f792(x4953,x4954,x4951),f792(x4953,x4954,x4952)) % 183.90/184.45 [496]~E(x4961,x4962)+E(f149(x4961,x4963,x4964),f149(x4962,x4963,x4964)) % 183.90/184.45 [497]~E(x4971,x4972)+E(f149(x4973,x4971,x4974),f149(x4973,x4972,x4974)) % 183.90/184.45 [498]~E(x4981,x4982)+E(f149(x4983,x4984,x4981),f149(x4983,x4984,x4982)) % 183.90/184.45 [499]~E(x4991,x4992)+E(f568(x4991,x4993,x4994,x4995),f568(x4992,x4993,x4994,x4995)) % 183.90/184.45 [500]~E(x5001,x5002)+E(f568(x5003,x5001,x5004,x5005),f568(x5003,x5002,x5004,x5005)) % 183.90/184.45 [501]~E(x5011,x5012)+E(f568(x5013,x5014,x5011,x5015),f568(x5013,x5014,x5012,x5015)) % 183.90/184.45 [502]~E(x5021,x5022)+E(f568(x5023,x5024,x5025,x5021),f568(x5023,x5024,x5025,x5022)) % 183.90/184.45 [503]~E(x5031,x5032)+E(f672(x5031,x5033,x5034,x5035,x5036),f672(x5032,x5033,x5034,x5035,x5036)) % 183.90/184.45 [504]~E(x5041,x5042)+E(f672(x5043,x5041,x5044,x5045,x5046),f672(x5043,x5042,x5044,x5045,x5046)) % 183.90/184.45 [505]~E(x5051,x5052)+E(f672(x5053,x5054,x5051,x5055,x5056),f672(x5053,x5054,x5052,x5055,x5056)) % 183.90/184.45 [506]~E(x5061,x5062)+E(f672(x5063,x5064,x5065,x5061,x5066),f672(x5063,x5064,x5065,x5062,x5066)) % 183.90/184.45 [507]~E(x5071,x5072)+E(f672(x5073,x5074,x5075,x5076,x5071),f672(x5073,x5074,x5075,x5076,x5072)) % 183.90/184.45 [508]~E(x5081,x5082)+E(f266(x5081,x5083),f266(x5082,x5083)) % 183.90/184.45 [509]~E(x5091,x5092)+E(f266(x5093,x5091),f266(x5093,x5092)) % 183.90/184.45 [510]~E(x5101,x5102)+E(f627(x5101,x5103,x5104),f627(x5102,x5103,x5104)) % 183.90/184.45 [511]~E(x5111,x5112)+E(f627(x5113,x5111,x5114),f627(x5113,x5112,x5114)) % 183.90/184.45 [512]~E(x5121,x5122)+E(f627(x5123,x5124,x5121),f627(x5123,x5124,x5122)) % 183.90/184.45 [513]~E(x5131,x5132)+E(f85(x5131,x5133),f85(x5132,x5133)) % 183.90/184.45 [514]~E(x5141,x5142)+E(f85(x5143,x5141),f85(x5143,x5142)) % 183.90/184.45 [515]~E(x5151,x5152)+E(f255(x5151),f255(x5152)) % 183.90/184.45 [516]~E(x5161,x5162)+E(f552(x5161),f552(x5162)) % 183.90/184.45 [517]~E(x5171,x5172)+E(f194(x5171),f194(x5172)) % 183.90/184.45 [518]~E(x5181,x5182)+E(f770(x5181,x5183,x5184,x5185,x5186),f770(x5182,x5183,x5184,x5185,x5186)) % 183.90/184.45 [519]~E(x5191,x5192)+E(f770(x5193,x5191,x5194,x5195,x5196),f770(x5193,x5192,x5194,x5195,x5196)) % 183.90/184.45 [520]~E(x5201,x5202)+E(f770(x5203,x5204,x5201,x5205,x5206),f770(x5203,x5204,x5202,x5205,x5206)) % 183.90/184.45 [521]~E(x5211,x5212)+E(f770(x5213,x5214,x5215,x5211,x5216),f770(x5213,x5214,x5215,x5212,x5216)) % 183.90/184.45 [522]~E(x5221,x5222)+E(f770(x5223,x5224,x5225,x5226,x5221),f770(x5223,x5224,x5225,x5226,x5222)) % 183.90/184.45 [523]~E(x5231,x5232)+E(f193(x5231,x5233,x5234,x5235),f193(x5232,x5233,x5234,x5235)) % 183.90/184.45 [524]~E(x5241,x5242)+E(f193(x5243,x5241,x5244,x5245),f193(x5243,x5242,x5244,x5245)) % 183.90/184.45 [525]~E(x5251,x5252)+E(f193(x5253,x5254,x5251,x5255),f193(x5253,x5254,x5252,x5255)) % 183.90/184.45 [526]~E(x5261,x5262)+E(f193(x5263,x5264,x5265,x5261),f193(x5263,x5264,x5265,x5262)) % 183.90/184.45 [527]~E(x5271,x5272)+E(f849(x5271,x5273,x5274),f849(x5272,x5273,x5274)) % 183.90/184.45 [528]~E(x5281,x5282)+E(f849(x5283,x5281,x5284),f849(x5283,x5282,x5284)) % 183.90/184.45 [529]~E(x5291,x5292)+E(f849(x5293,x5294,x5291),f849(x5293,x5294,x5292)) % 183.90/184.45 [530]~E(x5301,x5302)+E(f588(x5301,x5303),f588(x5302,x5303)) % 183.90/184.45 [531]~E(x5311,x5312)+E(f588(x5313,x5311),f588(x5313,x5312)) % 183.90/184.45 [532]~E(x5321,x5322)+E(f11(x5321,x5323,x5324),f11(x5322,x5323,x5324)) % 183.90/184.45 [533]~E(x5331,x5332)+E(f11(x5333,x5331,x5334),f11(x5333,x5332,x5334)) % 183.90/184.45 [534]~E(x5341,x5342)+E(f11(x5343,x5344,x5341),f11(x5343,x5344,x5342)) % 183.90/184.45 [535]~E(x5351,x5352)+E(f65(x5351,x5353,x5354),f65(x5352,x5353,x5354)) % 183.90/184.45 [536]~E(x5361,x5362)+E(f65(x5363,x5361,x5364),f65(x5363,x5362,x5364)) % 183.90/184.45 [537]~E(x5371,x5372)+E(f65(x5373,x5374,x5371),f65(x5373,x5374,x5372)) % 183.90/184.45 [538]~E(x5381,x5382)+E(f765(x5381,x5383),f765(x5382,x5383)) % 183.90/184.45 [539]~E(x5391,x5392)+E(f765(x5393,x5391),f765(x5393,x5392)) % 183.90/184.45 [540]~E(x5401,x5402)+E(f162(x5401,x5403),f162(x5402,x5403)) % 183.90/184.45 [541]~E(x5411,x5412)+E(f162(x5413,x5411),f162(x5413,x5412)) % 183.90/184.45 [542]~E(x5421,x5422)+E(f717(x5421,x5423),f717(x5422,x5423)) % 183.90/184.45 [543]~E(x5431,x5432)+E(f717(x5433,x5431),f717(x5433,x5432)) % 183.90/184.45 [544]~E(x5441,x5442)+E(f126(x5441,x5443),f126(x5442,x5443)) % 183.90/184.45 [545]~E(x5451,x5452)+E(f126(x5453,x5451),f126(x5453,x5452)) % 183.90/184.45 [546]~E(x5461,x5462)+E(f507(x5461,x5463),f507(x5462,x5463)) % 183.90/184.45 [547]~E(x5471,x5472)+E(f507(x5473,x5471),f507(x5473,x5472)) % 183.90/184.45 [548]~E(x5481,x5482)+E(f778(x5481,x5483,x5484),f778(x5482,x5483,x5484)) % 183.90/184.45 [549]~E(x5491,x5492)+E(f778(x5493,x5491,x5494),f778(x5493,x5492,x5494)) % 183.90/184.45 [550]~E(x5501,x5502)+E(f778(x5503,x5504,x5501),f778(x5503,x5504,x5502)) % 183.90/184.45 [551]~E(x5511,x5512)+E(f239(x5511,x5513),f239(x5512,x5513)) % 183.90/184.45 [552]~E(x5521,x5522)+E(f239(x5523,x5521),f239(x5523,x5522)) % 183.90/184.45 [553]~E(x5531,x5532)+E(f446(x5531,x5533,x5534,x5535),f446(x5532,x5533,x5534,x5535)) % 183.90/184.45 [554]~E(x5541,x5542)+E(f446(x5543,x5541,x5544,x5545),f446(x5543,x5542,x5544,x5545)) % 183.90/184.45 [555]~E(x5551,x5552)+E(f446(x5553,x5554,x5551,x5555),f446(x5553,x5554,x5552,x5555)) % 183.90/184.45 [556]~E(x5561,x5562)+E(f446(x5563,x5564,x5565,x5561),f446(x5563,x5564,x5565,x5562)) % 183.90/184.45 [557]~E(x5571,x5572)+E(f265(x5571,x5573),f265(x5572,x5573)) % 183.90/184.45 [558]~E(x5581,x5582)+E(f265(x5583,x5581),f265(x5583,x5582)) % 183.90/184.45 [559]~E(x5591,x5592)+E(f183(x5591),f183(x5592)) % 183.90/184.45 [560]~E(x5601,x5602)+E(f164(x5601,x5603,x5604,x5605),f164(x5602,x5603,x5604,x5605)) % 183.90/184.45 [561]~E(x5611,x5612)+E(f164(x5613,x5611,x5614,x5615),f164(x5613,x5612,x5614,x5615)) % 183.90/184.45 [562]~E(x5621,x5622)+E(f164(x5623,x5624,x5621,x5625),f164(x5623,x5624,x5622,x5625)) % 183.90/184.45 [563]~E(x5631,x5632)+E(f164(x5633,x5634,x5635,x5631),f164(x5633,x5634,x5635,x5632)) % 183.90/184.45 [564]~E(x5641,x5642)+E(f269(x5641,x5643,x5644,x5645,x5646),f269(x5642,x5643,x5644,x5645,x5646)) % 183.90/184.45 [565]~E(x5651,x5652)+E(f269(x5653,x5651,x5654,x5655,x5656),f269(x5653,x5652,x5654,x5655,x5656)) % 183.90/184.45 [566]~E(x5661,x5662)+E(f269(x5663,x5664,x5661,x5665,x5666),f269(x5663,x5664,x5662,x5665,x5666)) % 183.90/184.45 [567]~E(x5671,x5672)+E(f269(x5673,x5674,x5675,x5671,x5676),f269(x5673,x5674,x5675,x5672,x5676)) % 183.90/184.45 [568]~E(x5681,x5682)+E(f269(x5683,x5684,x5685,x5686,x5681),f269(x5683,x5684,x5685,x5686,x5682)) % 183.90/184.45 [569]~E(x5691,x5692)+E(f646(x5691,x5693,x5694,x5695,x5696),f646(x5692,x5693,x5694,x5695,x5696)) % 183.90/184.45 [570]~E(x5701,x5702)+E(f646(x5703,x5701,x5704,x5705,x5706),f646(x5703,x5702,x5704,x5705,x5706)) % 183.90/184.45 [571]~E(x5711,x5712)+E(f646(x5713,x5714,x5711,x5715,x5716),f646(x5713,x5714,x5712,x5715,x5716)) % 183.90/184.45 [572]~E(x5721,x5722)+E(f646(x5723,x5724,x5725,x5721,x5726),f646(x5723,x5724,x5725,x5722,x5726)) % 183.90/184.45 [573]~E(x5731,x5732)+E(f646(x5733,x5734,x5735,x5736,x5731),f646(x5733,x5734,x5735,x5736,x5732)) % 183.90/184.45 [574]~E(x5741,x5742)+E(f834(x5741,x5743,x5744,x5745),f834(x5742,x5743,x5744,x5745)) % 183.90/184.45 [575]~E(x5751,x5752)+E(f834(x5753,x5751,x5754,x5755),f834(x5753,x5752,x5754,x5755)) % 183.90/184.45 [576]~E(x5761,x5762)+E(f834(x5763,x5764,x5761,x5765),f834(x5763,x5764,x5762,x5765)) % 183.90/184.45 [577]~E(x5771,x5772)+E(f834(x5773,x5774,x5775,x5771),f834(x5773,x5774,x5775,x5772)) % 183.90/184.45 [578]~E(x5781,x5782)+E(f327(x5781,x5783,x5784),f327(x5782,x5783,x5784)) % 183.90/184.45 [579]~E(x5791,x5792)+E(f327(x5793,x5791,x5794),f327(x5793,x5792,x5794)) % 183.90/184.45 [580]~E(x5801,x5802)+E(f327(x5803,x5804,x5801),f327(x5803,x5804,x5802)) % 183.90/184.45 [581]~E(x5811,x5812)+E(f525(x5811,x5813,x5814),f525(x5812,x5813,x5814)) % 183.90/184.45 [582]~E(x5821,x5822)+E(f525(x5823,x5821,x5824),f525(x5823,x5822,x5824)) % 183.90/184.45 [583]~E(x5831,x5832)+E(f525(x5833,x5834,x5831),f525(x5833,x5834,x5832)) % 183.90/184.45 [584]~E(x5841,x5842)+E(f494(x5841,x5843,x5844,x5845,x5846,x5847),f494(x5842,x5843,x5844,x5845,x5846,x5847)) % 183.90/184.45 [585]~E(x5851,x5852)+E(f494(x5853,x5851,x5854,x5855,x5856,x5857),f494(x5853,x5852,x5854,x5855,x5856,x5857)) % 183.90/184.45 [586]~E(x5861,x5862)+E(f494(x5863,x5864,x5861,x5865,x5866,x5867),f494(x5863,x5864,x5862,x5865,x5866,x5867)) % 183.90/184.45 [587]~E(x5871,x5872)+E(f494(x5873,x5874,x5875,x5871,x5876,x5877),f494(x5873,x5874,x5875,x5872,x5876,x5877)) % 183.90/184.45 [588]~E(x5881,x5882)+E(f494(x5883,x5884,x5885,x5886,x5881,x5887),f494(x5883,x5884,x5885,x5886,x5882,x5887)) % 183.90/184.45 [589]~E(x5891,x5892)+E(f494(x5893,x5894,x5895,x5896,x5897,x5891),f494(x5893,x5894,x5895,x5896,x5897,x5892)) % 183.90/184.45 [590]~E(x5901,x5902)+E(f813(x5901,x5903,x5904),f813(x5902,x5903,x5904)) % 183.90/184.45 [591]~E(x5911,x5912)+E(f813(x5913,x5911,x5914),f813(x5913,x5912,x5914)) % 183.90/184.45 [592]~E(x5921,x5922)+E(f813(x5923,x5924,x5921),f813(x5923,x5924,x5922)) % 183.90/184.45 [593]~E(x5931,x5932)+E(f572(x5931,x5933,x5934,x5935),f572(x5932,x5933,x5934,x5935)) % 183.90/184.45 [594]~E(x5941,x5942)+E(f572(x5943,x5941,x5944,x5945),f572(x5943,x5942,x5944,x5945)) % 183.90/184.45 [595]~E(x5951,x5952)+E(f572(x5953,x5954,x5951,x5955),f572(x5953,x5954,x5952,x5955)) % 183.90/184.45 [596]~E(x5961,x5962)+E(f572(x5963,x5964,x5965,x5961),f572(x5963,x5964,x5965,x5962)) % 183.90/184.45 [597]~E(x5971,x5972)+E(f43(x5971),f43(x5972)) % 183.90/184.45 [598]~E(x5981,x5982)+E(f398(x5981,x5983,x5984,x5985,x5986),f398(x5982,x5983,x5984,x5985,x5986)) % 183.90/184.45 [599]~E(x5991,x5992)+E(f398(x5993,x5991,x5994,x5995,x5996),f398(x5993,x5992,x5994,x5995,x5996)) % 183.90/184.45 [600]~E(x6001,x6002)+E(f398(x6003,x6004,x6001,x6005,x6006),f398(x6003,x6004,x6002,x6005,x6006)) % 183.90/184.45 [601]~E(x6011,x6012)+E(f398(x6013,x6014,x6015,x6011,x6016),f398(x6013,x6014,x6015,x6012,x6016)) % 183.90/184.45 [602]~E(x6021,x6022)+E(f398(x6023,x6024,x6025,x6026,x6021),f398(x6023,x6024,x6025,x6026,x6022)) % 183.90/184.45 [603]~E(x6031,x6032)+E(f227(x6031,x6033),f227(x6032,x6033)) % 183.90/184.45 [604]~E(x6041,x6042)+E(f227(x6043,x6041),f227(x6043,x6042)) % 183.90/184.45 [605]~E(x6051,x6052)+E(f806(x6051,x6053,x6054),f806(x6052,x6053,x6054)) % 183.90/184.45 [606]~E(x6061,x6062)+E(f806(x6063,x6061,x6064),f806(x6063,x6062,x6064)) % 183.90/184.45 [607]~E(x6071,x6072)+E(f806(x6073,x6074,x6071),f806(x6073,x6074,x6072)) % 183.90/184.45 [608]~E(x6081,x6082)+E(f756(x6081,x6083,x6084),f756(x6082,x6083,x6084)) % 183.90/184.45 [609]~E(x6091,x6092)+E(f756(x6093,x6091,x6094),f756(x6093,x6092,x6094)) % 183.90/184.45 [610]~E(x6101,x6102)+E(f756(x6103,x6104,x6101),f756(x6103,x6104,x6102)) % 183.90/184.45 [611]~E(x6111,x6112)+E(f257(x6111,x6113,x6114),f257(x6112,x6113,x6114)) % 183.90/184.45 [612]~E(x6121,x6122)+E(f257(x6123,x6121,x6124),f257(x6123,x6122,x6124)) % 183.90/184.45 [613]~E(x6131,x6132)+E(f257(x6133,x6134,x6131),f257(x6133,x6134,x6132)) % 183.90/184.45 [614]~E(x6141,x6142)+E(f850(x6141,x6143,x6144),f850(x6142,x6143,x6144)) % 183.90/184.45 [615]~E(x6151,x6152)+E(f850(x6153,x6151,x6154),f850(x6153,x6152,x6154)) % 183.90/184.45 [616]~E(x6161,x6162)+E(f850(x6163,x6164,x6161),f850(x6163,x6164,x6162)) % 183.90/184.45 [617]~E(x6171,x6172)+E(f315(x6171,x6173,x6174),f315(x6172,x6173,x6174)) % 183.90/184.45 [618]~E(x6181,x6182)+E(f315(x6183,x6181,x6184),f315(x6183,x6182,x6184)) % 183.90/184.45 [619]~E(x6191,x6192)+E(f315(x6193,x6194,x6191),f315(x6193,x6194,x6192)) % 183.90/184.45 [620]~E(x6201,x6202)+E(f851(x6201,x6203,x6204),f851(x6202,x6203,x6204)) % 183.90/184.45 [621]~E(x6211,x6212)+E(f851(x6213,x6211,x6214),f851(x6213,x6212,x6214)) % 183.90/184.45 [622]~E(x6221,x6222)+E(f851(x6223,x6224,x6221),f851(x6223,x6224,x6222)) % 183.90/184.45 [623]~E(x6231,x6232)+E(f523(x6231,x6233,x6234,x6235),f523(x6232,x6233,x6234,x6235)) % 183.90/184.45 [624]~E(x6241,x6242)+E(f523(x6243,x6241,x6244,x6245),f523(x6243,x6242,x6244,x6245)) % 183.90/184.45 [625]~E(x6251,x6252)+E(f523(x6253,x6254,x6251,x6255),f523(x6253,x6254,x6252,x6255)) % 183.90/184.45 [626]~E(x6261,x6262)+E(f523(x6263,x6264,x6265,x6261),f523(x6263,x6264,x6265,x6262)) % 183.90/184.45 [627]~E(x6271,x6272)+E(f615(x6271,x6273,x6274),f615(x6272,x6273,x6274)) % 183.90/184.45 [628]~E(x6281,x6282)+E(f615(x6283,x6281,x6284),f615(x6283,x6282,x6284)) % 183.90/184.45 [629]~E(x6291,x6292)+E(f615(x6293,x6294,x6291),f615(x6293,x6294,x6292)) % 183.90/184.45 [630]~E(x6301,x6302)+E(f172(x6301,x6303,x6304),f172(x6302,x6303,x6304)) % 183.90/184.45 [631]~E(x6311,x6312)+E(f172(x6313,x6311,x6314),f172(x6313,x6312,x6314)) % 183.90/184.45 [632]~E(x6321,x6322)+E(f172(x6323,x6324,x6321),f172(x6323,x6324,x6322)) % 183.90/184.45 [633]~E(x6331,x6332)+E(f632(x6331,x6333),f632(x6332,x6333)) % 183.90/184.45 [634]~E(x6341,x6342)+E(f632(x6343,x6341),f632(x6343,x6342)) % 183.90/184.45 [635]~E(x6351,x6352)+E(f361(x6351,x6353,x6354),f361(x6352,x6353,x6354)) % 183.90/184.45 [636]~E(x6361,x6362)+E(f361(x6363,x6361,x6364),f361(x6363,x6362,x6364)) % 183.90/184.45 [637]~E(x6371,x6372)+E(f361(x6373,x6374,x6371),f361(x6373,x6374,x6372)) % 183.90/184.45 [638]~E(x6381,x6382)+E(f645(x6381,x6383,x6384,x6385,x6386),f645(x6382,x6383,x6384,x6385,x6386)) % 183.90/184.45 [639]~E(x6391,x6392)+E(f645(x6393,x6391,x6394,x6395,x6396),f645(x6393,x6392,x6394,x6395,x6396)) % 183.90/184.45 [640]~E(x6401,x6402)+E(f645(x6403,x6404,x6401,x6405,x6406),f645(x6403,x6404,x6402,x6405,x6406)) % 183.90/184.45 [641]~E(x6411,x6412)+E(f645(x6413,x6414,x6415,x6411,x6416),f645(x6413,x6414,x6415,x6412,x6416)) % 183.90/184.45 [642]~E(x6421,x6422)+E(f645(x6423,x6424,x6425,x6426,x6421),f645(x6423,x6424,x6425,x6426,x6422)) % 183.90/184.45 [643]~E(x6431,x6432)+E(f81(x6431,x6433),f81(x6432,x6433)) % 183.90/184.45 [644]~E(x6441,x6442)+E(f81(x6443,x6441),f81(x6443,x6442)) % 183.90/184.45 [645]~E(x6451,x6452)+E(f578(x6451,x6453,x6454,x6455),f578(x6452,x6453,x6454,x6455)) % 183.90/184.45 [646]~E(x6461,x6462)+E(f578(x6463,x6461,x6464,x6465),f578(x6463,x6462,x6464,x6465)) % 183.90/184.45 [647]~E(x6471,x6472)+E(f578(x6473,x6474,x6471,x6475),f578(x6473,x6474,x6472,x6475)) % 183.90/184.45 [648]~E(x6481,x6482)+E(f578(x6483,x6484,x6485,x6481),f578(x6483,x6484,x6485,x6482)) % 183.90/184.45 [649]~E(x6491,x6492)+E(f76(x6491,x6493,x6494,x6495),f76(x6492,x6493,x6494,x6495)) % 183.90/184.45 [650]~E(x6501,x6502)+E(f76(x6503,x6501,x6504,x6505),f76(x6503,x6502,x6504,x6505)) % 183.90/184.45 [651]~E(x6511,x6512)+E(f76(x6513,x6514,x6511,x6515),f76(x6513,x6514,x6512,x6515)) % 183.90/184.45 [652]~E(x6521,x6522)+E(f76(x6523,x6524,x6525,x6521),f76(x6523,x6524,x6525,x6522)) % 183.90/184.45 [653]~E(x6531,x6532)+E(f807(x6531,x6533,x6534),f807(x6532,x6533,x6534)) % 183.90/184.45 [654]~E(x6541,x6542)+E(f807(x6543,x6541,x6544),f807(x6543,x6542,x6544)) % 183.90/184.45 [655]~E(x6551,x6552)+E(f807(x6553,x6554,x6551),f807(x6553,x6554,x6552)) % 183.90/184.45 [656]~E(x6561,x6562)+E(f659(x6561,x6563,x6564,x6565),f659(x6562,x6563,x6564,x6565)) % 183.90/184.45 [657]~E(x6571,x6572)+E(f659(x6573,x6571,x6574,x6575),f659(x6573,x6572,x6574,x6575)) % 183.90/184.45 [658]~E(x6581,x6582)+E(f659(x6583,x6584,x6581,x6585),f659(x6583,x6584,x6582,x6585)) % 183.90/184.45 [659]~E(x6591,x6592)+E(f659(x6593,x6594,x6595,x6591),f659(x6593,x6594,x6595,x6592)) % 183.90/184.45 [660]~E(x6601,x6602)+E(f818(x6601,x6603,x6604),f818(x6602,x6603,x6604)) % 183.90/184.45 [661]~E(x6611,x6612)+E(f818(x6613,x6611,x6614),f818(x6613,x6612,x6614)) % 183.90/184.45 [662]~E(x6621,x6622)+E(f818(x6623,x6624,x6621),f818(x6623,x6624,x6622)) % 183.90/184.45 [663]~E(x6631,x6632)+E(f168(x6631,x6633,x6634),f168(x6632,x6633,x6634)) % 183.90/184.45 [664]~E(x6641,x6642)+E(f168(x6643,x6641,x6644),f168(x6643,x6642,x6644)) % 183.90/184.45 [665]~E(x6651,x6652)+E(f168(x6653,x6654,x6651),f168(x6653,x6654,x6652)) % 183.90/184.45 [666]~E(x6661,x6662)+E(f766(x6661,x6663),f766(x6662,x6663)) % 183.90/184.45 [667]~E(x6671,x6672)+E(f766(x6673,x6671),f766(x6673,x6672)) % 183.90/184.45 [668]~E(x6681,x6682)+E(f647(x6681,x6683,x6684,x6685,x6686),f647(x6682,x6683,x6684,x6685,x6686)) % 183.90/184.45 [669]~E(x6691,x6692)+E(f647(x6693,x6691,x6694,x6695,x6696),f647(x6693,x6692,x6694,x6695,x6696)) % 183.90/184.45 [670]~E(x6701,x6702)+E(f647(x6703,x6704,x6701,x6705,x6706),f647(x6703,x6704,x6702,x6705,x6706)) % 183.90/184.45 [671]~E(x6711,x6712)+E(f647(x6713,x6714,x6715,x6711,x6716),f647(x6713,x6714,x6715,x6712,x6716)) % 183.90/184.45 [672]~E(x6721,x6722)+E(f647(x6723,x6724,x6725,x6726,x6721),f647(x6723,x6724,x6725,x6726,x6722)) % 183.90/184.45 [673]~E(x6731,x6732)+E(f242(x6731,x6733,x6734,x6735),f242(x6732,x6733,x6734,x6735)) % 183.90/184.45 [674]~E(x6741,x6742)+E(f242(x6743,x6741,x6744,x6745),f242(x6743,x6742,x6744,x6745)) % 183.90/184.45 [675]~E(x6751,x6752)+E(f242(x6753,x6754,x6751,x6755),f242(x6753,x6754,x6752,x6755)) % 183.90/184.45 [676]~E(x6761,x6762)+E(f242(x6763,x6764,x6765,x6761),f242(x6763,x6764,x6765,x6762)) % 183.90/184.45 [677]~E(x6771,x6772)+E(f858(x6771,x6773,x6774),f858(x6772,x6773,x6774)) % 183.90/184.45 [678]~E(x6781,x6782)+E(f858(x6783,x6781,x6784),f858(x6783,x6782,x6784)) % 183.90/184.45 [679]~E(x6791,x6792)+E(f858(x6793,x6794,x6791),f858(x6793,x6794,x6792)) % 183.90/184.45 [680]~E(x6801,x6802)+E(f161(x6801,x6803),f161(x6802,x6803)) % 183.90/184.45 [681]~E(x6811,x6812)+E(f161(x6813,x6811),f161(x6813,x6812)) % 183.90/184.45 [682]~E(x6821,x6822)+E(f785(x6821,x6823,x6824,x6825,x6826),f785(x6822,x6823,x6824,x6825,x6826)) % 183.90/184.45 [683]~E(x6831,x6832)+E(f785(x6833,x6831,x6834,x6835,x6836),f785(x6833,x6832,x6834,x6835,x6836)) % 183.90/184.45 [684]~E(x6841,x6842)+E(f785(x6843,x6844,x6841,x6845,x6846),f785(x6843,x6844,x6842,x6845,x6846)) % 183.90/184.45 [685]~E(x6851,x6852)+E(f785(x6853,x6854,x6855,x6851,x6856),f785(x6853,x6854,x6855,x6852,x6856)) % 183.90/184.45 [686]~E(x6861,x6862)+E(f785(x6863,x6864,x6865,x6866,x6861),f785(x6863,x6864,x6865,x6866,x6862)) % 183.90/184.45 [687]~E(x6871,x6872)+E(f145(x6871,x6873),f145(x6872,x6873)) % 183.90/184.45 [688]~E(x6881,x6882)+E(f145(x6883,x6881),f145(x6883,x6882)) % 183.90/184.45 [689]~E(x6891,x6892)+E(f574(x6891,x6893,x6894,x6895),f574(x6892,x6893,x6894,x6895)) % 183.90/184.45 [690]~E(x6901,x6902)+E(f574(x6903,x6901,x6904,x6905),f574(x6903,x6902,x6904,x6905)) % 183.90/184.45 [691]~E(x6911,x6912)+E(f574(x6913,x6914,x6911,x6915),f574(x6913,x6914,x6912,x6915)) % 183.90/184.45 [692]~E(x6921,x6922)+E(f574(x6923,x6924,x6925,x6921),f574(x6923,x6924,x6925,x6922)) % 183.90/184.45 [693]~E(x6931,x6932)+E(f217(x6931,x6933,x6934,x6935),f217(x6932,x6933,x6934,x6935)) % 183.90/184.45 [694]~E(x6941,x6942)+E(f217(x6943,x6941,x6944,x6945),f217(x6943,x6942,x6944,x6945)) % 183.90/184.45 [695]~E(x6951,x6952)+E(f217(x6953,x6954,x6951,x6955),f217(x6953,x6954,x6952,x6955)) % 183.90/184.45 [696]~E(x6961,x6962)+E(f217(x6963,x6964,x6965,x6961),f217(x6963,x6964,x6965,x6962)) % 183.90/184.45 [697]~E(x6971,x6972)+E(f823(x6971,x6973,x6974),f823(x6972,x6973,x6974)) % 183.90/184.45 [698]~E(x6981,x6982)+E(f823(x6983,x6981,x6984),f823(x6983,x6982,x6984)) % 183.90/184.45 [699]~E(x6991,x6992)+E(f823(x6993,x6994,x6991),f823(x6993,x6994,x6992)) % 183.90/184.45 [700]~E(x7001,x7002)+E(f150(x7001,x7003,x7004,x7005,x7006),f150(x7002,x7003,x7004,x7005,x7006)) % 183.90/184.45 [701]~E(x7011,x7012)+E(f150(x7013,x7011,x7014,x7015,x7016),f150(x7013,x7012,x7014,x7015,x7016)) % 183.90/184.45 [702]~E(x7021,x7022)+E(f150(x7023,x7024,x7021,x7025,x7026),f150(x7023,x7024,x7022,x7025,x7026)) % 183.90/184.45 [703]~E(x7031,x7032)+E(f150(x7033,x7034,x7035,x7031,x7036),f150(x7033,x7034,x7035,x7032,x7036)) % 183.90/184.45 [704]~E(x7041,x7042)+E(f150(x7043,x7044,x7045,x7046,x7041),f150(x7043,x7044,x7045,x7046,x7042)) % 183.90/184.45 [705]~E(x7051,x7052)+E(f129(x7051),f129(x7052)) % 183.90/184.45 [706]~E(x7061,x7062)+E(f640(x7061,x7063,x7064,x7065,x7066),f640(x7062,x7063,x7064,x7065,x7066)) % 183.90/184.45 [707]~E(x7071,x7072)+E(f640(x7073,x7071,x7074,x7075,x7076),f640(x7073,x7072,x7074,x7075,x7076)) % 183.90/184.45 [708]~E(x7081,x7082)+E(f640(x7083,x7084,x7081,x7085,x7086),f640(x7083,x7084,x7082,x7085,x7086)) % 183.90/184.45 [709]~E(x7091,x7092)+E(f640(x7093,x7094,x7095,x7091,x7096),f640(x7093,x7094,x7095,x7092,x7096)) % 183.90/184.45 [710]~E(x7101,x7102)+E(f640(x7103,x7104,x7105,x7106,x7101),f640(x7103,x7104,x7105,x7106,x7102)) % 183.90/184.45 [711]~E(x7111,x7112)+E(f590(x7111,x7113,x7114),f590(x7112,x7113,x7114)) % 183.90/184.45 [712]~E(x7121,x7122)+E(f590(x7123,x7121,x7124),f590(x7123,x7122,x7124)) % 183.90/184.45 [713]~E(x7131,x7132)+E(f590(x7133,x7134,x7131),f590(x7133,x7134,x7132)) % 183.90/184.45 [714]~E(x7141,x7142)+E(f392(x7141,x7143,x7144),f392(x7142,x7143,x7144)) % 183.90/184.45 [715]~E(x7151,x7152)+E(f392(x7153,x7151,x7154),f392(x7153,x7152,x7154)) % 183.90/184.45 [716]~E(x7161,x7162)+E(f392(x7163,x7164,x7161),f392(x7163,x7164,x7162)) % 183.90/184.45 [717]~E(x7171,x7172)+E(f345(x7171),f345(x7172)) % 183.90/184.45 [718]~E(x7181,x7182)+E(f274(x7181,x7183,x7184,x7185),f274(x7182,x7183,x7184,x7185)) % 183.90/184.45 [719]~E(x7191,x7192)+E(f274(x7193,x7191,x7194,x7195),f274(x7193,x7192,x7194,x7195)) % 183.90/184.45 [720]~E(x7201,x7202)+E(f274(x7203,x7204,x7201,x7205),f274(x7203,x7204,x7202,x7205)) % 183.90/184.45 [721]~E(x7211,x7212)+E(f274(x7213,x7214,x7215,x7211),f274(x7213,x7214,x7215,x7212)) % 183.90/184.45 [722]~E(x7221,x7222)+E(f383(x7221,x7223),f383(x7222,x7223)) % 183.90/184.45 [723]~E(x7231,x7232)+E(f383(x7233,x7231),f383(x7233,x7232)) % 183.90/184.45 [724]~E(x7241,x7242)+E(f121(x7241,x7243,x7244),f121(x7242,x7243,x7244)) % 183.90/184.45 [725]~E(x7251,x7252)+E(f121(x7253,x7251,x7254),f121(x7253,x7252,x7254)) % 183.90/184.45 [726]~E(x7261,x7262)+E(f121(x7263,x7264,x7261),f121(x7263,x7264,x7262)) % 183.90/184.45 [727]~E(x7271,x7272)+E(f491(x7271,x7273),f491(x7272,x7273)) % 183.90/184.45 [728]~E(x7281,x7282)+E(f491(x7283,x7281),f491(x7283,x7282)) % 183.90/184.45 [729]~E(x7291,x7292)+E(f46(x7291,x7293),f46(x7292,x7293)) % 183.90/184.45 [730]~E(x7301,x7302)+E(f46(x7303,x7301),f46(x7303,x7302)) % 183.90/184.45 [731]~E(x7311,x7312)+E(f562(x7311,x7313,x7314,x7315),f562(x7312,x7313,x7314,x7315)) % 183.90/184.45 [732]~E(x7321,x7322)+E(f562(x7323,x7321,x7324,x7325),f562(x7323,x7322,x7324,x7325)) % 183.90/184.45 [733]~E(x7331,x7332)+E(f562(x7333,x7334,x7331,x7335),f562(x7333,x7334,x7332,x7335)) % 183.90/184.45 [734]~E(x7341,x7342)+E(f562(x7343,x7344,x7345,x7341),f562(x7343,x7344,x7345,x7342)) % 183.90/184.45 [735]~E(x7351,x7352)+E(f543(x7351,x7353,x7354,x7355,x7356,x7357,x7358),f543(x7352,x7353,x7354,x7355,x7356,x7357,x7358)) % 183.90/184.45 [736]~E(x7361,x7362)+E(f543(x7363,x7361,x7364,x7365,x7366,x7367,x7368),f543(x7363,x7362,x7364,x7365,x7366,x7367,x7368)) % 183.90/184.45 [737]~E(x7371,x7372)+E(f543(x7373,x7374,x7371,x7375,x7376,x7377,x7378),f543(x7373,x7374,x7372,x7375,x7376,x7377,x7378)) % 183.90/184.45 [738]~E(x7381,x7382)+E(f543(x7383,x7384,x7385,x7381,x7386,x7387,x7388),f543(x7383,x7384,x7385,x7382,x7386,x7387,x7388)) % 183.90/184.45 [739]~E(x7391,x7392)+E(f543(x7393,x7394,x7395,x7396,x7391,x7397,x7398),f543(x7393,x7394,x7395,x7396,x7392,x7397,x7398)) % 183.90/184.45 [740]~E(x7401,x7402)+E(f543(x7403,x7404,x7405,x7406,x7407,x7401,x7408),f543(x7403,x7404,x7405,x7406,x7407,x7402,x7408)) % 183.90/184.45 [741]~E(x7411,x7412)+E(f543(x7413,x7414,x7415,x7416,x7417,x7418,x7411),f543(x7413,x7414,x7415,x7416,x7417,x7418,x7412)) % 183.90/184.45 [742]~E(x7421,x7422)+E(f388(x7421,x7423),f388(x7422,x7423)) % 183.90/184.45 [743]~E(x7431,x7432)+E(f388(x7433,x7431),f388(x7433,x7432)) % 183.90/184.45 [744]~E(x7441,x7442)+E(f404(x7441,x7443),f404(x7442,x7443)) % 183.90/184.45 [745]~E(x7451,x7452)+E(f404(x7453,x7451),f404(x7453,x7452)) % 183.90/184.45 [746]~E(x7461,x7462)+E(f608(x7461,x7463,x7464,x7465,x7466,x7467),f608(x7462,x7463,x7464,x7465,x7466,x7467)) % 183.90/184.45 [747]~E(x7471,x7472)+E(f608(x7473,x7471,x7474,x7475,x7476,x7477),f608(x7473,x7472,x7474,x7475,x7476,x7477)) % 183.90/184.45 [748]~E(x7481,x7482)+E(f608(x7483,x7484,x7481,x7485,x7486,x7487),f608(x7483,x7484,x7482,x7485,x7486,x7487)) % 183.90/184.45 [749]~E(x7491,x7492)+E(f608(x7493,x7494,x7495,x7491,x7496,x7497),f608(x7493,x7494,x7495,x7492,x7496,x7497)) % 183.90/184.45 [750]~E(x7501,x7502)+E(f608(x7503,x7504,x7505,x7506,x7501,x7507),f608(x7503,x7504,x7505,x7506,x7502,x7507)) % 183.90/184.45 [751]~E(x7511,x7512)+E(f608(x7513,x7514,x7515,x7516,x7517,x7511),f608(x7513,x7514,x7515,x7516,x7517,x7512)) % 183.90/184.45 [752]~E(x7521,x7522)+E(f298(x7521,x7523,x7524,x7525,x7526),f298(x7522,x7523,x7524,x7525,x7526)) % 183.90/184.45 [753]~E(x7531,x7532)+E(f298(x7533,x7531,x7534,x7535,x7536),f298(x7533,x7532,x7534,x7535,x7536)) % 183.90/184.45 [754]~E(x7541,x7542)+E(f298(x7543,x7544,x7541,x7545,x7546),f298(x7543,x7544,x7542,x7545,x7546)) % 183.90/184.45 [755]~E(x7551,x7552)+E(f298(x7553,x7554,x7555,x7551,x7556),f298(x7553,x7554,x7555,x7552,x7556)) % 183.90/184.45 [756]~E(x7561,x7562)+E(f298(x7563,x7564,x7565,x7566,x7561),f298(x7563,x7564,x7565,x7566,x7562)) % 183.90/184.45 [757]~E(x7571,x7572)+E(f471(x7571,x7573,x7574),f471(x7572,x7573,x7574)) % 183.90/184.45 [758]~E(x7581,x7582)+E(f471(x7583,x7581,x7584),f471(x7583,x7582,x7584)) % 183.90/184.45 [759]~E(x7591,x7592)+E(f471(x7593,x7594,x7591),f471(x7593,x7594,x7592)) % 183.90/184.45 [760]~E(x7601,x7602)+E(f781(x7601,x7603,x7604,x7605,x7606),f781(x7602,x7603,x7604,x7605,x7606)) % 183.90/184.45 [761]~E(x7611,x7612)+E(f781(x7613,x7611,x7614,x7615,x7616),f781(x7613,x7612,x7614,x7615,x7616)) % 183.90/184.45 [762]~E(x7621,x7622)+E(f781(x7623,x7624,x7621,x7625,x7626),f781(x7623,x7624,x7622,x7625,x7626)) % 183.90/184.45 [763]~E(x7631,x7632)+E(f781(x7633,x7634,x7635,x7631,x7636),f781(x7633,x7634,x7635,x7632,x7636)) % 183.90/184.45 [764]~E(x7641,x7642)+E(f781(x7643,x7644,x7645,x7646,x7641),f781(x7643,x7644,x7645,x7646,x7642)) % 183.90/184.45 [765]~E(x7651,x7652)+E(f593(x7651,x7653,x7654),f593(x7652,x7653,x7654)) % 183.90/184.45 [766]~E(x7661,x7662)+E(f593(x7663,x7661,x7664),f593(x7663,x7662,x7664)) % 183.90/184.45 [767]~E(x7671,x7672)+E(f593(x7673,x7674,x7671),f593(x7673,x7674,x7672)) % 183.90/184.45 [768]~E(x7681,x7682)+E(f667(x7681,x7683,x7684),f667(x7682,x7683,x7684)) % 183.90/184.45 [769]~E(x7691,x7692)+E(f667(x7693,x7691,x7694),f667(x7693,x7692,x7694)) % 183.90/184.45 [770]~E(x7701,x7702)+E(f667(x7703,x7704,x7701),f667(x7703,x7704,x7702)) % 183.90/184.45 [771]~E(x7711,x7712)+E(f801(x7711,x7713,x7714),f801(x7712,x7713,x7714)) % 183.90/184.45 [772]~E(x7721,x7722)+E(f801(x7723,x7721,x7724),f801(x7723,x7722,x7724)) % 183.90/184.45 [773]~E(x7731,x7732)+E(f801(x7733,x7734,x7731),f801(x7733,x7734,x7732)) % 183.90/184.45 [774]~E(x7741,x7742)+E(f737(x7741,x7743,x7744,x7745,x7746),f737(x7742,x7743,x7744,x7745,x7746)) % 183.90/184.45 [775]~E(x7751,x7752)+E(f737(x7753,x7751,x7754,x7755,x7756),f737(x7753,x7752,x7754,x7755,x7756)) % 183.90/184.45 [776]~E(x7761,x7762)+E(f737(x7763,x7764,x7761,x7765,x7766),f737(x7763,x7764,x7762,x7765,x7766)) % 183.90/184.45 [777]~E(x7771,x7772)+E(f737(x7773,x7774,x7775,x7771,x7776),f737(x7773,x7774,x7775,x7772,x7776)) % 183.90/184.45 [778]~E(x7781,x7782)+E(f737(x7783,x7784,x7785,x7786,x7781),f737(x7783,x7784,x7785,x7786,x7782)) % 183.90/184.45 [779]~E(x7791,x7792)+E(f573(x7791,x7793,x7794,x7795),f573(x7792,x7793,x7794,x7795)) % 183.90/184.45 [780]~E(x7801,x7802)+E(f573(x7803,x7801,x7804,x7805),f573(x7803,x7802,x7804,x7805)) % 183.90/184.45 [781]~E(x7811,x7812)+E(f573(x7813,x7814,x7811,x7815),f573(x7813,x7814,x7812,x7815)) % 183.90/184.45 [782]~E(x7821,x7822)+E(f573(x7823,x7824,x7825,x7821),f573(x7823,x7824,x7825,x7822)) % 183.90/184.45 [783]~E(x7831,x7832)+E(f261(x7831,x7833),f261(x7832,x7833)) % 183.90/184.45 [784]~E(x7841,x7842)+E(f261(x7843,x7841),f261(x7843,x7842)) % 183.90/184.45 [785]~E(x7851,x7852)+E(f680(x7851,x7853,x7854,x7855),f680(x7852,x7853,x7854,x7855)) % 183.90/184.45 [786]~E(x7861,x7862)+E(f680(x7863,x7861,x7864,x7865),f680(x7863,x7862,x7864,x7865)) % 183.90/184.45 [787]~E(x7871,x7872)+E(f680(x7873,x7874,x7871,x7875),f680(x7873,x7874,x7872,x7875)) % 183.90/184.45 [788]~E(x7881,x7882)+E(f680(x7883,x7884,x7885,x7881),f680(x7883,x7884,x7885,x7882)) % 183.90/184.45 [789]~E(x7891,x7892)+E(f838(x7891,x7893,x7894,x7895,x7896),f838(x7892,x7893,x7894,x7895,x7896)) % 183.90/184.45 [790]~E(x7901,x7902)+E(f838(x7903,x7901,x7904,x7905,x7906),f838(x7903,x7902,x7904,x7905,x7906)) % 183.90/184.45 [791]~E(x7911,x7912)+E(f838(x7913,x7914,x7911,x7915,x7916),f838(x7913,x7914,x7912,x7915,x7916)) % 183.90/184.45 [792]~E(x7921,x7922)+E(f838(x7923,x7924,x7925,x7921,x7926),f838(x7923,x7924,x7925,x7922,x7926)) % 183.90/184.45 [793]~E(x7931,x7932)+E(f838(x7933,x7934,x7935,x7936,x7931),f838(x7933,x7934,x7935,x7936,x7932)) % 183.90/184.45 [794]~E(x7941,x7942)+E(f426(x7941,x7943,x7944,x7945),f426(x7942,x7943,x7944,x7945)) % 183.90/184.45 [795]~E(x7951,x7952)+E(f426(x7953,x7951,x7954,x7955),f426(x7953,x7952,x7954,x7955)) % 183.90/184.45 [796]~E(x7961,x7962)+E(f426(x7963,x7964,x7961,x7965),f426(x7963,x7964,x7962,x7965)) % 183.90/184.45 [797]~E(x7971,x7972)+E(f426(x7973,x7974,x7975,x7971),f426(x7973,x7974,x7975,x7972)) % 183.90/184.45 [798]~E(x7981,x7982)+E(f206(x7981,x7983,x7984,x7985),f206(x7982,x7983,x7984,x7985)) % 183.90/184.45 [799]~E(x7991,x7992)+E(f206(x7993,x7991,x7994,x7995),f206(x7993,x7992,x7994,x7995)) % 183.90/184.45 [800]~E(x8001,x8002)+E(f206(x8003,x8004,x8001,x8005),f206(x8003,x8004,x8002,x8005)) % 183.90/184.45 [801]~E(x8011,x8012)+E(f206(x8013,x8014,x8015,x8011),f206(x8013,x8014,x8015,x8012)) % 183.90/184.45 [802]~E(x8021,x8022)+E(f529(x8021,x8023,x8024,x8025),f529(x8022,x8023,x8024,x8025)) % 183.90/184.45 [803]~E(x8031,x8032)+E(f529(x8033,x8031,x8034,x8035),f529(x8033,x8032,x8034,x8035)) % 183.90/184.45 [804]~E(x8041,x8042)+E(f529(x8043,x8044,x8041,x8045),f529(x8043,x8044,x8042,x8045)) % 183.90/184.45 [805]~E(x8051,x8052)+E(f529(x8053,x8054,x8055,x8051),f529(x8053,x8054,x8055,x8052)) % 183.90/184.45 [806]~E(x8061,x8062)+E(f92(x8061,x8063,x8064),f92(x8062,x8063,x8064)) % 183.90/184.45 [807]~E(x8071,x8072)+E(f92(x8073,x8071,x8074),f92(x8073,x8072,x8074)) % 183.90/184.45 [808]~E(x8081,x8082)+E(f92(x8083,x8084,x8081),f92(x8083,x8084,x8082)) % 183.90/184.45 [809]~E(x8091,x8092)+E(f363(x8091,x8093,x8094),f363(x8092,x8093,x8094)) % 183.90/184.45 [810]~E(x8101,x8102)+E(f363(x8103,x8101,x8104),f363(x8103,x8102,x8104)) % 183.90/184.45 [811]~E(x8111,x8112)+E(f363(x8113,x8114,x8111),f363(x8113,x8114,x8112)) % 183.90/184.45 [812]~E(x8121,x8122)+E(f808(x8121,x8123,x8124),f808(x8122,x8123,x8124)) % 183.90/184.45 [813]~E(x8131,x8132)+E(f808(x8133,x8131,x8134),f808(x8133,x8132,x8134)) % 183.90/184.45 [814]~E(x8141,x8142)+E(f808(x8143,x8144,x8141),f808(x8143,x8144,x8142)) % 183.90/184.45 [815]~E(x8151,x8152)+E(f655(x8151,x8153,x8154),f655(x8152,x8153,x8154)) % 183.90/184.45 [816]~E(x8161,x8162)+E(f655(x8163,x8161,x8164),f655(x8163,x8162,x8164)) % 183.90/184.45 [817]~E(x8171,x8172)+E(f655(x8173,x8174,x8171),f655(x8173,x8174,x8172)) % 183.90/184.45 [818]~E(x8181,x8182)+E(f498(x8181,x8183,x8184,x8185,x8186),f498(x8182,x8183,x8184,x8185,x8186)) % 183.90/184.45 [819]~E(x8191,x8192)+E(f498(x8193,x8191,x8194,x8195,x8196),f498(x8193,x8192,x8194,x8195,x8196)) % 183.90/184.45 [820]~E(x8201,x8202)+E(f498(x8203,x8204,x8201,x8205,x8206),f498(x8203,x8204,x8202,x8205,x8206)) % 183.90/184.45 [821]~E(x8211,x8212)+E(f498(x8213,x8214,x8215,x8211,x8216),f498(x8213,x8214,x8215,x8212,x8216)) % 183.90/184.45 [822]~E(x8221,x8222)+E(f498(x8223,x8224,x8225,x8226,x8221),f498(x8223,x8224,x8225,x8226,x8222)) % 183.90/184.45 [823]~E(x8231,x8232)+E(f689(x8231,x8233,x8234,x8235),f689(x8232,x8233,x8234,x8235)) % 183.90/184.45 [824]~E(x8241,x8242)+E(f689(x8243,x8241,x8244,x8245),f689(x8243,x8242,x8244,x8245)) % 183.90/184.45 [825]~E(x8251,x8252)+E(f689(x8253,x8254,x8251,x8255),f689(x8253,x8254,x8252,x8255)) % 183.90/184.45 [826]~E(x8261,x8262)+E(f689(x8263,x8264,x8265,x8261),f689(x8263,x8264,x8265,x8262)) % 183.90/184.45 [827]~E(x8271,x8272)+E(f492(x8271,x8273),f492(x8272,x8273)) % 183.90/184.45 [828]~E(x8281,x8282)+E(f492(x8283,x8281),f492(x8283,x8282)) % 183.90/184.45 [829]~E(x8291,x8292)+E(f738(x8291,x8293,x8294,x8295,x8296),f738(x8292,x8293,x8294,x8295,x8296)) % 183.90/184.45 [830]~E(x8301,x8302)+E(f738(x8303,x8301,x8304,x8305,x8306),f738(x8303,x8302,x8304,x8305,x8306)) % 183.90/184.45 [831]~E(x8311,x8312)+E(f738(x8313,x8314,x8311,x8315,x8316),f738(x8313,x8314,x8312,x8315,x8316)) % 183.90/184.45 [832]~E(x8321,x8322)+E(f738(x8323,x8324,x8325,x8321,x8326),f738(x8323,x8324,x8325,x8322,x8326)) % 183.90/184.45 [833]~E(x8331,x8332)+E(f738(x8333,x8334,x8335,x8336,x8331),f738(x8333,x8334,x8335,x8336,x8332)) % 183.90/184.45 [834]~E(x8341,x8342)+E(f156(x8341,x8343,x8344),f156(x8342,x8343,x8344)) % 183.90/184.45 [835]~E(x8351,x8352)+E(f156(x8353,x8351,x8354),f156(x8353,x8352,x8354)) % 183.90/184.45 [836]~E(x8361,x8362)+E(f156(x8363,x8364,x8361),f156(x8363,x8364,x8362)) % 183.90/184.45 [837]~E(x8371,x8372)+E(f522(x8371,x8373,x8374),f522(x8372,x8373,x8374)) % 183.90/184.45 [838]~E(x8381,x8382)+E(f522(x8383,x8381,x8384),f522(x8383,x8382,x8384)) % 183.90/184.45 [839]~E(x8391,x8392)+E(f522(x8393,x8394,x8391),f522(x8393,x8394,x8392)) % 183.90/184.45 [840]~E(x8401,x8402)+E(f374(x8401),f374(x8402)) % 183.90/184.45 [841]~E(x8411,x8412)+E(f364(x8411,x8413,x8414,x8415),f364(x8412,x8413,x8414,x8415)) % 183.90/184.45 [842]~E(x8421,x8422)+E(f364(x8423,x8421,x8424,x8425),f364(x8423,x8422,x8424,x8425)) % 183.90/184.45 [843]~E(x8431,x8432)+E(f364(x8433,x8434,x8431,x8435),f364(x8433,x8434,x8432,x8435)) % 183.90/184.45 [844]~E(x8441,x8442)+E(f364(x8443,x8444,x8445,x8441),f364(x8443,x8444,x8445,x8442)) % 183.90/184.45 [845]~E(x8451,x8452)+E(f362(x8451,x8453,x8454),f362(x8452,x8453,x8454)) % 183.90/184.45 [846]~E(x8461,x8462)+E(f362(x8463,x8461,x8464),f362(x8463,x8462,x8464)) % 183.90/184.45 [847]~E(x8471,x8472)+E(f362(x8473,x8474,x8471),f362(x8473,x8474,x8472)) % 183.90/184.45 [848]~E(x8481,x8482)+E(f658(x8481,x8483,x8484,x8485,x8486),f658(x8482,x8483,x8484,x8485,x8486)) % 183.90/184.45 [849]~E(x8491,x8492)+E(f658(x8493,x8491,x8494,x8495,x8496),f658(x8493,x8492,x8494,x8495,x8496)) % 183.90/184.45 [850]~E(x8501,x8502)+E(f658(x8503,x8504,x8501,x8505,x8506),f658(x8503,x8504,x8502,x8505,x8506)) % 183.90/184.45 [851]~E(x8511,x8512)+E(f658(x8513,x8514,x8515,x8511,x8516),f658(x8513,x8514,x8515,x8512,x8516)) % 183.90/184.45 [852]~E(x8521,x8522)+E(f658(x8523,x8524,x8525,x8526,x8521),f658(x8523,x8524,x8525,x8526,x8522)) % 183.90/184.45 [853]~E(x8531,x8532)+E(f282(x8531,x8533,x8534,x8535),f282(x8532,x8533,x8534,x8535)) % 183.90/184.45 [854]~E(x8541,x8542)+E(f282(x8543,x8541,x8544,x8545),f282(x8543,x8542,x8544,x8545)) % 183.90/184.45 [855]~E(x8551,x8552)+E(f282(x8553,x8554,x8551,x8555),f282(x8553,x8554,x8552,x8555)) % 183.90/184.45 [856]~E(x8561,x8562)+E(f282(x8563,x8564,x8565,x8561),f282(x8563,x8564,x8565,x8562)) % 183.90/184.45 [857]~E(x8571,x8572)+E(f408(x8571,x8573),f408(x8572,x8573)) % 183.90/184.45 [858]~E(x8581,x8582)+E(f408(x8583,x8581),f408(x8583,x8582)) % 183.90/184.45 [859]~E(x8591,x8592)+E(f58(x8591),f58(x8592)) % 183.90/184.45 [860]~E(x8601,x8602)+E(f710(x8601,x8603,x8604,x8605,x8606),f710(x8602,x8603,x8604,x8605,x8606)) % 183.90/184.45 [861]~E(x8611,x8612)+E(f710(x8613,x8611,x8614,x8615,x8616),f710(x8613,x8612,x8614,x8615,x8616)) % 183.90/184.45 [862]~E(x8621,x8622)+E(f710(x8623,x8624,x8621,x8625,x8626),f710(x8623,x8624,x8622,x8625,x8626)) % 183.90/184.45 [863]~E(x8631,x8632)+E(f710(x8633,x8634,x8635,x8631,x8636),f710(x8633,x8634,x8635,x8632,x8636)) % 183.90/184.45 [864]~E(x8641,x8642)+E(f710(x8643,x8644,x8645,x8646,x8641),f710(x8643,x8644,x8645,x8646,x8642)) % 183.90/184.45 [865]~E(x8651,x8652)+E(f814(x8651,x8653,x8654),f814(x8652,x8653,x8654)) % 183.90/184.45 [866]~E(x8661,x8662)+E(f814(x8663,x8661,x8664),f814(x8663,x8662,x8664)) % 183.90/184.45 [867]~E(x8671,x8672)+E(f814(x8673,x8674,x8671),f814(x8673,x8674,x8672)) % 183.90/184.45 [868]~E(x8681,x8682)+E(f198(x8681,x8683,x8684,x8685),f198(x8682,x8683,x8684,x8685)) % 183.90/184.45 [869]~E(x8691,x8692)+E(f198(x8693,x8691,x8694,x8695),f198(x8693,x8692,x8694,x8695)) % 183.90/184.45 [870]~E(x8701,x8702)+E(f198(x8703,x8704,x8701,x8705),f198(x8703,x8704,x8702,x8705)) % 183.90/184.45 [871]~E(x8711,x8712)+E(f198(x8713,x8714,x8715,x8711),f198(x8713,x8714,x8715,x8712)) % 183.90/184.45 [872]~E(x8721,x8722)+E(f704(x8721,x8723,x8724,x8725),f704(x8722,x8723,x8724,x8725)) % 183.90/184.45 [873]~E(x8731,x8732)+E(f704(x8733,x8731,x8734,x8735),f704(x8733,x8732,x8734,x8735)) % 183.90/184.45 [874]~E(x8741,x8742)+E(f704(x8743,x8744,x8741,x8745),f704(x8743,x8744,x8742,x8745)) % 183.90/184.45 [875]~E(x8751,x8752)+E(f704(x8753,x8754,x8755,x8751),f704(x8753,x8754,x8755,x8752)) % 183.90/184.45 [876]~E(x8761,x8762)+E(f62(x8761,x8763,x8764),f62(x8762,x8763,x8764)) % 183.90/184.45 [877]~E(x8771,x8772)+E(f62(x8773,x8771,x8774),f62(x8773,x8772,x8774)) % 183.90/184.45 [878]~E(x8781,x8782)+E(f62(x8783,x8784,x8781),f62(x8783,x8784,x8782)) % 183.90/184.45 [879]~E(x8791,x8792)+E(f200(x8791,x8793),f200(x8792,x8793)) % 183.90/184.45 [880]~E(x8801,x8802)+E(f200(x8803,x8801),f200(x8803,x8802)) % 183.90/184.45 [881]~E(x8811,x8812)+E(f501(x8811,x8813,x8814,x8815),f501(x8812,x8813,x8814,x8815)) % 183.90/184.45 [882]~E(x8821,x8822)+E(f501(x8823,x8821,x8824,x8825),f501(x8823,x8822,x8824,x8825)) % 183.90/184.45 [883]~E(x8831,x8832)+E(f501(x8833,x8834,x8831,x8835),f501(x8833,x8834,x8832,x8835)) % 183.90/184.45 [884]~E(x8841,x8842)+E(f501(x8843,x8844,x8845,x8841),f501(x8843,x8844,x8845,x8842)) % 183.90/184.45 [885]~E(x8851,x8852)+E(f122(x8851,x8853),f122(x8852,x8853)) % 183.90/184.45 [886]~E(x8861,x8862)+E(f122(x8863,x8861),f122(x8863,x8862)) % 183.90/184.45 [887]~E(x8871,x8872)+E(f131(x8871,x8873,x8874,x8875,x8876),f131(x8872,x8873,x8874,x8875,x8876)) % 183.90/184.45 [888]~E(x8881,x8882)+E(f131(x8883,x8881,x8884,x8885,x8886),f131(x8883,x8882,x8884,x8885,x8886)) % 183.90/184.45 [889]~E(x8891,x8892)+E(f131(x8893,x8894,x8891,x8895,x8896),f131(x8893,x8894,x8892,x8895,x8896)) % 183.90/184.45 [890]~E(x8901,x8902)+E(f131(x8903,x8904,x8905,x8901,x8906),f131(x8903,x8904,x8905,x8902,x8906)) % 183.90/184.45 [891]~E(x8911,x8912)+E(f131(x8913,x8914,x8915,x8916,x8911),f131(x8913,x8914,x8915,x8916,x8912)) % 183.90/184.45 [892]~E(x8921,x8922)+E(f322(x8921,x8923),f322(x8922,x8923)) % 183.90/184.45 [893]~E(x8931,x8932)+E(f322(x8933,x8931),f322(x8933,x8932)) % 183.90/184.45 [894]~E(x8941,x8942)+E(f796(x8941,x8943,x8944),f796(x8942,x8943,x8944)) % 183.90/184.45 [895]~E(x8951,x8952)+E(f796(x8953,x8951,x8954),f796(x8953,x8952,x8954)) % 183.90/184.45 [896]~E(x8961,x8962)+E(f796(x8963,x8964,x8961),f796(x8963,x8964,x8962)) % 183.90/184.45 [897]~E(x8971,x8972)+E(f300(x8971,x8973,x8974,x8975),f300(x8972,x8973,x8974,x8975)) % 183.90/184.45 [898]~E(x8981,x8982)+E(f300(x8983,x8981,x8984,x8985),f300(x8983,x8982,x8984,x8985)) % 183.90/184.45 [899]~E(x8991,x8992)+E(f300(x8993,x8994,x8991,x8995),f300(x8993,x8994,x8992,x8995)) % 183.90/184.45 [900]~E(x9001,x9002)+E(f300(x9003,x9004,x9005,x9001),f300(x9003,x9004,x9005,x9002)) % 183.90/184.45 [901]~E(x9011,x9012)+E(f848(x9011,x9013,x9014),f848(x9012,x9013,x9014)) % 183.90/184.45 [902]~E(x9021,x9022)+E(f848(x9023,x9021,x9024),f848(x9023,x9022,x9024)) % 183.90/184.45 [903]~E(x9031,x9032)+E(f848(x9033,x9034,x9031),f848(x9033,x9034,x9032)) % 183.90/184.45 [904]~E(x9041,x9042)+E(f496(x9041,x9043,x9044,x9045),f496(x9042,x9043,x9044,x9045)) % 183.90/184.45 [905]~E(x9051,x9052)+E(f496(x9053,x9051,x9054,x9055),f496(x9053,x9052,x9054,x9055)) % 183.90/184.45 [906]~E(x9061,x9062)+E(f496(x9063,x9064,x9061,x9065),f496(x9063,x9064,x9062,x9065)) % 183.90/184.45 [907]~E(x9071,x9072)+E(f496(x9073,x9074,x9075,x9071),f496(x9073,x9074,x9075,x9072)) % 183.90/184.45 [908]~E(x9081,x9082)+E(f133(x9081,x9083),f133(x9082,x9083)) % 183.90/184.45 [909]~E(x9091,x9092)+E(f133(x9093,x9091),f133(x9093,x9092)) % 183.90/184.45 [910]~E(x9101,x9102)+E(f779(x9101,x9103,x9104,x9105),f779(x9102,x9103,x9104,x9105)) % 183.90/184.45 [911]~E(x9111,x9112)+E(f779(x9113,x9111,x9114,x9115),f779(x9113,x9112,x9114,x9115)) % 183.90/184.45 [912]~E(x9121,x9122)+E(f779(x9123,x9124,x9121,x9125),f779(x9123,x9124,x9122,x9125)) % 183.90/184.45 [913]~E(x9131,x9132)+E(f779(x9133,x9134,x9135,x9131),f779(x9133,x9134,x9135,x9132)) % 183.90/184.45 [914]~E(x9141,x9142)+E(f634(x9141,x9143),f634(x9142,x9143)) % 183.90/184.45 [915]~E(x9151,x9152)+E(f634(x9153,x9151),f634(x9153,x9152)) % 183.90/184.45 [916]~E(x9161,x9162)+E(f819(x9161,x9163,x9164),f819(x9162,x9163,x9164)) % 183.90/184.45 [917]~E(x9171,x9172)+E(f819(x9173,x9171,x9174),f819(x9173,x9172,x9174)) % 183.90/184.45 [918]~E(x9181,x9182)+E(f819(x9183,x9184,x9181),f819(x9183,x9184,x9182)) % 183.90/184.45 [919]~E(x9191,x9192)+E(f745(x9191,x9193,x9194),f745(x9192,x9193,x9194)) % 183.90/184.45 [920]~E(x9201,x9202)+E(f745(x9203,x9201,x9204),f745(x9203,x9202,x9204)) % 183.90/184.45 [921]~E(x9211,x9212)+E(f745(x9213,x9214,x9211),f745(x9213,x9214,x9212)) % 183.90/184.45 [922]~E(x9221,x9222)+E(f419(x9221,x9223,x9224),f419(x9222,x9223,x9224)) % 183.90/184.45 [923]~E(x9231,x9232)+E(f419(x9233,x9231,x9234),f419(x9233,x9232,x9234)) % 183.90/184.45 [924]~E(x9241,x9242)+E(f419(x9243,x9244,x9241),f419(x9243,x9244,x9242)) % 183.90/184.45 [925]~E(x9251,x9252)+E(f489(x9251,x9253,x9254),f489(x9252,x9253,x9254)) % 183.90/184.45 [926]~E(x9261,x9262)+E(f489(x9263,x9261,x9264),f489(x9263,x9262,x9264)) % 183.90/184.45 [927]~E(x9271,x9272)+E(f489(x9273,x9274,x9271),f489(x9273,x9274,x9272)) % 183.90/184.45 [928]~E(x9281,x9282)+E(f802(x9281,x9283,x9284,x9285),f802(x9282,x9283,x9284,x9285)) % 183.90/184.45 [929]~E(x9291,x9292)+E(f802(x9293,x9291,x9294,x9295),f802(x9293,x9292,x9294,x9295)) % 183.90/184.45 [930]~E(x9301,x9302)+E(f802(x9303,x9304,x9301,x9305),f802(x9303,x9304,x9302,x9305)) % 183.90/184.45 [931]~E(x9311,x9312)+E(f802(x9313,x9314,x9315,x9311),f802(x9313,x9314,x9315,x9312)) % 183.90/184.45 [932]~E(x9321,x9322)+E(f739(x9321,x9323,x9324,x9325,x9326,x9327,x9328),f739(x9322,x9323,x9324,x9325,x9326,x9327,x9328)) % 183.90/184.45 [933]~E(x9331,x9332)+E(f739(x9333,x9331,x9334,x9335,x9336,x9337,x9338),f739(x9333,x9332,x9334,x9335,x9336,x9337,x9338)) % 183.90/184.45 [934]~E(x9341,x9342)+E(f739(x9343,x9344,x9341,x9345,x9346,x9347,x9348),f739(x9343,x9344,x9342,x9345,x9346,x9347,x9348)) % 183.90/184.45 [935]~E(x9351,x9352)+E(f739(x9353,x9354,x9355,x9351,x9356,x9357,x9358),f739(x9353,x9354,x9355,x9352,x9356,x9357,x9358)) % 183.90/184.45 [936]~E(x9361,x9362)+E(f739(x9363,x9364,x9365,x9366,x9361,x9367,x9368),f739(x9363,x9364,x9365,x9366,x9362,x9367,x9368)) % 183.90/184.45 [937]~E(x9371,x9372)+E(f739(x9373,x9374,x9375,x9376,x9377,x9371,x9378),f739(x9373,x9374,x9375,x9376,x9377,x9372,x9378)) % 183.90/184.45 [938]~E(x9381,x9382)+E(f739(x9383,x9384,x9385,x9386,x9387,x9388,x9381),f739(x9383,x9384,x9385,x9386,x9387,x9388,x9382)) % 183.90/184.45 [939]~E(x9391,x9392)+E(f93(x9391),f93(x9392)) % 183.90/184.45 [940]~E(x9401,x9402)+E(f356(x9401,x9403,x9404,x9405),f356(x9402,x9403,x9404,x9405)) % 183.90/184.45 [941]~E(x9411,x9412)+E(f356(x9413,x9411,x9414,x9415),f356(x9413,x9412,x9414,x9415)) % 183.90/184.45 [942]~E(x9421,x9422)+E(f356(x9423,x9424,x9421,x9425),f356(x9423,x9424,x9422,x9425)) % 183.90/184.45 [943]~E(x9431,x9432)+E(f356(x9433,x9434,x9435,x9431),f356(x9433,x9434,x9435,x9432)) % 183.90/184.45 [944]~E(x9441,x9442)+E(f384(x9441,x9443),f384(x9442,x9443)) % 183.90/184.45 [945]~E(x9451,x9452)+E(f384(x9453,x9451),f384(x9453,x9452)) % 183.90/184.45 [946]~E(x9461,x9462)+E(f280(x9461,x9463),f280(x9462,x9463)) % 183.90/184.45 [947]~E(x9471,x9472)+E(f280(x9473,x9471),f280(x9473,x9472)) % 183.90/184.45 [948]~E(x9481,x9482)+E(f673(x9481,x9483,x9484,x9485,x9486),f673(x9482,x9483,x9484,x9485,x9486)) % 183.90/184.45 [949]~E(x9491,x9492)+E(f673(x9493,x9491,x9494,x9495,x9496),f673(x9493,x9492,x9494,x9495,x9496)) % 183.90/184.45 [950]~E(x9501,x9502)+E(f673(x9503,x9504,x9501,x9505,x9506),f673(x9503,x9504,x9502,x9505,x9506)) % 183.90/184.45 [951]~E(x9511,x9512)+E(f673(x9513,x9514,x9515,x9511,x9516),f673(x9513,x9514,x9515,x9512,x9516)) % 183.90/184.45 [952]~E(x9521,x9522)+E(f673(x9523,x9524,x9525,x9526,x9521),f673(x9523,x9524,x9525,x9526,x9522)) % 183.90/184.45 [953]~E(x9531,x9532)+E(f286(x9531),f286(x9532)) % 183.90/184.45 [954]~E(x9541,x9542)+E(f87(x9541),f87(x9542)) % 183.90/184.45 [955]~E(x9551,x9552)+E(f663(x9551,x9553,x9554,x9555,x9556,x9557),f663(x9552,x9553,x9554,x9555,x9556,x9557)) % 183.90/184.45 [956]~E(x9561,x9562)+E(f663(x9563,x9561,x9564,x9565,x9566,x9567),f663(x9563,x9562,x9564,x9565,x9566,x9567)) % 183.90/184.45 [957]~E(x9571,x9572)+E(f663(x9573,x9574,x9571,x9575,x9576,x9577),f663(x9573,x9574,x9572,x9575,x9576,x9577)) % 183.90/184.45 [958]~E(x9581,x9582)+E(f663(x9583,x9584,x9585,x9581,x9586,x9587),f663(x9583,x9584,x9585,x9582,x9586,x9587)) % 183.90/184.45 [959]~E(x9591,x9592)+E(f663(x9593,x9594,x9595,x9596,x9591,x9597),f663(x9593,x9594,x9595,x9596,x9592,x9597)) % 183.90/184.45 [960]~E(x9601,x9602)+E(f663(x9603,x9604,x9605,x9606,x9607,x9601),f663(x9603,x9604,x9605,x9606,x9607,x9602)) % 183.90/184.45 [961]~E(x9611,x9612)+E(f17(x9611,x9613,x9614,x9615),f17(x9612,x9613,x9614,x9615)) % 183.90/184.45 [962]~E(x9621,x9622)+E(f17(x9623,x9621,x9624,x9625),f17(x9623,x9622,x9624,x9625)) % 183.90/184.45 [963]~E(x9631,x9632)+E(f17(x9633,x9634,x9631,x9635),f17(x9633,x9634,x9632,x9635)) % 183.90/184.45 [964]~E(x9641,x9642)+E(f17(x9643,x9644,x9645,x9641),f17(x9643,x9644,x9645,x9642)) % 183.90/184.45 [965]~E(x9651,x9652)+E(f424(x9651,x9653,x9654,x9655),f424(x9652,x9653,x9654,x9655)) % 183.90/184.45 [966]~E(x9661,x9662)+E(f424(x9663,x9661,x9664,x9665),f424(x9663,x9662,x9664,x9665)) % 183.90/184.45 [967]~E(x9671,x9672)+E(f424(x9673,x9674,x9671,x9675),f424(x9673,x9674,x9672,x9675)) % 183.90/184.45 [968]~E(x9681,x9682)+E(f424(x9683,x9684,x9685,x9681),f424(x9683,x9684,x9685,x9682)) % 183.90/184.45 [969]~E(x9691,x9692)+E(f867(x9691,x9693,x9694,x9695,x9696),f867(x9692,x9693,x9694,x9695,x9696)) % 183.90/184.45 [970]~E(x9701,x9702)+E(f867(x9703,x9701,x9704,x9705,x9706),f867(x9703,x9702,x9704,x9705,x9706)) % 183.90/184.45 [971]~E(x9711,x9712)+E(f867(x9713,x9714,x9711,x9715,x9716),f867(x9713,x9714,x9712,x9715,x9716)) % 183.90/184.45 [972]~E(x9721,x9722)+E(f867(x9723,x9724,x9725,x9721,x9726),f867(x9723,x9724,x9725,x9722,x9726)) % 183.90/184.45 [973]~E(x9731,x9732)+E(f867(x9733,x9734,x9735,x9736,x9731),f867(x9733,x9734,x9735,x9736,x9732)) % 183.90/184.45 [974]~E(x9741,x9742)+E(f760(x9741,x9743),f760(x9742,x9743)) % 183.90/184.45 [975]~E(x9751,x9752)+E(f760(x9753,x9751),f760(x9753,x9752)) % 183.90/184.45 [976]~E(x9761,x9762)+E(f700(x9761,x9763,x9764,x9765,x9766),f700(x9762,x9763,x9764,x9765,x9766)) % 183.90/184.45 [977]~E(x9771,x9772)+E(f700(x9773,x9771,x9774,x9775,x9776),f700(x9773,x9772,x9774,x9775,x9776)) % 183.90/184.45 [978]~E(x9781,x9782)+E(f700(x9783,x9784,x9781,x9785,x9786),f700(x9783,x9784,x9782,x9785,x9786)) % 183.90/184.45 [979]~E(x9791,x9792)+E(f700(x9793,x9794,x9795,x9791,x9796),f700(x9793,x9794,x9795,x9792,x9796)) % 183.90/184.45 [980]~E(x9801,x9802)+E(f700(x9803,x9804,x9805,x9806,x9801),f700(x9803,x9804,x9805,x9806,x9802)) % 183.90/184.45 [981]~E(x9811,x9812)+E(f859(x9811,x9813,x9814,x9815,x9816,x9817,x9818,x9819),f859(x9812,x9813,x9814,x9815,x9816,x9817,x9818,x9819)) % 183.90/184.45 [982]~E(x9821,x9822)+E(f859(x9823,x9821,x9824,x9825,x9826,x9827,x9828,x9829),f859(x9823,x9822,x9824,x9825,x9826,x9827,x9828,x9829)) % 183.90/184.45 [983]~E(x9831,x9832)+E(f859(x9833,x9834,x9831,x9835,x9836,x9837,x9838,x9839),f859(x9833,x9834,x9832,x9835,x9836,x9837,x9838,x9839)) % 183.90/184.45 [984]~E(x9841,x9842)+E(f859(x9843,x9844,x9845,x9841,x9846,x9847,x9848,x9849),f859(x9843,x9844,x9845,x9842,x9846,x9847,x9848,x9849)) % 183.90/184.45 [985]~E(x9851,x9852)+E(f859(x9853,x9854,x9855,x9856,x9851,x9857,x9858,x9859),f859(x9853,x9854,x9855,x9856,x9852,x9857,x9858,x9859)) % 183.90/184.45 [986]~E(x9861,x9862)+E(f859(x9863,x9864,x9865,x9866,x9867,x9861,x9868,x9869),f859(x9863,x9864,x9865,x9866,x9867,x9862,x9868,x9869)) % 183.90/184.45 [987]~E(x9871,x9872)+E(f859(x9873,x9874,x9875,x9876,x9877,x9878,x9871,x9879),f859(x9873,x9874,x9875,x9876,x9877,x9878,x9872,x9879)) % 183.90/184.45 [988]~E(x9881,x9882)+E(f859(x9883,x9884,x9885,x9886,x9887,x9888,x9889,x9881),f859(x9883,x9884,x9885,x9886,x9887,x9888,x9889,x9882)) % 183.90/184.45 [989]~E(x9891,x9892)+E(f694(x9891,x9893,x9894),f694(x9892,x9893,x9894)) % 183.90/184.45 [990]~E(x9901,x9902)+E(f694(x9903,x9901,x9904),f694(x9903,x9902,x9904)) % 183.90/184.45 [991]~E(x9911,x9912)+E(f694(x9913,x9914,x9911),f694(x9913,x9914,x9912)) % 183.90/184.45 [992]~E(x9921,x9922)+E(f224(x9921),f224(x9922)) % 183.90/184.45 [993]~E(x9931,x9932)+E(f470(x9931,x9933,x9934),f470(x9932,x9933,x9934)) % 183.90/184.45 [994]~E(x9941,x9942)+E(f470(x9943,x9941,x9944),f470(x9943,x9942,x9944)) % 183.90/184.45 [995]~E(x9951,x9952)+E(f470(x9953,x9954,x9951),f470(x9953,x9954,x9952)) % 183.90/184.45 [996]~E(x9961,x9962)+E(f728(x9961,x9963,x9964),f728(x9962,x9963,x9964)) % 183.90/184.45 [997]~E(x9971,x9972)+E(f728(x9973,x9971,x9974),f728(x9973,x9972,x9974)) % 183.90/184.45 [998]~E(x9981,x9982)+E(f728(x9983,x9984,x9981),f728(x9983,x9984,x9982)) % 183.90/184.45 [999]~E(x9991,x9992)+E(f537(x9991,x9993,x9994),f537(x9992,x9993,x9994)) % 183.90/184.45 [1000]~E(x10001,x10002)+E(f537(x10003,x10001,x10004),f537(x10003,x10002,x10004)) % 183.90/184.45 [1001]~E(x10011,x10012)+E(f537(x10013,x10014,x10011),f537(x10013,x10014,x10012)) % 183.90/184.45 [1002]~E(x10021,x10022)+E(f119(x10021,x10023,x10024),f119(x10022,x10023,x10024)) % 183.90/184.45 [1003]~E(x10031,x10032)+E(f119(x10033,x10031,x10034),f119(x10033,x10032,x10034)) % 183.90/184.45 [1004]~E(x10041,x10042)+E(f119(x10043,x10044,x10041),f119(x10043,x10044,x10042)) % 183.90/184.45 [1005]~E(x10051,x10052)+E(f210(x10051,x10053),f210(x10052,x10053)) % 183.90/184.45 [1006]~E(x10061,x10062)+E(f210(x10063,x10061),f210(x10063,x10062)) % 183.90/184.45 [1007]~E(x10071,x10072)+E(f284(x10071,x10073),f284(x10072,x10073)) % 183.90/184.45 [1008]~E(x10081,x10082)+E(f284(x10083,x10081),f284(x10083,x10082)) % 183.90/184.45 [1009]~E(x10091,x10092)+E(f790(x10091,x10093,x10094),f790(x10092,x10093,x10094)) % 183.90/184.45 [1010]~E(x10101,x10102)+E(f790(x10103,x10101,x10104),f790(x10103,x10102,x10104)) % 183.90/184.45 [1011]~E(x10111,x10112)+E(f790(x10113,x10114,x10111),f790(x10113,x10114,x10112)) % 183.90/184.45 [1012]~E(x10121,x10122)+E(f584(x10121,x10123,x10124,x10125,x10126),f584(x10122,x10123,x10124,x10125,x10126)) % 183.90/184.45 [1013]~E(x10131,x10132)+E(f584(x10133,x10131,x10134,x10135,x10136),f584(x10133,x10132,x10134,x10135,x10136)) % 183.90/184.45 [1014]~E(x10141,x10142)+E(f584(x10143,x10144,x10141,x10145,x10146),f584(x10143,x10144,x10142,x10145,x10146)) % 183.90/184.45 [1015]~E(x10151,x10152)+E(f584(x10153,x10154,x10155,x10151,x10156),f584(x10153,x10154,x10155,x10152,x10156)) % 183.90/184.45 [1016]~E(x10161,x10162)+E(f584(x10163,x10164,x10165,x10166,x10161),f584(x10163,x10164,x10165,x10166,x10162)) % 183.90/184.45 [1017]~E(x10171,x10172)+E(f825(x10171,x10173,x10174,x10175),f825(x10172,x10173,x10174,x10175)) % 183.90/184.45 [1018]~E(x10181,x10182)+E(f825(x10183,x10181,x10184,x10185),f825(x10183,x10182,x10184,x10185)) % 183.90/184.45 [1019]~E(x10191,x10192)+E(f825(x10193,x10194,x10191,x10195),f825(x10193,x10194,x10192,x10195)) % 183.90/184.45 [1020]~E(x10201,x10202)+E(f825(x10203,x10204,x10205,x10201),f825(x10203,x10204,x10205,x10202)) % 183.90/184.45 [1021]~E(x10211,x10212)+E(f53(x10211,x10213),f53(x10212,x10213)) % 183.90/184.45 [1022]~E(x10221,x10222)+E(f53(x10223,x10221),f53(x10223,x10222)) % 183.90/184.45 [1023]~E(x10231,x10232)+E(f736(x10231,x10233,x10234,x10235),f736(x10232,x10233,x10234,x10235)) % 183.90/184.45 [1024]~E(x10241,x10242)+E(f736(x10243,x10241,x10244,x10245),f736(x10243,x10242,x10244,x10245)) % 183.90/184.45 [1025]~E(x10251,x10252)+E(f736(x10253,x10254,x10251,x10255),f736(x10253,x10254,x10252,x10255)) % 183.90/184.45 [1026]~E(x10261,x10262)+E(f736(x10263,x10264,x10265,x10261),f736(x10263,x10264,x10265,x10262)) % 183.90/184.45 [1027]~E(x10271,x10272)+E(f530(x10271,x10273,x10274,x10275),f530(x10272,x10273,x10274,x10275)) % 183.90/184.45 [1028]~E(x10281,x10282)+E(f530(x10283,x10281,x10284,x10285),f530(x10283,x10282,x10284,x10285)) % 183.90/184.45 [1029]~E(x10291,x10292)+E(f530(x10293,x10294,x10291,x10295),f530(x10293,x10294,x10292,x10295)) % 183.90/184.45 [1030]~E(x10301,x10302)+E(f530(x10303,x10304,x10305,x10301),f530(x10303,x10304,x10305,x10302)) % 183.90/184.45 [1031]~E(x10311,x10312)+E(f722(x10311,x10313,x10314),f722(x10312,x10313,x10314)) % 183.90/184.45 [1032]~E(x10321,x10322)+E(f722(x10323,x10321,x10324),f722(x10323,x10322,x10324)) % 183.90/184.45 [1033]~E(x10331,x10332)+E(f722(x10333,x10334,x10331),f722(x10333,x10334,x10332)) % 183.90/184.45 [1034]~E(x10341,x10342)+E(f580(x10341,x10343,x10344,x10345,x10346,x10347),f580(x10342,x10343,x10344,x10345,x10346,x10347)) % 183.90/184.45 [1035]~E(x10351,x10352)+E(f580(x10353,x10351,x10354,x10355,x10356,x10357),f580(x10353,x10352,x10354,x10355,x10356,x10357)) % 183.90/184.45 [1036]~E(x10361,x10362)+E(f580(x10363,x10364,x10361,x10365,x10366,x10367),f580(x10363,x10364,x10362,x10365,x10366,x10367)) % 183.90/184.45 [1037]~E(x10371,x10372)+E(f580(x10373,x10374,x10375,x10371,x10376,x10377),f580(x10373,x10374,x10375,x10372,x10376,x10377)) % 183.90/184.45 [1038]~E(x10381,x10382)+E(f580(x10383,x10384,x10385,x10386,x10381,x10387),f580(x10383,x10384,x10385,x10386,x10382,x10387)) % 183.90/184.45 [1039]~E(x10391,x10392)+E(f580(x10393,x10394,x10395,x10396,x10397,x10391),f580(x10393,x10394,x10395,x10396,x10397,x10392)) % 183.90/184.45 [1040]~E(x10401,x10402)+E(f742(x10401,x10403),f742(x10402,x10403)) % 183.90/184.45 [1041]~E(x10411,x10412)+E(f742(x10413,x10411),f742(x10413,x10412)) % 183.90/184.45 [1042]~E(x10421,x10422)+E(f687(x10421,x10423,x10424,x10425),f687(x10422,x10423,x10424,x10425)) % 183.90/184.45 [1043]~E(x10431,x10432)+E(f687(x10433,x10431,x10434,x10435),f687(x10433,x10432,x10434,x10435)) % 183.90/184.45 [1044]~E(x10441,x10442)+E(f687(x10443,x10444,x10441,x10445),f687(x10443,x10444,x10442,x10445)) % 183.90/184.45 [1045]~E(x10451,x10452)+E(f687(x10453,x10454,x10455,x10451),f687(x10453,x10454,x10455,x10452)) % 183.90/184.45 [1046]~E(x10461,x10462)+E(f365(x10461,x10463,x10464,x10465),f365(x10462,x10463,x10464,x10465)) % 183.90/184.45 [1047]~E(x10471,x10472)+E(f365(x10473,x10471,x10474,x10475),f365(x10473,x10472,x10474,x10475)) % 183.90/184.45 [1048]~E(x10481,x10482)+E(f365(x10483,x10484,x10481,x10485),f365(x10483,x10484,x10482,x10485)) % 183.90/184.45 [1049]~E(x10491,x10492)+E(f365(x10493,x10494,x10495,x10491),f365(x10493,x10494,x10495,x10492)) % 183.90/184.45 [1050]~E(x10501,x10502)+E(f678(x10501,x10503,x10504),f678(x10502,x10503,x10504)) % 183.90/184.45 [1051]~E(x10511,x10512)+E(f678(x10513,x10511,x10514),f678(x10513,x10512,x10514)) % 183.90/184.45 [1052]~E(x10521,x10522)+E(f678(x10523,x10524,x10521),f678(x10523,x10524,x10522)) % 183.90/184.45 [1053]~E(x10531,x10532)+E(f394(x10531,x10533,x10534,x10535),f394(x10532,x10533,x10534,x10535)) % 183.90/184.45 [1054]~E(x10541,x10542)+E(f394(x10543,x10541,x10544,x10545),f394(x10543,x10542,x10544,x10545)) % 183.90/184.45 [1055]~E(x10551,x10552)+E(f394(x10553,x10554,x10551,x10555),f394(x10553,x10554,x10552,x10555)) % 183.90/184.45 [1056]~E(x10561,x10562)+E(f394(x10563,x10564,x10565,x10561),f394(x10563,x10564,x10565,x10562)) % 183.90/184.45 [1057]~E(x10571,x10572)+E(f289(x10571,x10573),f289(x10572,x10573)) % 183.90/184.45 [1058]~E(x10581,x10582)+E(f289(x10583,x10581),f289(x10583,x10582)) % 183.90/184.45 [1059]~E(x10591,x10592)+E(f141(x10591,x10593,x10594),f141(x10592,x10593,x10594)) % 183.90/184.45 [1060]~E(x10601,x10602)+E(f141(x10603,x10601,x10604),f141(x10603,x10602,x10604)) % 183.90/184.45 [1061]~E(x10611,x10612)+E(f141(x10613,x10614,x10611),f141(x10613,x10614,x10612)) % 183.90/184.45 [1062]~E(x10621,x10622)+E(f671(x10621,x10623,x10624,x10625),f671(x10622,x10623,x10624,x10625)) % 183.90/184.45 [1063]~E(x10631,x10632)+E(f671(x10633,x10631,x10634,x10635),f671(x10633,x10632,x10634,x10635)) % 183.90/184.45 [1064]~E(x10641,x10642)+E(f671(x10643,x10644,x10641,x10645),f671(x10643,x10644,x10642,x10645)) % 183.90/184.45 [1065]~E(x10651,x10652)+E(f671(x10653,x10654,x10655,x10651),f671(x10653,x10654,x10655,x10652)) % 183.90/184.45 [1066]~E(x10661,x10662)+E(f389(x10661,x10663),f389(x10662,x10663)) % 183.90/184.45 [1067]~E(x10671,x10672)+E(f389(x10673,x10671),f389(x10673,x10672)) % 183.90/184.45 [1068]~E(x10681,x10682)+E(f391(x10681,x10683,x10684),f391(x10682,x10683,x10684)) % 183.90/184.45 [1069]~E(x10691,x10692)+E(f391(x10693,x10691,x10694),f391(x10693,x10692,x10694)) % 183.90/184.45 [1070]~E(x10701,x10702)+E(f391(x10703,x10704,x10701),f391(x10703,x10704,x10702)) % 183.90/184.45 [1071]~E(x10711,x10712)+E(f146(x10711,x10713),f146(x10712,x10713)) % 183.90/184.45 [1072]~E(x10721,x10722)+E(f146(x10723,x10721),f146(x10723,x10722)) % 183.90/184.45 [1073]~E(x10731,x10732)+E(f853(x10731,x10733),f853(x10732,x10733)) % 183.90/184.45 [1074]~E(x10741,x10742)+E(f853(x10743,x10741),f853(x10743,x10742)) % 183.90/184.45 [1075]~E(x10751,x10752)+E(f846(x10751,x10753,x10754,x10755,x10756,x10757),f846(x10752,x10753,x10754,x10755,x10756,x10757)) % 183.90/184.45 [1076]~E(x10761,x10762)+E(f846(x10763,x10761,x10764,x10765,x10766,x10767),f846(x10763,x10762,x10764,x10765,x10766,x10767)) % 183.90/184.45 [1077]~E(x10771,x10772)+E(f846(x10773,x10774,x10771,x10775,x10776,x10777),f846(x10773,x10774,x10772,x10775,x10776,x10777)) % 183.90/184.45 [1078]~E(x10781,x10782)+E(f846(x10783,x10784,x10785,x10781,x10786,x10787),f846(x10783,x10784,x10785,x10782,x10786,x10787)) % 183.90/184.45 [1079]~E(x10791,x10792)+E(f846(x10793,x10794,x10795,x10796,x10791,x10797),f846(x10793,x10794,x10795,x10796,x10792,x10797)) % 183.90/184.45 [1080]~E(x10801,x10802)+E(f846(x10803,x10804,x10805,x10806,x10807,x10801),f846(x10803,x10804,x10805,x10806,x10807,x10802)) % 183.90/184.45 [1081]~E(x10811,x10812)+E(f292(x10811,x10813),f292(x10812,x10813)) % 183.90/184.45 [1082]~E(x10821,x10822)+E(f292(x10823,x10821),f292(x10823,x10822)) % 183.90/184.45 [1083]~E(x10831,x10832)+E(f226(x10831,x10833),f226(x10832,x10833)) % 183.90/184.45 [1084]~E(x10841,x10842)+E(f226(x10843,x10841),f226(x10843,x10842)) % 183.90/184.45 [1085]~E(x10851,x10852)+E(f165(x10851,x10853,x10854,x10855),f165(x10852,x10853,x10854,x10855)) % 183.90/184.45 [1086]~E(x10861,x10862)+E(f165(x10863,x10861,x10864,x10865),f165(x10863,x10862,x10864,x10865)) % 183.90/184.45 [1087]~E(x10871,x10872)+E(f165(x10873,x10874,x10871,x10875),f165(x10873,x10874,x10872,x10875)) % 183.90/184.45 [1088]~E(x10881,x10882)+E(f165(x10883,x10884,x10885,x10881),f165(x10883,x10884,x10885,x10882)) % 183.90/184.45 [1089]~E(x10891,x10892)+E(f474(x10891,x10893,x10894),f474(x10892,x10893,x10894)) % 183.90/184.45 [1090]~E(x10901,x10902)+E(f474(x10903,x10901,x10904),f474(x10903,x10902,x10904)) % 183.90/184.45 [1091]~E(x10911,x10912)+E(f474(x10913,x10914,x10911),f474(x10913,x10914,x10912)) % 183.90/184.45 [1092]~E(x10921,x10922)+E(f478(x10921,x10923,x10924,x10925),f478(x10922,x10923,x10924,x10925)) % 183.90/184.45 [1093]~E(x10931,x10932)+E(f478(x10933,x10931,x10934,x10935),f478(x10933,x10932,x10934,x10935)) % 183.90/184.45 [1094]~E(x10941,x10942)+E(f478(x10943,x10944,x10941,x10945),f478(x10943,x10944,x10942,x10945)) % 183.90/184.45 [1095]~E(x10951,x10952)+E(f478(x10953,x10954,x10955,x10951),f478(x10953,x10954,x10955,x10952)) % 183.90/184.45 [1096]~E(x10961,x10962)+E(f497(x10961,x10963,x10964),f497(x10962,x10963,x10964)) % 183.90/184.45 [1097]~E(x10971,x10972)+E(f497(x10973,x10971,x10974),f497(x10973,x10972,x10974)) % 183.90/184.45 [1098]~E(x10981,x10982)+E(f497(x10983,x10984,x10981),f497(x10983,x10984,x10982)) % 183.90/184.45 [1099]~E(x10991,x10992)+E(f175(x10991,x10993,x10994),f175(x10992,x10993,x10994)) % 183.90/184.45 [1100]~E(x11001,x11002)+E(f175(x11003,x11001,x11004),f175(x11003,x11002,x11004)) % 183.90/184.45 [1101]~E(x11011,x11012)+E(f175(x11013,x11014,x11011),f175(x11013,x11014,x11012)) % 183.90/184.45 [1102]~E(x11021,x11022)+E(f799(x11021,x11023,x11024),f799(x11022,x11023,x11024)) % 183.90/184.45 [1103]~E(x11031,x11032)+E(f799(x11033,x11031,x11034),f799(x11033,x11032,x11034)) % 183.90/184.45 [1104]~E(x11041,x11042)+E(f799(x11043,x11044,x11041),f799(x11043,x11044,x11042)) % 183.90/184.45 [1105]~E(x11051,x11052)+E(f776(x11051,x11053,x11054),f776(x11052,x11053,x11054)) % 183.90/184.45 [1106]~E(x11061,x11062)+E(f776(x11063,x11061,x11064),f776(x11063,x11062,x11064)) % 183.90/184.45 [1107]~E(x11071,x11072)+E(f776(x11073,x11074,x11071),f776(x11073,x11074,x11072)) % 183.90/184.45 [1108]~E(x11081,x11082)+E(f458(x11081,x11083,x11084,x11085,x11086),f458(x11082,x11083,x11084,x11085,x11086)) % 183.90/184.45 [1109]~E(x11091,x11092)+E(f458(x11093,x11091,x11094,x11095,x11096),f458(x11093,x11092,x11094,x11095,x11096)) % 183.90/184.45 [1110]~E(x11101,x11102)+E(f458(x11103,x11104,x11101,x11105,x11106),f458(x11103,x11104,x11102,x11105,x11106)) % 183.90/184.45 [1111]~E(x11111,x11112)+E(f458(x11113,x11114,x11115,x11111,x11116),f458(x11113,x11114,x11115,x11112,x11116)) % 183.90/184.45 [1112]~E(x11121,x11122)+E(f458(x11123,x11124,x11125,x11126,x11121),f458(x11123,x11124,x11125,x11126,x11122)) % 183.90/184.45 [1113]~E(x11131,x11132)+E(f852(x11131,x11133,x11134,x11135,x11136),f852(x11132,x11133,x11134,x11135,x11136)) % 183.90/184.45 [1114]~E(x11141,x11142)+E(f852(x11143,x11141,x11144,x11145,x11146),f852(x11143,x11142,x11144,x11145,x11146)) % 183.90/184.45 [1115]~E(x11151,x11152)+E(f852(x11153,x11154,x11151,x11155,x11156),f852(x11153,x11154,x11152,x11155,x11156)) % 183.90/184.45 [1116]~E(x11161,x11162)+E(f852(x11163,x11164,x11165,x11161,x11166),f852(x11163,x11164,x11165,x11162,x11166)) % 183.90/184.45 [1117]~E(x11171,x11172)+E(f852(x11173,x11174,x11175,x11176,x11171),f852(x11173,x11174,x11175,x11176,x11172)) % 183.90/184.45 [1118]~E(x11181,x11182)+E(f318(x11181),f318(x11182)) % 183.90/184.45 [1119]~E(x11191,x11192)+E(f747(x11191,x11193,x11194),f747(x11192,x11193,x11194)) % 183.90/184.45 [1120]~E(x11201,x11202)+E(f747(x11203,x11201,x11204),f747(x11203,x11202,x11204)) % 183.90/184.45 [1121]~E(x11211,x11212)+E(f747(x11213,x11214,x11211),f747(x11213,x11214,x11212)) % 183.90/184.45 [1122]~E(x11221,x11222)+E(f569(x11221,x11223,x11224,x11225),f569(x11222,x11223,x11224,x11225)) % 183.90/184.45 [1123]~E(x11231,x11232)+E(f569(x11233,x11231,x11234,x11235),f569(x11233,x11232,x11234,x11235)) % 183.90/184.45 [1124]~E(x11241,x11242)+E(f569(x11243,x11244,x11241,x11245),f569(x11243,x11244,x11242,x11245)) % 183.90/184.45 [1125]~E(x11251,x11252)+E(f569(x11253,x11254,x11255,x11251),f569(x11253,x11254,x11255,x11252)) % 183.90/184.45 [1126]~E(x11261,x11262)+E(f563(x11261,x11263),f563(x11262,x11263)) % 183.90/184.45 [1127]~E(x11271,x11272)+E(f563(x11273,x11271),f563(x11273,x11272)) % 183.90/184.45 [1128]~E(x11281,x11282)+E(f635(x11281,x11283,x11284),f635(x11282,x11283,x11284)) % 183.90/184.45 [1129]~E(x11291,x11292)+E(f635(x11293,x11291,x11294),f635(x11293,x11292,x11294)) % 183.90/184.45 [1130]~E(x11301,x11302)+E(f635(x11303,x11304,x11301),f635(x11303,x11304,x11302)) % 183.90/184.45 [1131]~E(x11311,x11312)+E(f681(x11311,x11313,x11314),f681(x11312,x11313,x11314)) % 183.90/184.45 [1132]~E(x11321,x11322)+E(f681(x11323,x11321,x11324),f681(x11323,x11322,x11324)) % 183.90/184.45 [1133]~E(x11331,x11332)+E(f681(x11333,x11334,x11331),f681(x11333,x11334,x11332)) % 183.90/184.45 [1134]~E(x11341,x11342)+E(f232(x11341,x11343),f232(x11342,x11343)) % 183.90/184.45 [1135]~E(x11351,x11352)+E(f232(x11353,x11351),f232(x11353,x11352)) % 183.90/184.45 [1136]~E(x11361,x11362)+E(f348(x11361,x11363,x11364,x11365),f348(x11362,x11363,x11364,x11365)) % 183.90/184.45 [1137]~E(x11371,x11372)+E(f348(x11373,x11371,x11374,x11375),f348(x11373,x11372,x11374,x11375)) % 183.90/184.45 [1138]~E(x11381,x11382)+E(f348(x11383,x11384,x11381,x11385),f348(x11383,x11384,x11382,x11385)) % 183.90/184.45 [1139]~E(x11391,x11392)+E(f348(x11393,x11394,x11395,x11391),f348(x11393,x11394,x11395,x11392)) % 183.90/184.45 [1140]~E(x11401,x11402)+E(f865(x11401,x11403,x11404),f865(x11402,x11403,x11404)) % 183.90/184.45 [1141]~E(x11411,x11412)+E(f865(x11413,x11411,x11414),f865(x11413,x11412,x11414)) % 183.90/184.45 [1142]~E(x11421,x11422)+E(f865(x11423,x11424,x11421),f865(x11423,x11424,x11422)) % 183.90/184.45 [1143]~E(x11431,x11432)+E(f448(x11431,x11433,x11434,x11435),f448(x11432,x11433,x11434,x11435)) % 183.90/184.45 [1144]~E(x11441,x11442)+E(f448(x11443,x11441,x11444,x11445),f448(x11443,x11442,x11444,x11445)) % 183.90/184.45 [1145]~E(x11451,x11452)+E(f448(x11453,x11454,x11451,x11455),f448(x11453,x11454,x11452,x11455)) % 183.90/184.45 [1146]~E(x11461,x11462)+E(f448(x11463,x11464,x11465,x11461),f448(x11463,x11464,x11465,x11462)) % 183.90/184.45 [1147]~E(x11471,x11472)+E(f854(x11471,x11473,x11474,x11475,x11476),f854(x11472,x11473,x11474,x11475,x11476)) % 183.90/184.45 [1148]~E(x11481,x11482)+E(f854(x11483,x11481,x11484,x11485,x11486),f854(x11483,x11482,x11484,x11485,x11486)) % 183.90/184.45 [1149]~E(x11491,x11492)+E(f854(x11493,x11494,x11491,x11495,x11496),f854(x11493,x11494,x11492,x11495,x11496)) % 183.90/184.45 [1150]~E(x11501,x11502)+E(f854(x11503,x11504,x11505,x11501,x11506),f854(x11503,x11504,x11505,x11502,x11506)) % 183.90/184.45 [1151]~E(x11511,x11512)+E(f854(x11513,x11514,x11515,x11516,x11511),f854(x11513,x11514,x11515,x11516,x11512)) % 183.90/184.45 [1152]~E(x11521,x11522)+E(f144(x11521,x11523),f144(x11522,x11523)) % 183.90/184.45 [1153]~E(x11531,x11532)+E(f144(x11533,x11531),f144(x11533,x11532)) % 183.90/184.45 [1154]~E(x11541,x11542)+E(f725(x11541,x11543,x11544,x11545,x11546,x11547,x11548),f725(x11542,x11543,x11544,x11545,x11546,x11547,x11548)) % 183.90/184.45 [1155]~E(x11551,x11552)+E(f725(x11553,x11551,x11554,x11555,x11556,x11557,x11558),f725(x11553,x11552,x11554,x11555,x11556,x11557,x11558)) % 183.90/184.45 [1156]~E(x11561,x11562)+E(f725(x11563,x11564,x11561,x11565,x11566,x11567,x11568),f725(x11563,x11564,x11562,x11565,x11566,x11567,x11568)) % 183.90/184.45 [1157]~E(x11571,x11572)+E(f725(x11573,x11574,x11575,x11571,x11576,x11577,x11578),f725(x11573,x11574,x11575,x11572,x11576,x11577,x11578)) % 183.90/184.45 [1158]~E(x11581,x11582)+E(f725(x11583,x11584,x11585,x11586,x11581,x11587,x11588),f725(x11583,x11584,x11585,x11586,x11582,x11587,x11588)) % 183.90/184.45 [1159]~E(x11591,x11592)+E(f725(x11593,x11594,x11595,x11596,x11597,x11591,x11598),f725(x11593,x11594,x11595,x11596,x11597,x11592,x11598)) % 183.90/184.45 [1160]~E(x11601,x11602)+E(f725(x11603,x11604,x11605,x11606,x11607,x11608,x11601),f725(x11603,x11604,x11605,x11606,x11607,x11608,x11602)) % 183.90/184.45 [1161]~E(x11611,x11612)+E(f626(x11611,x11613,x11614,x11615,x11616),f626(x11612,x11613,x11614,x11615,x11616)) % 183.90/184.45 [1162]~E(x11621,x11622)+E(f626(x11623,x11621,x11624,x11625,x11626),f626(x11623,x11622,x11624,x11625,x11626)) % 183.90/184.45 [1163]~E(x11631,x11632)+E(f626(x11633,x11634,x11631,x11635,x11636),f626(x11633,x11634,x11632,x11635,x11636)) % 183.90/184.45 [1164]~E(x11641,x11642)+E(f626(x11643,x11644,x11645,x11641,x11646),f626(x11643,x11644,x11645,x11642,x11646)) % 183.90/184.45 [1165]~E(x11651,x11652)+E(f626(x11653,x11654,x11655,x11656,x11651),f626(x11653,x11654,x11655,x11656,x11652)) % 183.90/184.45 [1166]~E(x11661,x11662)+E(f395(x11661,x11663,x11664,x11665),f395(x11662,x11663,x11664,x11665)) % 183.90/184.45 [1167]~E(x11671,x11672)+E(f395(x11673,x11671,x11674,x11675),f395(x11673,x11672,x11674,x11675)) % 183.90/184.45 [1168]~E(x11681,x11682)+E(f395(x11683,x11684,x11681,x11685),f395(x11683,x11684,x11682,x11685)) % 183.90/184.45 [1169]~E(x11691,x11692)+E(f395(x11693,x11694,x11695,x11691),f395(x11693,x11694,x11695,x11692)) % 183.90/184.45 [1170]~E(x11701,x11702)+E(f263(x11701,x11703,x11704),f263(x11702,x11703,x11704)) % 183.90/184.45 [1171]~E(x11711,x11712)+E(f263(x11713,x11711,x11714),f263(x11713,x11712,x11714)) % 183.90/184.45 [1172]~E(x11721,x11722)+E(f263(x11723,x11724,x11721),f263(x11723,x11724,x11722)) % 183.90/184.45 [1173]~E(x11731,x11732)+E(f682(x11731,x11733,x11734),f682(x11732,x11733,x11734)) % 183.90/184.45 [1174]~E(x11741,x11742)+E(f682(x11743,x11741,x11744),f682(x11743,x11742,x11744)) % 183.90/184.45 [1175]~E(x11751,x11752)+E(f682(x11753,x11754,x11751),f682(x11753,x11754,x11752)) % 183.90/184.45 [1176]~E(x11761,x11762)+E(f625(x11761,x11763,x11764),f625(x11762,x11763,x11764)) % 183.90/184.45 [1177]~E(x11771,x11772)+E(f625(x11773,x11771,x11774),f625(x11773,x11772,x11774)) % 183.90/184.45 [1178]~E(x11781,x11782)+E(f625(x11783,x11784,x11781),f625(x11783,x11784,x11782)) % 183.90/184.45 [1179]~E(x11791,x11792)+E(f764(x11791,x11793),f764(x11792,x11793)) % 183.90/184.45 [1180]~E(x11801,x11802)+E(f764(x11803,x11801),f764(x11803,x11802)) % 183.90/184.46 [1181]~E(x11811,x11812)+E(f637(x11811,x11813,x11814,x11815,x11816),f637(x11812,x11813,x11814,x11815,x11816)) % 183.90/184.46 [1182]~E(x11821,x11822)+E(f637(x11823,x11821,x11824,x11825,x11826),f637(x11823,x11822,x11824,x11825,x11826)) % 183.90/184.46 [1183]~E(x11831,x11832)+E(f637(x11833,x11834,x11831,x11835,x11836),f637(x11833,x11834,x11832,x11835,x11836)) % 183.90/184.46 [1184]~E(x11841,x11842)+E(f637(x11843,x11844,x11845,x11841,x11846),f637(x11843,x11844,x11845,x11842,x11846)) % 183.90/184.46 [1185]~E(x11851,x11852)+E(f637(x11853,x11854,x11855,x11856,x11851),f637(x11853,x11854,x11855,x11856,x11852)) % 183.90/184.46 [1186]~E(x11861,x11862)+E(f205(x11861,x11863,x11864,x11865),f205(x11862,x11863,x11864,x11865)) % 183.90/184.46 [1187]~E(x11871,x11872)+E(f205(x11873,x11871,x11874,x11875),f205(x11873,x11872,x11874,x11875)) % 183.90/184.46 [1188]~E(x11881,x11882)+E(f205(x11883,x11884,x11881,x11885),f205(x11883,x11884,x11882,x11885)) % 183.90/184.46 [1189]~E(x11891,x11892)+E(f205(x11893,x11894,x11895,x11891),f205(x11893,x11894,x11895,x11892)) % 183.90/184.46 [1190]~E(x11901,x11902)+E(f515(x11901,x11903,x11904),f515(x11902,x11903,x11904)) % 183.90/184.46 [1191]~E(x11911,x11912)+E(f515(x11913,x11911,x11914),f515(x11913,x11912,x11914)) % 183.90/184.46 [1192]~E(x11921,x11922)+E(f515(x11923,x11924,x11921),f515(x11923,x11924,x11922)) % 183.90/184.46 [1193]~E(x11931,x11932)+E(f211(x11931,x11933),f211(x11932,x11933)) % 183.90/184.46 [1194]~E(x11941,x11942)+E(f211(x11943,x11941),f211(x11943,x11942)) % 183.90/184.46 [1195]~E(x11951,x11952)+E(f54(x11951,x11953,x11954),f54(x11952,x11953,x11954)) % 183.90/184.46 [1196]~E(x11961,x11962)+E(f54(x11963,x11961,x11964),f54(x11963,x11962,x11964)) % 183.90/184.46 [1197]~E(x11971,x11972)+E(f54(x11973,x11974,x11971),f54(x11973,x11974,x11972)) % 183.90/184.46 [1198]~E(x11981,x11982)+E(f127(x11981),f127(x11982)) % 183.90/184.46 [1199]~E(x11991,x11992)+E(f777(x11991,x11993,x11994),f777(x11992,x11993,x11994)) % 183.90/184.46 [1200]~E(x12001,x12002)+E(f777(x12003,x12001,x12004),f777(x12003,x12002,x12004)) % 183.90/184.46 [1201]~E(x12011,x12012)+E(f777(x12013,x12014,x12011),f777(x12013,x12014,x12012)) % 183.90/184.46 [1202]~E(x12021,x12022)+E(f250(x12021,x12023),f250(x12022,x12023)) % 183.90/184.46 [1203]~E(x12031,x12032)+E(f250(x12033,x12031),f250(x12033,x12032)) % 183.90/184.46 [1204]~E(x12041,x12042)+E(f755(x12041,x12043),f755(x12042,x12043)) % 183.90/184.46 [1205]~E(x12051,x12052)+E(f755(x12053,x12051),f755(x12053,x12052)) % 183.90/184.46 [1206]~E(x12061,x12062)+E(f526(x12061,x12063,x12064),f526(x12062,x12063,x12064)) % 183.90/184.46 [1207]~E(x12071,x12072)+E(f526(x12073,x12071,x12074),f526(x12073,x12072,x12074)) % 183.90/184.46 [1208]~E(x12081,x12082)+E(f526(x12083,x12084,x12081),f526(x12083,x12084,x12082)) % 183.90/184.46 [1209]~E(x12091,x12092)+E(f842(x12091,x12093,x12094,x12095),f842(x12092,x12093,x12094,x12095)) % 183.90/184.46 [1210]~E(x12101,x12102)+E(f842(x12103,x12101,x12104,x12105),f842(x12103,x12102,x12104,x12105)) % 183.90/184.46 [1211]~E(x12111,x12112)+E(f842(x12113,x12114,x12111,x12115),f842(x12113,x12114,x12112,x12115)) % 183.90/184.46 [1212]~E(x12121,x12122)+E(f842(x12123,x12124,x12125,x12121),f842(x12123,x12124,x12125,x12122)) % 183.90/184.46 [1213]~E(x12131,x12132)+E(f546(x12131,x12133,x12134),f546(x12132,x12133,x12134)) % 183.90/184.46 [1214]~E(x12141,x12142)+E(f546(x12143,x12141,x12144),f546(x12143,x12142,x12144)) % 183.90/184.46 [1215]~E(x12151,x12152)+E(f546(x12153,x12154,x12151),f546(x12153,x12154,x12152)) % 183.90/184.46 [1216]~E(x12161,x12162)+E(f346(x12161,x12163,x12164),f346(x12162,x12163,x12164)) % 183.90/184.46 [1217]~E(x12171,x12172)+E(f346(x12173,x12171,x12174),f346(x12173,x12172,x12174)) % 183.90/184.46 [1218]~E(x12181,x12182)+E(f346(x12183,x12184,x12181),f346(x12183,x12184,x12182)) % 183.90/184.46 [1219]~E(x12191,x12192)+E(f609(x12191,x12193,x12194,x12195,x12196,x12197),f609(x12192,x12193,x12194,x12195,x12196,x12197)) % 183.90/184.46 [1220]~E(x12201,x12202)+E(f609(x12203,x12201,x12204,x12205,x12206,x12207),f609(x12203,x12202,x12204,x12205,x12206,x12207)) % 183.90/184.46 [1221]~E(x12211,x12212)+E(f609(x12213,x12214,x12211,x12215,x12216,x12217),f609(x12213,x12214,x12212,x12215,x12216,x12217)) % 183.90/184.46 [1222]~E(x12221,x12222)+E(f609(x12223,x12224,x12225,x12221,x12226,x12227),f609(x12223,x12224,x12225,x12222,x12226,x12227)) % 183.90/184.46 [1223]~E(x12231,x12232)+E(f609(x12233,x12234,x12235,x12236,x12231,x12237),f609(x12233,x12234,x12235,x12236,x12232,x12237)) % 183.90/184.46 [1224]~E(x12241,x12242)+E(f609(x12243,x12244,x12245,x12246,x12247,x12241),f609(x12243,x12244,x12245,x12246,x12247,x12242)) % 183.90/184.46 [1225]~E(x12251,x12252)+E(f869(x12251,x12253,x12254,x12255,x12256),f869(x12252,x12253,x12254,x12255,x12256)) % 183.90/184.46 [1226]~E(x12261,x12262)+E(f869(x12263,x12261,x12264,x12265,x12266),f869(x12263,x12262,x12264,x12265,x12266)) % 183.90/184.46 [1227]~E(x12271,x12272)+E(f869(x12273,x12274,x12271,x12275,x12276),f869(x12273,x12274,x12272,x12275,x12276)) % 183.90/184.46 [1228]~E(x12281,x12282)+E(f869(x12283,x12284,x12285,x12281,x12286),f869(x12283,x12284,x12285,x12282,x12286)) % 183.90/184.46 [1229]~E(x12291,x12292)+E(f869(x12293,x12294,x12295,x12296,x12291),f869(x12293,x12294,x12295,x12296,x12292)) % 183.90/184.46 [1230]~E(x12301,x12302)+E(f800(x12301,x12303,x12304),f800(x12302,x12303,x12304)) % 183.90/184.46 [1231]~E(x12311,x12312)+E(f800(x12313,x12311,x12314),f800(x12313,x12312,x12314)) % 183.90/184.46 [1232]~E(x12321,x12322)+E(f800(x12323,x12324,x12321),f800(x12323,x12324,x12322)) % 183.90/184.46 [1233]~E(x12331,x12332)+E(f551(x12331,x12333,x12334),f551(x12332,x12333,x12334)) % 183.90/184.46 [1234]~E(x12341,x12342)+E(f551(x12343,x12341,x12344),f551(x12343,x12342,x12344)) % 183.90/184.46 [1235]~E(x12351,x12352)+E(f551(x12353,x12354,x12351),f551(x12353,x12354,x12352)) % 183.90/184.46 [1236]~E(x12361,x12362)+E(f73(x12361,x12363),f73(x12362,x12363)) % 183.90/184.46 [1237]~E(x12371,x12372)+E(f73(x12373,x12371),f73(x12373,x12372)) % 183.90/184.46 [1238]~E(x12381,x12382)+E(f461(x12381,x12383,x12384),f461(x12382,x12383,x12384)) % 183.90/184.46 [1239]~E(x12391,x12392)+E(f461(x12393,x12391,x12394),f461(x12393,x12392,x12394)) % 183.90/184.46 [1240]~E(x12401,x12402)+E(f461(x12403,x12404,x12401),f461(x12403,x12404,x12402)) % 183.90/184.46 [1241]~E(x12411,x12412)+E(f860(x12411,x12413,x12414,x12415),f860(x12412,x12413,x12414,x12415)) % 183.90/184.46 [1242]~E(x12421,x12422)+E(f860(x12423,x12421,x12424,x12425),f860(x12423,x12422,x12424,x12425)) % 183.90/184.46 [1243]~E(x12431,x12432)+E(f860(x12433,x12434,x12431,x12435),f860(x12433,x12434,x12432,x12435)) % 183.90/184.46 [1244]~E(x12441,x12442)+E(f860(x12443,x12444,x12445,x12441),f860(x12443,x12444,x12445,x12442)) % 183.90/184.46 [1245]~E(x12451,x12452)+E(f662(x12451,x12453,x12454,x12455),f662(x12452,x12453,x12454,x12455)) % 183.90/184.46 [1246]~E(x12461,x12462)+E(f662(x12463,x12461,x12464,x12465),f662(x12463,x12462,x12464,x12465)) % 183.90/184.46 [1247]~E(x12471,x12472)+E(f662(x12473,x12474,x12471,x12475),f662(x12473,x12474,x12472,x12475)) % 183.90/184.46 [1248]~E(x12481,x12482)+E(f662(x12483,x12484,x12485,x12481),f662(x12483,x12484,x12485,x12482)) % 183.90/184.46 [1249]~E(x12491,x12492)+E(f405(x12491,x12493,x12494),f405(x12492,x12493,x12494)) % 183.90/184.46 [1250]~E(x12501,x12502)+E(f405(x12503,x12501,x12504),f405(x12503,x12502,x12504)) % 183.90/184.46 [1251]~E(x12511,x12512)+E(f405(x12513,x12514,x12511),f405(x12513,x12514,x12512)) % 183.90/184.46 [1252]~E(x12521,x12522)+E(f844(x12521,x12523,x12524,x12525,x12526,x12527),f844(x12522,x12523,x12524,x12525,x12526,x12527)) % 183.90/184.46 [1253]~E(x12531,x12532)+E(f844(x12533,x12531,x12534,x12535,x12536,x12537),f844(x12533,x12532,x12534,x12535,x12536,x12537)) % 183.90/184.46 [1254]~E(x12541,x12542)+E(f844(x12543,x12544,x12541,x12545,x12546,x12547),f844(x12543,x12544,x12542,x12545,x12546,x12547)) % 183.90/184.46 [1255]~E(x12551,x12552)+E(f844(x12553,x12554,x12555,x12551,x12556,x12557),f844(x12553,x12554,x12555,x12552,x12556,x12557)) % 183.90/184.46 [1256]~E(x12561,x12562)+E(f844(x12563,x12564,x12565,x12566,x12561,x12567),f844(x12563,x12564,x12565,x12566,x12562,x12567)) % 183.90/184.46 [1257]~E(x12571,x12572)+E(f844(x12573,x12574,x12575,x12576,x12577,x12571),f844(x12573,x12574,x12575,x12576,x12577,x12572)) % 183.90/184.46 [1258]~E(x12581,x12582)+E(f293(x12581,x12583),f293(x12582,x12583)) % 183.90/184.46 [1259]~E(x12591,x12592)+E(f293(x12593,x12591),f293(x12593,x12592)) % 183.90/184.46 [1260]~E(x12601,x12602)+E(f740(x12601,x12603,x12604),f740(x12602,x12603,x12604)) % 183.90/184.46 [1261]~E(x12611,x12612)+E(f740(x12613,x12611,x12614),f740(x12613,x12612,x12614)) % 183.90/184.46 [1262]~E(x12621,x12622)+E(f740(x12623,x12624,x12621),f740(x12623,x12624,x12622)) % 183.90/184.46 [1263]~E(x12631,x12632)+E(f599(x12631,x12633),f599(x12632,x12633)) % 183.90/184.46 [1264]~E(x12641,x12642)+E(f599(x12643,x12641),f599(x12643,x12642)) % 183.90/184.46 [1265]~E(x12651,x12652)+E(f664(x12651,x12653,x12654,x12655,x12656,x12657),f664(x12652,x12653,x12654,x12655,x12656,x12657)) % 183.90/184.46 [1266]~E(x12661,x12662)+E(f664(x12663,x12661,x12664,x12665,x12666,x12667),f664(x12663,x12662,x12664,x12665,x12666,x12667)) % 183.90/184.46 [1267]~E(x12671,x12672)+E(f664(x12673,x12674,x12671,x12675,x12676,x12677),f664(x12673,x12674,x12672,x12675,x12676,x12677)) % 183.90/184.46 [1268]~E(x12681,x12682)+E(f664(x12683,x12684,x12685,x12681,x12686,x12687),f664(x12683,x12684,x12685,x12682,x12686,x12687)) % 183.90/184.46 [1269]~E(x12691,x12692)+E(f664(x12693,x12694,x12695,x12696,x12691,x12697),f664(x12693,x12694,x12695,x12696,x12692,x12697)) % 183.90/184.46 [1270]~E(x12701,x12702)+E(f664(x12703,x12704,x12705,x12706,x12707,x12701),f664(x12703,x12704,x12705,x12706,x12707,x12702)) % 183.90/184.46 [1271]~E(x12711,x12712)+E(f314(x12711,x12713),f314(x12712,x12713)) % 183.90/184.46 [1272]~E(x12721,x12722)+E(f314(x12723,x12721),f314(x12723,x12722)) % 183.90/184.46 [1273]~E(x12731,x12732)+E(f665(x12731,x12733,x12734,x12735,x12736,x12737),f665(x12732,x12733,x12734,x12735,x12736,x12737)) % 183.90/184.46 [1274]~E(x12741,x12742)+E(f665(x12743,x12741,x12744,x12745,x12746,x12747),f665(x12743,x12742,x12744,x12745,x12746,x12747)) % 183.90/184.46 [1275]~E(x12751,x12752)+E(f665(x12753,x12754,x12751,x12755,x12756,x12757),f665(x12753,x12754,x12752,x12755,x12756,x12757)) % 183.90/184.46 [1276]~E(x12761,x12762)+E(f665(x12763,x12764,x12765,x12761,x12766,x12767),f665(x12763,x12764,x12765,x12762,x12766,x12767)) % 183.90/184.46 [1277]~E(x12771,x12772)+E(f665(x12773,x12774,x12775,x12776,x12771,x12777),f665(x12773,x12774,x12775,x12776,x12772,x12777)) % 183.90/184.46 [1278]~E(x12781,x12782)+E(f665(x12783,x12784,x12785,x12786,x12787,x12781),f665(x12783,x12784,x12785,x12786,x12787,x12782)) % 183.90/184.46 [1279]~E(x12791,x12792)+E(f544(x12791,x12793,x12794),f544(x12792,x12793,x12794)) % 183.90/184.46 [1280]~E(x12801,x12802)+E(f544(x12803,x12801,x12804),f544(x12803,x12802,x12804)) % 183.90/184.46 [1281]~E(x12811,x12812)+E(f544(x12813,x12814,x12811),f544(x12813,x12814,x12812)) % 183.90/184.46 [1282]~E(x12821,x12822)+E(f460(x12821,x12823,x12824,x12825,x12826),f460(x12822,x12823,x12824,x12825,x12826)) % 183.90/184.46 [1283]~E(x12831,x12832)+E(f460(x12833,x12831,x12834,x12835,x12836),f460(x12833,x12832,x12834,x12835,x12836)) % 183.90/184.46 [1284]~E(x12841,x12842)+E(f460(x12843,x12844,x12841,x12845,x12846),f460(x12843,x12844,x12842,x12845,x12846)) % 183.90/184.46 [1285]~E(x12851,x12852)+E(f460(x12853,x12854,x12855,x12851,x12856),f460(x12853,x12854,x12855,x12852,x12856)) % 183.90/184.46 [1286]~E(x12861,x12862)+E(f460(x12863,x12864,x12865,x12866,x12861),f460(x12863,x12864,x12865,x12866,x12862)) % 183.90/184.46 [1287]~E(x12871,x12872)+E(f128(x12871,x12873,x12874),f128(x12872,x12873,x12874)) % 183.90/184.46 [1288]~E(x12881,x12882)+E(f128(x12883,x12881,x12884),f128(x12883,x12882,x12884)) % 183.90/184.46 [1289]~E(x12891,x12892)+E(f128(x12893,x12894,x12891),f128(x12893,x12894,x12892)) % 183.90/184.46 [1290]~E(x12901,x12902)+E(f502(x12901,x12903),f502(x12902,x12903)) % 183.90/184.46 [1291]~E(x12911,x12912)+E(f502(x12913,x12911),f502(x12913,x12912)) % 183.90/184.46 [1292]~E(x12921,x12922)+E(f547(x12921,x12923,x12924),f547(x12922,x12923,x12924)) % 183.90/184.46 [1293]~E(x12931,x12932)+E(f547(x12933,x12931,x12934),f547(x12933,x12932,x12934)) % 183.90/184.46 [1294]~E(x12941,x12942)+E(f547(x12943,x12944,x12941),f547(x12943,x12944,x12942)) % 183.90/184.46 [1295]~E(x12951,x12952)+E(f294(x12951,x12953,x12954),f294(x12952,x12953,x12954)) % 183.90/184.46 [1296]~E(x12961,x12962)+E(f294(x12963,x12961,x12964),f294(x12963,x12962,x12964)) % 183.90/184.46 [1297]~E(x12971,x12972)+E(f294(x12973,x12974,x12971),f294(x12973,x12974,x12972)) % 183.90/184.46 [1298]~E(x12981,x12982)+E(f216(x12981),f216(x12982)) % 183.90/184.46 [1299]~E(x12991,x12992)+E(f822(x12991,x12993,x12994),f822(x12992,x12993,x12994)) % 183.90/184.46 [1300]~E(x13001,x13002)+E(f822(x13003,x13001,x13004),f822(x13003,x13002,x13004)) % 183.90/184.46 [1301]~E(x13011,x13012)+E(f822(x13013,x13014,x13011),f822(x13013,x13014,x13012)) % 183.90/184.46 [1302]~E(x13021,x13022)+E(f724(x13021,x13023),f724(x13022,x13023)) % 183.90/184.46 [1303]~E(x13031,x13032)+E(f724(x13033,x13031),f724(x13033,x13032)) % 183.90/184.46 [1304]~E(x13041,x13042)+E(f262(x13041,x13043,x13044),f262(x13042,x13043,x13044)) % 183.90/184.46 [1305]~E(x13051,x13052)+E(f262(x13053,x13051,x13054),f262(x13053,x13052,x13054)) % 183.90/184.46 [1306]~E(x13061,x13062)+E(f262(x13063,x13064,x13061),f262(x13063,x13064,x13062)) % 183.90/184.46 [1307]~E(x13071,x13072)+E(f692(x13071,x13073,x13074,x13075),f692(x13072,x13073,x13074,x13075)) % 183.90/184.46 [1308]~E(x13081,x13082)+E(f692(x13083,x13081,x13084,x13085),f692(x13083,x13082,x13084,x13085)) % 183.90/184.46 [1309]~E(x13091,x13092)+E(f692(x13093,x13094,x13091,x13095),f692(x13093,x13094,x13092,x13095)) % 183.90/184.46 [1310]~E(x13101,x13102)+E(f692(x13103,x13104,x13105,x13101),f692(x13103,x13104,x13105,x13102)) % 183.90/184.46 [1311]~E(x13111,x13112)+E(f506(x13111,x13113),f506(x13112,x13113)) % 183.90/184.46 [1312]~E(x13121,x13122)+E(f506(x13123,x13121),f506(x13123,x13122)) % 183.90/184.46 [1313]~E(x13131,x13132)+E(f863(x13131,x13133,x13134),f863(x13132,x13133,x13134)) % 183.90/184.46 [1314]~E(x13141,x13142)+E(f863(x13143,x13141,x13144),f863(x13143,x13142,x13144)) % 183.90/184.46 [1315]~E(x13151,x13152)+E(f863(x13153,x13154,x13151),f863(x13153,x13154,x13152)) % 183.90/184.46 [1316]~E(x13161,x13162)+E(f481(x13161,x13163,x13164,x13165,x13166),f481(x13162,x13163,x13164,x13165,x13166)) % 183.90/184.46 [1317]~E(x13171,x13172)+E(f481(x13173,x13171,x13174,x13175,x13176),f481(x13173,x13172,x13174,x13175,x13176)) % 183.90/184.46 [1318]~E(x13181,x13182)+E(f481(x13183,x13184,x13181,x13185,x13186),f481(x13183,x13184,x13182,x13185,x13186)) % 183.90/184.46 [1319]~E(x13191,x13192)+E(f481(x13193,x13194,x13195,x13191,x13196),f481(x13193,x13194,x13195,x13192,x13196)) % 183.90/184.46 [1320]~E(x13201,x13202)+E(f481(x13203,x13204,x13205,x13206,x13201),f481(x13203,x13204,x13205,x13206,x13202)) % 183.90/184.46 [1321]~E(x13211,x13212)+E(f684(x13211,x13213,x13214,x13215),f684(x13212,x13213,x13214,x13215)) % 183.90/184.46 [1322]~E(x13221,x13222)+E(f684(x13223,x13221,x13224,x13225),f684(x13223,x13222,x13224,x13225)) % 183.90/184.46 [1323]~E(x13231,x13232)+E(f684(x13233,x13234,x13231,x13235),f684(x13233,x13234,x13232,x13235)) % 183.90/184.46 [1324]~E(x13241,x13242)+E(f684(x13243,x13244,x13245,x13241),f684(x13243,x13244,x13245,x13242)) % 183.90/184.46 [1325]~E(x13251,x13252)+E(f278(x13251),f278(x13252)) % 183.90/184.46 [1326]~E(x13261,x13262)+E(f597(x13261,x13263,x13264,x13265),f597(x13262,x13263,x13264,x13265)) % 183.90/184.46 [1327]~E(x13271,x13272)+E(f597(x13273,x13271,x13274,x13275),f597(x13273,x13272,x13274,x13275)) % 183.90/184.46 [1328]~E(x13281,x13282)+E(f597(x13283,x13284,x13281,x13285),f597(x13283,x13284,x13282,x13285)) % 183.90/184.46 [1329]~E(x13291,x13292)+E(f597(x13293,x13294,x13295,x13291),f597(x13293,x13294,x13295,x13292)) % 183.90/184.46 [1330]~E(x13301,x13302)+E(f617(x13301,x13303,x13304),f617(x13302,x13303,x13304)) % 183.90/184.46 [1331]~E(x13311,x13312)+E(f617(x13313,x13311,x13314),f617(x13313,x13312,x13314)) % 183.90/184.46 [1332]~E(x13321,x13322)+E(f617(x13323,x13324,x13321),f617(x13323,x13324,x13322)) % 183.90/184.46 [1333]~E(x13331,x13332)+E(f483(x13331,x13333,x13334,x13335),f483(x13332,x13333,x13334,x13335)) % 183.90/184.46 [1334]~E(x13341,x13342)+E(f483(x13343,x13341,x13344,x13345),f483(x13343,x13342,x13344,x13345)) % 183.90/184.46 [1335]~E(x13351,x13352)+E(f483(x13353,x13354,x13351,x13355),f483(x13353,x13354,x13352,x13355)) % 183.90/184.46 [1336]~E(x13361,x13362)+E(f483(x13363,x13364,x13365,x13361),f483(x13363,x13364,x13365,x13362)) % 183.90/184.46 [1337]~E(x13371,x13372)+E(f387(x13371,x13373,x13374,x13375,x13376,x13377,x13378,x13379),f387(x13372,x13373,x13374,x13375,x13376,x13377,x13378,x13379)) % 183.90/184.46 [1338]~E(x13381,x13382)+E(f387(x13383,x13381,x13384,x13385,x13386,x13387,x13388,x13389),f387(x13383,x13382,x13384,x13385,x13386,x13387,x13388,x13389)) % 183.90/184.46 [1339]~E(x13391,x13392)+E(f387(x13393,x13394,x13391,x13395,x13396,x13397,x13398,x13399),f387(x13393,x13394,x13392,x13395,x13396,x13397,x13398,x13399)) % 183.90/184.46 [1340]~E(x13401,x13402)+E(f387(x13403,x13404,x13405,x13401,x13406,x13407,x13408,x13409),f387(x13403,x13404,x13405,x13402,x13406,x13407,x13408,x13409)) % 183.90/184.46 [1341]~E(x13411,x13412)+E(f387(x13413,x13414,x13415,x13416,x13411,x13417,x13418,x13419),f387(x13413,x13414,x13415,x13416,x13412,x13417,x13418,x13419)) % 183.90/184.46 [1342]~E(x13421,x13422)+E(f387(x13423,x13424,x13425,x13426,x13427,x13421,x13428,x13429),f387(x13423,x13424,x13425,x13426,x13427,x13422,x13428,x13429)) % 183.90/184.46 [1343]~E(x13431,x13432)+E(f387(x13433,x13434,x13435,x13436,x13437,x13438,x13431,x13439),f387(x13433,x13434,x13435,x13436,x13437,x13438,x13432,x13439)) % 183.90/184.46 [1344]~E(x13441,x13442)+E(f387(x13443,x13444,x13445,x13446,x13447,x13448,x13449,x13441),f387(x13443,x13444,x13445,x13446,x13447,x13448,x13449,x13442)) % 183.90/184.46 [1345]~E(x13451,x13452)+E(f283(x13451,x13453,x13454),f283(x13452,x13453,x13454)) % 183.90/184.46 [1346]~E(x13461,x13462)+E(f283(x13463,x13461,x13464),f283(x13463,x13462,x13464)) % 183.90/184.46 [1347]~E(x13471,x13472)+E(f283(x13473,x13474,x13471),f283(x13473,x13474,x13472)) % 183.90/184.46 [1348]~E(x13481,x13482)+E(f702(x13481,x13483,x13484,x13485),f702(x13482,x13483,x13484,x13485)) % 183.90/184.46 [1349]~E(x13491,x13492)+E(f702(x13493,x13491,x13494,x13495),f702(x13493,x13492,x13494,x13495)) % 183.90/184.46 [1350]~E(x13501,x13502)+E(f702(x13503,x13504,x13501,x13505),f702(x13503,x13504,x13502,x13505)) % 183.90/184.46 [1351]~E(x13511,x13512)+E(f702(x13513,x13514,x13515,x13511),f702(x13513,x13514,x13515,x13512)) % 183.90/184.46 [1352]~E(x13521,x13522)+E(f827(x13521,x13523,x13524,x13525),f827(x13522,x13523,x13524,x13525)) % 183.90/184.46 [1353]~E(x13531,x13532)+E(f827(x13533,x13531,x13534,x13535),f827(x13533,x13532,x13534,x13535)) % 183.90/184.46 [1354]~E(x13541,x13542)+E(f827(x13543,x13544,x13541,x13545),f827(x13543,x13544,x13542,x13545)) % 183.90/184.46 [1355]~E(x13551,x13552)+E(f827(x13553,x13554,x13555,x13551),f827(x13553,x13554,x13555,x13552)) % 183.90/184.46 [1356]~E(x13561,x13562)+E(f479(x13561,x13563,x13564,x13565),f479(x13562,x13563,x13564,x13565)) % 183.90/184.46 [1357]~E(x13571,x13572)+E(f479(x13573,x13571,x13574,x13575),f479(x13573,x13572,x13574,x13575)) % 183.90/184.46 [1358]~E(x13581,x13582)+E(f479(x13583,x13584,x13581,x13585),f479(x13583,x13584,x13582,x13585)) % 183.90/184.46 [1359]~E(x13591,x13592)+E(f479(x13593,x13594,x13595,x13591),f479(x13593,x13594,x13595,x13592)) % 183.90/184.46 [1360]~E(x13601,x13602)+E(f482(x13601,x13603,x13604,x13605),f482(x13602,x13603,x13604,x13605)) % 183.90/184.46 [1361]~E(x13611,x13612)+E(f482(x13613,x13611,x13614,x13615),f482(x13613,x13612,x13614,x13615)) % 183.90/184.46 [1362]~E(x13621,x13622)+E(f482(x13623,x13624,x13621,x13625),f482(x13623,x13624,x13622,x13625)) % 183.90/184.46 [1363]~E(x13631,x13632)+E(f482(x13633,x13634,x13635,x13631),f482(x13633,x13634,x13635,x13632)) % 183.90/184.46 [1364]~E(x13641,x13642)+E(f192(x13641,x13643,x13644),f192(x13642,x13643,x13644)) % 183.90/184.46 [1365]~E(x13651,x13652)+E(f192(x13653,x13651,x13654),f192(x13653,x13652,x13654)) % 183.90/184.46 [1366]~E(x13661,x13662)+E(f192(x13663,x13664,x13661),f192(x13663,x13664,x13662)) % 183.90/184.46 [1367]~E(x13671,x13672)+E(f407(x13671),f407(x13672)) % 183.90/184.46 [1368]~E(x13681,x13682)+E(f545(x13681,x13683,x13684),f545(x13682,x13683,x13684)) % 183.90/184.46 [1369]~E(x13691,x13692)+E(f545(x13693,x13691,x13694),f545(x13693,x13692,x13694)) % 183.90/184.46 [1370]~E(x13701,x13702)+E(f545(x13703,x13704,x13701),f545(x13703,x13704,x13702)) % 183.90/184.46 [1371]~E(x13711,x13712)+E(f587(x13711,x13713,x13714,x13715,x13716,x13717,x13718,x13719),f587(x13712,x13713,x13714,x13715,x13716,x13717,x13718,x13719)) % 183.90/184.46 [1372]~E(x13721,x13722)+E(f587(x13723,x13721,x13724,x13725,x13726,x13727,x13728,x13729),f587(x13723,x13722,x13724,x13725,x13726,x13727,x13728,x13729)) % 183.90/184.46 [1373]~E(x13731,x13732)+E(f587(x13733,x13734,x13731,x13735,x13736,x13737,x13738,x13739),f587(x13733,x13734,x13732,x13735,x13736,x13737,x13738,x13739)) % 183.90/184.46 [1374]~E(x13741,x13742)+E(f587(x13743,x13744,x13745,x13741,x13746,x13747,x13748,x13749),f587(x13743,x13744,x13745,x13742,x13746,x13747,x13748,x13749)) % 183.90/184.46 [1375]~E(x13751,x13752)+E(f587(x13753,x13754,x13755,x13756,x13751,x13757,x13758,x13759),f587(x13753,x13754,x13755,x13756,x13752,x13757,x13758,x13759)) % 183.90/184.46 [1376]~E(x13761,x13762)+E(f587(x13763,x13764,x13765,x13766,x13767,x13761,x13768,x13769),f587(x13763,x13764,x13765,x13766,x13767,x13762,x13768,x13769)) % 183.90/184.46 [1377]~E(x13771,x13772)+E(f587(x13773,x13774,x13775,x13776,x13777,x13778,x13771,x13779),f587(x13773,x13774,x13775,x13776,x13777,x13778,x13772,x13779)) % 183.90/184.46 [1378]~E(x13781,x13782)+E(f587(x13783,x13784,x13785,x13786,x13787,x13788,x13789,x13781),f587(x13783,x13784,x13785,x13786,x13787,x13788,x13789,x13782)) % 183.90/184.46 [1379]~E(x13791,x13792)+E(f276(x13791,x13793,x13794,x13795,x13796),f276(x13792,x13793,x13794,x13795,x13796)) % 183.90/184.46 [1380]~E(x13801,x13802)+E(f276(x13803,x13801,x13804,x13805,x13806),f276(x13803,x13802,x13804,x13805,x13806)) % 183.90/184.46 [1381]~E(x13811,x13812)+E(f276(x13813,x13814,x13811,x13815,x13816),f276(x13813,x13814,x13812,x13815,x13816)) % 183.90/184.46 [1382]~E(x13821,x13822)+E(f276(x13823,x13824,x13825,x13821,x13826),f276(x13823,x13824,x13825,x13822,x13826)) % 183.90/184.46 [1383]~E(x13831,x13832)+E(f276(x13833,x13834,x13835,x13836,x13831),f276(x13833,x13834,x13835,x13836,x13832)) % 183.90/184.46 [1384]~E(x13841,x13842)+E(f780(x13841,x13843,x13844,x13845),f780(x13842,x13843,x13844,x13845)) % 183.90/184.46 [1385]~E(x13851,x13852)+E(f780(x13853,x13851,x13854,x13855),f780(x13853,x13852,x13854,x13855)) % 183.90/184.46 [1386]~E(x13861,x13862)+E(f780(x13863,x13864,x13861,x13865),f780(x13863,x13864,x13862,x13865)) % 183.90/184.46 [1387]~E(x13871,x13872)+E(f780(x13873,x13874,x13875,x13871),f780(x13873,x13874,x13875,x13872)) % 183.90/184.46 [1388]~E(x13881,x13882)+E(f468(x13881,x13883,x13884),f468(x13882,x13883,x13884)) % 183.90/184.46 [1389]~E(x13891,x13892)+E(f468(x13893,x13891,x13894),f468(x13893,x13892,x13894)) % 183.90/184.46 [1390]~E(x13901,x13902)+E(f468(x13903,x13904,x13901),f468(x13903,x13904,x13902)) % 183.90/184.46 [1391]~E(x13911,x13912)+E(f835(x13911,x13913,x13914,x13915,x13916),f835(x13912,x13913,x13914,x13915,x13916)) % 183.90/184.46 [1392]~E(x13921,x13922)+E(f835(x13923,x13921,x13924,x13925,x13926),f835(x13923,x13922,x13924,x13925,x13926)) % 183.90/184.46 [1393]~E(x13931,x13932)+E(f835(x13933,x13934,x13931,x13935,x13936),f835(x13933,x13934,x13932,x13935,x13936)) % 183.90/184.46 [1394]~E(x13941,x13942)+E(f835(x13943,x13944,x13945,x13941,x13946),f835(x13943,x13944,x13945,x13942,x13946)) % 183.90/184.46 [1395]~E(x13951,x13952)+E(f835(x13953,x13954,x13955,x13956,x13951),f835(x13953,x13954,x13955,x13956,x13952)) % 183.90/184.46 [1396]~E(x13961,x13962)+E(f230(x13961,x13963),f230(x13962,x13963)) % 183.90/184.46 [1397]~E(x13971,x13972)+E(f230(x13973,x13971),f230(x13973,x13972)) % 183.90/184.46 [1398]~E(x13981,x13982)+E(f856(x13981,x13983,x13984,x13985,x13986,x13987),f856(x13982,x13983,x13984,x13985,x13986,x13987)) % 183.90/184.46 [1399]~E(x13991,x13992)+E(f856(x13993,x13991,x13994,x13995,x13996,x13997),f856(x13993,x13992,x13994,x13995,x13996,x13997)) % 183.90/184.46 [1400]~E(x14001,x14002)+E(f856(x14003,x14004,x14001,x14005,x14006,x14007),f856(x14003,x14004,x14002,x14005,x14006,x14007)) % 183.90/184.46 [1401]~E(x14011,x14012)+E(f856(x14013,x14014,x14015,x14011,x14016,x14017),f856(x14013,x14014,x14015,x14012,x14016,x14017)) % 183.90/184.46 [1402]~E(x14021,x14022)+E(f856(x14023,x14024,x14025,x14026,x14021,x14027),f856(x14023,x14024,x14025,x14026,x14022,x14027)) % 183.90/184.46 [1403]~E(x14031,x14032)+E(f856(x14033,x14034,x14035,x14036,x14037,x14031),f856(x14033,x14034,x14035,x14036,x14037,x14032)) % 183.90/184.46 [1404]~E(x14041,x14042)+E(f453(x14041,x14043),f453(x14042,x14043)) % 183.90/184.46 [1405]~E(x14051,x14052)+E(f453(x14053,x14051),f453(x14053,x14052)) % 183.90/184.46 [1406]~E(x14061,x14062)+E(f686(x14061,x14063),f686(x14062,x14063)) % 183.90/184.46 [1407]~E(x14071,x14072)+E(f686(x14073,x14071),f686(x14073,x14072)) % 183.90/184.46 [1408]~E(x14081,x14082)+E(f163(x14081,x14083),f163(x14082,x14083)) % 183.90/184.46 [1409]~E(x14091,x14092)+E(f163(x14093,x14091),f163(x14093,x14092)) % 183.90/184.46 [1410]~E(x14101,x14102)+E(f357(x14101,x14103,x14104,x14105),f357(x14102,x14103,x14104,x14105)) % 183.90/184.46 [1411]~E(x14111,x14112)+E(f357(x14113,x14111,x14114,x14115),f357(x14113,x14112,x14114,x14115)) % 183.90/184.46 [1412]~E(x14121,x14122)+E(f357(x14123,x14124,x14121,x14125),f357(x14123,x14124,x14122,x14125)) % 183.90/184.46 [1413]~E(x14131,x14132)+E(f357(x14133,x14134,x14135,x14131),f357(x14133,x14134,x14135,x14132)) % 183.90/184.46 [1414]~E(x14141,x14142)+E(f528(x14141,x14143,x14144),f528(x14142,x14143,x14144)) % 183.90/184.46 [1415]~E(x14151,x14152)+E(f528(x14153,x14151,x14154),f528(x14153,x14152,x14154)) % 183.90/184.46 [1416]~E(x14161,x14162)+E(f528(x14163,x14164,x14161),f528(x14163,x14164,x14162)) % 183.90/184.46 [1417]~E(x14171,x14172)+E(f241(x14171,x14173,x14174),f241(x14172,x14173,x14174)) % 183.90/184.46 [1418]~E(x14181,x14182)+E(f241(x14183,x14181,x14184),f241(x14183,x14182,x14184)) % 183.90/184.46 [1419]~E(x14191,x14192)+E(f241(x14193,x14194,x14191),f241(x14193,x14194,x14192)) % 183.90/184.46 [1420]~E(x14201,x14202)+E(f443(x14201,x14203,x14204,x14205,x14206,x14207,x14208,x14209,x142010),f443(x14202,x14203,x14204,x14205,x14206,x14207,x14208,x14209,x142010)) % 183.90/184.46 [1421]~E(x14211,x14212)+E(f443(x14213,x14211,x14214,x14215,x14216,x14217,x14218,x14219,x142110),f443(x14213,x14212,x14214,x14215,x14216,x14217,x14218,x14219,x142110)) % 183.90/184.46 [1422]~E(x14221,x14222)+E(f443(x14223,x14224,x14221,x14225,x14226,x14227,x14228,x14229,x142210),f443(x14223,x14224,x14222,x14225,x14226,x14227,x14228,x14229,x142210)) % 183.90/184.46 [1423]~E(x14231,x14232)+E(f443(x14233,x14234,x14235,x14231,x14236,x14237,x14238,x14239,x142310),f443(x14233,x14234,x14235,x14232,x14236,x14237,x14238,x14239,x142310)) % 183.90/184.46 [1424]~E(x14241,x14242)+E(f443(x14243,x14244,x14245,x14246,x14241,x14247,x14248,x14249,x142410),f443(x14243,x14244,x14245,x14246,x14242,x14247,x14248,x14249,x142410)) % 183.90/184.46 [1425]~E(x14251,x14252)+E(f443(x14253,x14254,x14255,x14256,x14257,x14251,x14258,x14259,x142510),f443(x14253,x14254,x14255,x14256,x14257,x14252,x14258,x14259,x142510)) % 183.90/184.46 [1426]~E(x14261,x14262)+E(f443(x14263,x14264,x14265,x14266,x14267,x14268,x14261,x14269,x142610),f443(x14263,x14264,x14265,x14266,x14267,x14268,x14262,x14269,x142610)) % 183.90/184.46 [1427]~E(x14271,x14272)+E(f443(x14273,x14274,x14275,x14276,x14277,x14278,x14279,x14271,x142710),f443(x14273,x14274,x14275,x14276,x14277,x14278,x14279,x14272,x142710)) % 183.90/184.46 [1428]~E(x14281,x14282)+E(f443(x14283,x14284,x14285,x14286,x14287,x14288,x14289,x142810,x14281),f443(x14283,x14284,x14285,x14286,x14287,x14288,x14289,x142810,x14282)) % 183.90/184.46 [1429]~E(x14291,x14292)+E(f531(x14291,x14293,x14294,x14295),f531(x14292,x14293,x14294,x14295)) % 183.90/184.46 [1430]~E(x14301,x14302)+E(f531(x14303,x14301,x14304,x14305),f531(x14303,x14302,x14304,x14305)) % 183.90/184.46 [1431]~E(x14311,x14312)+E(f531(x14313,x14314,x14311,x14315),f531(x14313,x14314,x14312,x14315)) % 183.90/184.46 [1432]~E(x14321,x14322)+E(f531(x14323,x14324,x14325,x14321),f531(x14323,x14324,x14325,x14322)) % 183.90/184.46 [1433]~E(x14331,x14332)+E(f228(x14331,x14333),f228(x14332,x14333)) % 183.90/184.46 [1434]~E(x14341,x14342)+E(f228(x14343,x14341),f228(x14343,x14342)) % 183.90/184.46 [1435]~E(x14351,x14352)+E(f866(x14351,x14353,x14354,x14355),f866(x14352,x14353,x14354,x14355)) % 183.90/184.46 [1436]~E(x14361,x14362)+E(f866(x14363,x14361,x14364,x14365),f866(x14363,x14362,x14364,x14365)) % 183.90/184.46 [1437]~E(x14371,x14372)+E(f866(x14373,x14374,x14371,x14375),f866(x14373,x14374,x14372,x14375)) % 183.90/184.46 [1438]~E(x14381,x14382)+E(f866(x14383,x14384,x14385,x14381),f866(x14383,x14384,x14385,x14382)) % 183.90/184.46 [1439]~E(x14391,x14392)+E(f631(x14391,x14393,x14394),f631(x14392,x14393,x14394)) % 183.90/184.46 [1440]~E(x14401,x14402)+E(f631(x14403,x14401,x14404),f631(x14403,x14402,x14404)) % 183.90/184.46 [1441]~E(x14411,x14412)+E(f631(x14413,x14414,x14411),f631(x14413,x14414,x14412)) % 183.90/184.46 [1442]~E(x14421,x14422)+E(f188(x14421,x14423,x14424),f188(x14422,x14423,x14424)) % 183.90/184.46 [1443]~E(x14431,x14432)+E(f188(x14433,x14431,x14434),f188(x14433,x14432,x14434)) % 183.90/184.46 [1444]~E(x14441,x14442)+E(f188(x14443,x14444,x14441),f188(x14443,x14444,x14442)) % 183.90/184.46 [1445]~E(x14451,x14452)+E(f751(x14451,x14453),f751(x14452,x14453)) % 183.90/184.46 [1446]~E(x14461,x14462)+E(f751(x14463,x14461),f751(x14463,x14462)) % 183.90/184.46 [1447]~E(x14471,x14472)+E(f285(x14471,x14473,x14474,x14475),f285(x14472,x14473,x14474,x14475)) % 183.90/184.46 [1448]~E(x14481,x14482)+E(f285(x14483,x14481,x14484,x14485),f285(x14483,x14482,x14484,x14485)) % 183.90/184.46 [1449]~E(x14491,x14492)+E(f285(x14493,x14494,x14491,x14495),f285(x14493,x14494,x14492,x14495)) % 183.90/184.46 [1450]~E(x14501,x14502)+E(f285(x14503,x14504,x14505,x14501),f285(x14503,x14504,x14505,x14502)) % 183.90/184.46 [1451]~E(x14511,x14512)+E(f297(x14511,x14513,x14514,x14515),f297(x14512,x14513,x14514,x14515)) % 183.90/184.46 [1452]~E(x14521,x14522)+E(f297(x14523,x14521,x14524,x14525),f297(x14523,x14522,x14524,x14525)) % 183.90/184.46 [1453]~E(x14531,x14532)+E(f297(x14533,x14534,x14531,x14535),f297(x14533,x14534,x14532,x14535)) % 183.90/184.46 [1454]~E(x14541,x14542)+E(f297(x14543,x14544,x14545,x14541),f297(x14543,x14544,x14545,x14542)) % 183.90/184.46 [1455]~E(x14551,x14552)+E(f788(x14551,x14553,x14554,x14555,x14556,x14557,x14558),f788(x14552,x14553,x14554,x14555,x14556,x14557,x14558)) % 183.90/184.46 [1456]~E(x14561,x14562)+E(f788(x14563,x14561,x14564,x14565,x14566,x14567,x14568),f788(x14563,x14562,x14564,x14565,x14566,x14567,x14568)) % 183.90/184.46 [1457]~E(x14571,x14572)+E(f788(x14573,x14574,x14571,x14575,x14576,x14577,x14578),f788(x14573,x14574,x14572,x14575,x14576,x14577,x14578)) % 183.90/184.46 [1458]~E(x14581,x14582)+E(f788(x14583,x14584,x14585,x14581,x14586,x14587,x14588),f788(x14583,x14584,x14585,x14582,x14586,x14587,x14588)) % 183.90/184.46 [1459]~E(x14591,x14592)+E(f788(x14593,x14594,x14595,x14596,x14591,x14597,x14598),f788(x14593,x14594,x14595,x14596,x14592,x14597,x14598)) % 183.90/184.46 [1460]~E(x14601,x14602)+E(f788(x14603,x14604,x14605,x14606,x14607,x14601,x14608),f788(x14603,x14604,x14605,x14606,x14607,x14602,x14608)) % 183.90/184.46 [1461]~E(x14611,x14612)+E(f788(x14613,x14614,x14615,x14616,x14617,x14618,x14611),f788(x14613,x14614,x14615,x14616,x14617,x14618,x14612)) % 183.90/184.46 [1462]~E(x14621,x14622)+E(f381(x14621,x14623,x14624,x14625,x14626,x14627),f381(x14622,x14623,x14624,x14625,x14626,x14627)) % 183.90/184.46 [1463]~E(x14631,x14632)+E(f381(x14633,x14631,x14634,x14635,x14636,x14637),f381(x14633,x14632,x14634,x14635,x14636,x14637)) % 183.90/184.46 [1464]~E(x14641,x14642)+E(f381(x14643,x14644,x14641,x14645,x14646,x14647),f381(x14643,x14644,x14642,x14645,x14646,x14647)) % 183.90/184.46 [1465]~E(x14651,x14652)+E(f381(x14653,x14654,x14655,x14651,x14656,x14657),f381(x14653,x14654,x14655,x14652,x14656,x14657)) % 183.90/184.46 [1466]~E(x14661,x14662)+E(f381(x14663,x14664,x14665,x14666,x14661,x14667),f381(x14663,x14664,x14665,x14666,x14662,x14667)) % 183.90/184.46 [1467]~E(x14671,x14672)+E(f381(x14673,x14674,x14675,x14676,x14677,x14671),f381(x14673,x14674,x14675,x14676,x14677,x14672)) % 183.90/184.46 [1468]~E(x14681,x14682)+E(f679(x14681,x14683,x14684),f679(x14682,x14683,x14684)) % 183.90/184.46 [1469]~E(x14691,x14692)+E(f679(x14693,x14691,x14694),f679(x14693,x14692,x14694)) % 183.90/184.46 [1470]~E(x14701,x14702)+E(f679(x14703,x14704,x14701),f679(x14703,x14704,x14702)) % 183.90/184.46 [1471]~E(x14711,x14712)+E(f735(x14711,x14713,x14714,x14715),f735(x14712,x14713,x14714,x14715)) % 183.90/184.46 [1472]~E(x14721,x14722)+E(f735(x14723,x14721,x14724,x14725),f735(x14723,x14722,x14724,x14725)) % 183.90/184.46 [1473]~E(x14731,x14732)+E(f735(x14733,x14734,x14731,x14735),f735(x14733,x14734,x14732,x14735)) % 183.90/184.46 [1474]~E(x14741,x14742)+E(f735(x14743,x14744,x14745,x14741),f735(x14743,x14744,x14745,x14742)) % 183.90/184.46 [1475]~E(x14751,x14752)+E(f592(x14751,x14753,x14754),f592(x14752,x14753,x14754)) % 183.90/184.46 [1476]~E(x14761,x14762)+E(f592(x14763,x14761,x14764),f592(x14763,x14762,x14764)) % 183.90/184.46 [1477]~E(x14771,x14772)+E(f592(x14773,x14774,x14771),f592(x14773,x14774,x14772)) % 183.90/184.46 [1478]~E(x14781,x14782)+E(f789(x14781,x14783,x14784,x14785,x14786,x14787,x14788),f789(x14782,x14783,x14784,x14785,x14786,x14787,x14788)) % 183.90/184.46 [1479]~E(x14791,x14792)+E(f789(x14793,x14791,x14794,x14795,x14796,x14797,x14798),f789(x14793,x14792,x14794,x14795,x14796,x14797,x14798)) % 183.90/184.46 [1480]~E(x14801,x14802)+E(f789(x14803,x14804,x14801,x14805,x14806,x14807,x14808),f789(x14803,x14804,x14802,x14805,x14806,x14807,x14808)) % 183.90/184.46 [1481]~E(x14811,x14812)+E(f789(x14813,x14814,x14815,x14811,x14816,x14817,x14818),f789(x14813,x14814,x14815,x14812,x14816,x14817,x14818)) % 183.90/184.46 [1482]~E(x14821,x14822)+E(f789(x14823,x14824,x14825,x14826,x14821,x14827,x14828),f789(x14823,x14824,x14825,x14826,x14822,x14827,x14828)) % 183.90/184.46 [1483]~E(x14831,x14832)+E(f789(x14833,x14834,x14835,x14836,x14837,x14831,x14838),f789(x14833,x14834,x14835,x14836,x14837,x14832,x14838)) % 183.90/184.46 [1484]~E(x14841,x14842)+E(f789(x14843,x14844,x14845,x14846,x14847,x14848,x14841),f789(x14843,x14844,x14845,x14846,x14847,x14848,x14842)) % 183.90/184.46 [1485]~E(x14851,x14852)+E(f430(x14851,x14853,x14854,x14855),f430(x14852,x14853,x14854,x14855)) % 183.90/184.46 [1486]~E(x14861,x14862)+E(f430(x14863,x14861,x14864,x14865),f430(x14863,x14862,x14864,x14865)) % 183.90/184.46 [1487]~E(x14871,x14872)+E(f430(x14873,x14874,x14871,x14875),f430(x14873,x14874,x14872,x14875)) % 183.90/184.46 [1488]~E(x14881,x14882)+E(f430(x14883,x14884,x14885,x14881),f430(x14883,x14884,x14885,x14882)) % 183.90/184.46 [1489]~E(x14891,x14892)+E(f771(x14891,x14893,x14894,x14895,x14896),f771(x14892,x14893,x14894,x14895,x14896)) % 183.90/184.46 [1490]~E(x14901,x14902)+E(f771(x14903,x14901,x14904,x14905,x14906),f771(x14903,x14902,x14904,x14905,x14906)) % 183.90/184.46 [1491]~E(x14911,x14912)+E(f771(x14913,x14914,x14911,x14915,x14916),f771(x14913,x14914,x14912,x14915,x14916)) % 183.90/184.46 [1492]~E(x14921,x14922)+E(f771(x14923,x14924,x14925,x14921,x14926),f771(x14923,x14924,x14925,x14922,x14926)) % 183.90/184.46 [1493]~E(x14931,x14932)+E(f771(x14933,x14934,x14935,x14936,x14931),f771(x14933,x14934,x14935,x14936,x14932)) % 183.90/184.46 [1494]~E(x14941,x14942)+E(f832(x14941,x14943,x14944,x14945),f832(x14942,x14943,x14944,x14945)) % 183.90/184.46 [1495]~E(x14951,x14952)+E(f832(x14953,x14951,x14954,x14955),f832(x14953,x14952,x14954,x14955)) % 183.90/184.46 [1496]~E(x14961,x14962)+E(f832(x14963,x14964,x14961,x14965),f832(x14963,x14964,x14962,x14965)) % 183.90/184.46 [1497]~E(x14971,x14972)+E(f832(x14973,x14974,x14975,x14971),f832(x14973,x14974,x14975,x14972)) % 183.90/184.46 [1498]~E(x14981,x14982)+E(f214(x14981,x14983),f214(x14982,x14983)) % 183.90/184.46 [1499]~E(x14991,x14992)+E(f214(x14993,x14991),f214(x14993,x14992)) % 183.90/184.46 [1500]~E(x15001,x15002)+E(f281(x15001,x15003),f281(x15002,x15003)) % 183.90/184.46 [1501]~E(x15011,x15012)+E(f281(x15013,x15011),f281(x15013,x15012)) % 183.90/184.46 [1502]~E(x15021,x15022)+E(f769(x15021,x15023,x15024,x15025),f769(x15022,x15023,x15024,x15025)) % 183.90/184.46 [1503]~E(x15031,x15032)+E(f769(x15033,x15031,x15034,x15035),f769(x15033,x15032,x15034,x15035)) % 183.90/184.46 [1504]~E(x15041,x15042)+E(f769(x15043,x15044,x15041,x15045),f769(x15043,x15044,x15042,x15045)) % 183.90/184.46 [1505]~E(x15051,x15052)+E(f769(x15053,x15054,x15055,x15051),f769(x15053,x15054,x15055,x15052)) % 183.90/184.46 [1506]~E(x15061,x15062)+E(f447(x15061,x15063,x15064,x15065),f447(x15062,x15063,x15064,x15065)) % 183.90/184.46 [1507]~E(x15071,x15072)+E(f447(x15073,x15071,x15074,x15075),f447(x15073,x15072,x15074,x15075)) % 183.90/184.46 [1508]~E(x15081,x15082)+E(f447(x15083,x15084,x15081,x15085),f447(x15083,x15084,x15082,x15085)) % 183.90/184.46 [1509]~E(x15091,x15092)+E(f447(x15093,x15094,x15095,x15091),f447(x15093,x15094,x15095,x15092)) % 183.90/184.46 [1510]~E(x15101,x15102)+E(f831(x15101,x15103,x15104),f831(x15102,x15103,x15104)) % 183.90/184.46 [1511]~E(x15111,x15112)+E(f831(x15113,x15111,x15114),f831(x15113,x15112,x15114)) % 183.90/184.46 [1512]~E(x15121,x15122)+E(f831(x15123,x15124,x15121),f831(x15123,x15124,x15122)) % 183.90/184.46 [1513]~E(x15131,x15132)+E(f475(x15131,x15133,x15134),f475(x15132,x15133,x15134)) % 183.90/184.46 [1514]~E(x15141,x15142)+E(f475(x15143,x15141,x15144),f475(x15143,x15142,x15144)) % 183.90/184.46 [1515]~E(x15151,x15152)+E(f475(x15153,x15154,x15151),f475(x15153,x15154,x15152)) % 183.90/184.46 [1516]~E(x15161,x15162)+E(f620(x15161,x15163),f620(x15162,x15163)) % 183.90/184.46 [1517]~E(x15171,x15172)+E(f620(x15173,x15171),f620(x15173,x15172)) % 183.90/184.46 [1518]~E(x15181,x15182)+E(f734(x15181,x15183,x15184,x15185),f734(x15182,x15183,x15184,x15185)) % 183.90/184.46 [1519]~E(x15191,x15192)+E(f734(x15193,x15191,x15194,x15195),f734(x15193,x15192,x15194,x15195)) % 183.90/184.46 [1520]~E(x15201,x15202)+E(f734(x15203,x15204,x15201,x15205),f734(x15203,x15204,x15202,x15205)) % 183.90/184.46 [1521]~E(x15211,x15212)+E(f734(x15213,x15214,x15215,x15211),f734(x15213,x15214,x15215,x15212)) % 183.90/184.46 [1522]~E(x15221,x15222)+E(f633(x15221,x15223,x15224),f633(x15222,x15223,x15224)) % 183.90/184.46 [1523]~E(x15231,x15232)+E(f633(x15233,x15231,x15234),f633(x15233,x15232,x15234)) % 183.90/184.46 [1524]~E(x15241,x15242)+E(f633(x15243,x15244,x15241),f633(x15243,x15244,x15242)) % 183.90/184.46 [1525]~E(x15251,x15252)+E(f59(x15251,x15253,x15254,x15255),f59(x15252,x15253,x15254,x15255)) % 183.90/184.46 [1526]~E(x15261,x15262)+E(f59(x15263,x15261,x15264,x15265),f59(x15263,x15262,x15264,x15265)) % 183.90/184.46 [1527]~E(x15271,x15272)+E(f59(x15273,x15274,x15271,x15275),f59(x15273,x15274,x15272,x15275)) % 183.90/184.46 [1528]~E(x15281,x15282)+E(f59(x15283,x15284,x15285,x15281),f59(x15283,x15284,x15285,x15282)) % 183.90/184.46 [1529]~E(x15291,x15292)+E(f500(x15291,x15293,x15294),f500(x15292,x15293,x15294)) % 183.90/184.46 [1530]~E(x15301,x15302)+E(f500(x15303,x15301,x15304),f500(x15303,x15302,x15304)) % 183.90/184.46 [1531]~E(x15311,x15312)+E(f500(x15313,x15314,x15311),f500(x15313,x15314,x15312)) % 183.90/184.46 [1532]~E(x15321,x15322)+E(f510(x15321,x15323,x15324),f510(x15322,x15323,x15324)) % 183.90/184.46 [1533]~E(x15331,x15332)+E(f510(x15333,x15331,x15334),f510(x15333,x15332,x15334)) % 183.90/184.46 [1534]~E(x15341,x15342)+E(f510(x15343,x15344,x15341),f510(x15343,x15344,x15342)) % 183.90/184.46 [1535]~E(x15351,x15352)+E(f836(x15351,x15353,x15354,x15355,x15356),f836(x15352,x15353,x15354,x15355,x15356)) % 183.90/184.46 [1536]~E(x15361,x15362)+E(f836(x15363,x15361,x15364,x15365,x15366),f836(x15363,x15362,x15364,x15365,x15366)) % 183.90/184.46 [1537]~E(x15371,x15372)+E(f836(x15373,x15374,x15371,x15375,x15376),f836(x15373,x15374,x15372,x15375,x15376)) % 183.90/184.46 [1538]~E(x15381,x15382)+E(f836(x15383,x15384,x15385,x15381,x15386),f836(x15383,x15384,x15385,x15382,x15386)) % 183.90/184.46 [1539]~E(x15391,x15392)+E(f836(x15393,x15394,x15395,x15396,x15391),f836(x15393,x15394,x15395,x15396,x15392)) % 183.90/184.46 [1540]~E(x15401,x15402)+E(f648(x15401,x15403,x15404,x15405,x15406),f648(x15402,x15403,x15404,x15405,x15406)) % 183.90/184.46 [1541]~E(x15411,x15412)+E(f648(x15413,x15411,x15414,x15415,x15416),f648(x15413,x15412,x15414,x15415,x15416)) % 183.90/184.46 [1542]~E(x15421,x15422)+E(f648(x15423,x15424,x15421,x15425,x15426),f648(x15423,x15424,x15422,x15425,x15426)) % 183.90/184.46 [1543]~E(x15431,x15432)+E(f648(x15433,x15434,x15435,x15431,x15436),f648(x15433,x15434,x15435,x15432,x15436)) % 183.90/184.46 [1544]~E(x15441,x15442)+E(f648(x15443,x15444,x15445,x15446,x15441),f648(x15443,x15444,x15445,x15446,x15442)) % 183.90/184.46 [1545]~E(x15451,x15452)+E(f797(x15451,x15453,x15454),f797(x15452,x15453,x15454)) % 183.90/184.46 [1546]~E(x15461,x15462)+E(f797(x15463,x15461,x15464),f797(x15463,x15462,x15464)) % 183.90/184.46 [1547]~E(x15471,x15472)+E(f797(x15473,x15474,x15471),f797(x15473,x15474,x15472)) % 183.90/184.46 [1548]~E(x15481,x15482)+E(f548(x15481,x15483,x15484),f548(x15482,x15483,x15484)) % 183.90/184.46 [1549]~E(x15491,x15492)+E(f548(x15493,x15491,x15494),f548(x15493,x15492,x15494)) % 183.90/184.46 [1550]~E(x15501,x15502)+E(f548(x15503,x15504,x15501),f548(x15503,x15504,x15502)) % 183.90/184.46 [1551]~E(x15511,x15512)+E(f409(x15511,x15513,x15514,x15515),f409(x15512,x15513,x15514,x15515)) % 183.90/184.46 [1552]~E(x15521,x15522)+E(f409(x15523,x15521,x15524,x15525),f409(x15523,x15522,x15524,x15525)) % 183.90/184.46 [1553]~E(x15531,x15532)+E(f409(x15533,x15534,x15531,x15535),f409(x15533,x15534,x15532,x15535)) % 183.90/184.46 [1554]~E(x15541,x15542)+E(f409(x15543,x15544,x15545,x15541),f409(x15543,x15544,x15545,x15542)) % 183.90/184.46 [1555]~E(x15551,x15552)+E(f803(x15551,x15553,x15554,x15555),f803(x15552,x15553,x15554,x15555)) % 183.90/184.46 [1556]~E(x15561,x15562)+E(f803(x15563,x15561,x15564,x15565),f803(x15563,x15562,x15564,x15565)) % 183.90/184.46 [1557]~E(x15571,x15572)+E(f803(x15573,x15574,x15571,x15575),f803(x15573,x15574,x15572,x15575)) % 183.90/184.46 [1558]~E(x15581,x15582)+E(f803(x15583,x15584,x15585,x15581),f803(x15583,x15584,x15585,x15582)) % 183.90/184.46 [1559]~E(x15591,x15592)+E(f712(x15591,x15593,x15594,x15595,x15596),f712(x15592,x15593,x15594,x15595,x15596)) % 183.90/184.46 [1560]~E(x15601,x15602)+E(f712(x15603,x15601,x15604,x15605,x15606),f712(x15603,x15602,x15604,x15605,x15606)) % 183.90/184.46 [1561]~E(x15611,x15612)+E(f712(x15613,x15614,x15611,x15615,x15616),f712(x15613,x15614,x15612,x15615,x15616)) % 183.90/184.46 [1562]~E(x15621,x15622)+E(f712(x15623,x15624,x15625,x15621,x15626),f712(x15623,x15624,x15625,x15622,x15626)) % 183.90/184.46 [1563]~E(x15631,x15632)+E(f712(x15633,x15634,x15635,x15636,x15631),f712(x15633,x15634,x15635,x15636,x15632)) % 183.90/184.46 [1564]~E(x15641,x15642)+E(f576(x15641,x15643),f576(x15642,x15643)) % 183.90/184.46 [1565]~E(x15651,x15652)+E(f576(x15653,x15651),f576(x15653,x15652)) % 183.90/184.46 [1566]~E(x15661,x15662)+E(f581(x15661,x15663,x15664,x15665,x15666,x15667),f581(x15662,x15663,x15664,x15665,x15666,x15667)) % 183.90/184.46 [1567]~E(x15671,x15672)+E(f581(x15673,x15671,x15674,x15675,x15676,x15677),f581(x15673,x15672,x15674,x15675,x15676,x15677)) % 183.90/184.46 [1568]~E(x15681,x15682)+E(f581(x15683,x15684,x15681,x15685,x15686,x15687),f581(x15683,x15684,x15682,x15685,x15686,x15687)) % 183.90/184.46 [1569]~E(x15691,x15692)+E(f581(x15693,x15694,x15695,x15691,x15696,x15697),f581(x15693,x15694,x15695,x15692,x15696,x15697)) % 183.90/184.46 [1570]~E(x15701,x15702)+E(f581(x15703,x15704,x15705,x15706,x15701,x15707),f581(x15703,x15704,x15705,x15706,x15702,x15707)) % 183.90/184.46 [1571]~E(x15711,x15712)+E(f581(x15713,x15714,x15715,x15716,x15717,x15711),f581(x15713,x15714,x15715,x15716,x15717,x15712)) % 183.90/184.46 [1572]~E(x15721,x15722)+E(f746(x15721,x15723,x15724),f746(x15722,x15723,x15724)) % 183.90/184.46 [1573]~E(x15731,x15732)+E(f746(x15733,x15731,x15734),f746(x15733,x15732,x15734)) % 183.90/184.46 [1574]~E(x15741,x15742)+E(f746(x15743,x15744,x15741),f746(x15743,x15744,x15742)) % 183.90/184.46 [1575]~E(x15751,x15752)+E(f688(x15751,x15753,x15754,x15755),f688(x15752,x15753,x15754,x15755)) % 183.90/184.46 [1576]~E(x15761,x15762)+E(f688(x15763,x15761,x15764,x15765),f688(x15763,x15762,x15764,x15765)) % 183.90/184.46 [1577]~E(x15771,x15772)+E(f688(x15773,x15774,x15771,x15775),f688(x15773,x15774,x15772,x15775)) % 183.90/184.46 [1578]~E(x15781,x15782)+E(f688(x15783,x15784,x15785,x15781),f688(x15783,x15784,x15785,x15782)) % 183.90/184.46 [1579]~E(x15791,x15792)+E(f845(x15791,x15793,x15794,x15795,x15796,x15797,x15798),f845(x15792,x15793,x15794,x15795,x15796,x15797,x15798)) % 183.90/184.46 [1580]~E(x15801,x15802)+E(f845(x15803,x15801,x15804,x15805,x15806,x15807,x15808),f845(x15803,x15802,x15804,x15805,x15806,x15807,x15808)) % 183.90/184.46 [1581]~E(x15811,x15812)+E(f845(x15813,x15814,x15811,x15815,x15816,x15817,x15818),f845(x15813,x15814,x15812,x15815,x15816,x15817,x15818)) % 183.90/184.46 [1582]~E(x15821,x15822)+E(f845(x15823,x15824,x15825,x15821,x15826,x15827,x15828),f845(x15823,x15824,x15825,x15822,x15826,x15827,x15828)) % 183.90/184.46 [1583]~E(x15831,x15832)+E(f845(x15833,x15834,x15835,x15836,x15831,x15837,x15838),f845(x15833,x15834,x15835,x15836,x15832,x15837,x15838)) % 183.90/184.46 [1584]~E(x15841,x15842)+E(f845(x15843,x15844,x15845,x15846,x15847,x15841,x15848),f845(x15843,x15844,x15845,x15846,x15847,x15842,x15848)) % 183.90/184.46 [1585]~E(x15851,x15852)+E(f845(x15853,x15854,x15855,x15856,x15857,x15858,x15851),f845(x15853,x15854,x15855,x15856,x15857,x15858,x15852)) % 183.90/184.46 [1586]~E(x15861,x15862)+E(f377(x15861,x15863),f377(x15862,x15863)) % 183.90/184.46 [1587]~E(x15871,x15872)+E(f377(x15873,x15871),f377(x15873,x15872)) % 183.90/184.46 [1588]~E(x15881,x15882)+E(f536(x15881,x15883),f536(x15882,x15883)) % 183.90/184.46 [1589]~E(x15891,x15892)+E(f536(x15893,x15891),f536(x15893,x15892)) % 183.90/184.46 [1590]~E(x15901,x15902)+E(f706(x15901,x15903,x15904),f706(x15902,x15903,x15904)) % 183.90/184.46 [1591]~E(x15911,x15912)+E(f706(x15913,x15911,x15914),f706(x15913,x15912,x15914)) % 183.90/184.46 [1592]~E(x15921,x15922)+E(f706(x15923,x15924,x15921),f706(x15923,x15924,x15922)) % 183.90/184.46 [1593]~E(x15931,x15932)+E(f754(x15931,x15933,x15934,x15935,x15936),f754(x15932,x15933,x15934,x15935,x15936)) % 183.90/184.46 [1594]~E(x15941,x15942)+E(f754(x15943,x15941,x15944,x15945,x15946),f754(x15943,x15942,x15944,x15945,x15946)) % 183.90/184.46 [1595]~E(x15951,x15952)+E(f754(x15953,x15954,x15951,x15955,x15956),f754(x15953,x15954,x15952,x15955,x15956)) % 183.90/184.46 [1596]~E(x15961,x15962)+E(f754(x15963,x15964,x15965,x15961,x15966),f754(x15963,x15964,x15965,x15962,x15966)) % 183.90/184.46 [1597]~E(x15971,x15972)+E(f754(x15973,x15974,x15975,x15976,x15971),f754(x15973,x15974,x15975,x15976,x15972)) % 183.90/184.46 [1598]~E(x15981,x15982)+E(f695(x15981,x15983,x15984,x15985),f695(x15982,x15983,x15984,x15985)) % 183.90/184.46 [1599]~E(x15991,x15992)+E(f695(x15993,x15991,x15994,x15995),f695(x15993,x15992,x15994,x15995)) % 183.90/184.46 [1600]~E(x16001,x16002)+E(f695(x16003,x16004,x16001,x16005),f695(x16003,x16004,x16002,x16005)) % 183.90/184.46 [1601]~E(x16011,x16012)+E(f695(x16013,x16014,x16015,x16011),f695(x16013,x16014,x16015,x16012)) % 183.90/184.46 [1602]~E(x16021,x16022)+E(f436(x16021,x16023,x16024,x16025),f436(x16022,x16023,x16024,x16025)) % 183.90/184.46 [1603]~E(x16031,x16032)+E(f436(x16033,x16031,x16034,x16035),f436(x16033,x16032,x16034,x16035)) % 183.90/184.46 [1604]~E(x16041,x16042)+E(f436(x16043,x16044,x16041,x16045),f436(x16043,x16044,x16042,x16045)) % 183.90/184.46 [1605]~E(x16051,x16052)+E(f436(x16053,x16054,x16055,x16051),f436(x16053,x16054,x16055,x16052)) % 183.90/184.46 [1606]~E(x16061,x16062)+E(f120(x16061,x16063,x16064),f120(x16062,x16063,x16064)) % 183.90/184.46 [1607]~E(x16071,x16072)+E(f120(x16073,x16071,x16074),f120(x16073,x16072,x16074)) % 183.90/184.46 [1608]~E(x16081,x16082)+E(f120(x16083,x16084,x16081),f120(x16083,x16084,x16082)) % 183.90/184.46 [1609]~E(x16091,x16092)+E(f472(x16091,x16093,x16094),f472(x16092,x16093,x16094)) % 183.90/184.46 [1610]~E(x16101,x16102)+E(f472(x16103,x16101,x16104),f472(x16103,x16102,x16104)) % 183.90/184.46 [1611]~E(x16111,x16112)+E(f472(x16113,x16114,x16111),f472(x16113,x16114,x16112)) % 183.90/184.46 [1612]~E(x16121,x16122)+E(f723(x16121,x16123),f723(x16122,x16123)) % 183.90/184.46 [1613]~E(x16131,x16132)+E(f723(x16133,x16131),f723(x16133,x16132)) % 183.90/184.46 [1614]~E(x16141,x16142)+E(f403(x16141),f403(x16142)) % 183.90/184.46 [1615]~E(x16151,x16152)+E(f614(x16151,x16153,x16154),f614(x16152,x16153,x16154)) % 183.90/184.46 [1616]~E(x16161,x16162)+E(f614(x16163,x16161,x16164),f614(x16163,x16162,x16164)) % 183.90/184.46 [1617]~E(x16171,x16172)+E(f614(x16173,x16174,x16171),f614(x16173,x16174,x16172)) % 183.90/184.46 [1618]~E(x16181,x16182)+E(f406(x16181,x16183),f406(x16182,x16183)) % 183.90/184.46 [1619]~E(x16191,x16192)+E(f406(x16193,x16191),f406(x16193,x16192)) % 183.90/184.46 [1620]~E(x16201,x16202)+E(f440(x16201,x16203,x16204,x16205),f440(x16202,x16203,x16204,x16205)) % 183.90/184.46 [1621]~E(x16211,x16212)+E(f440(x16213,x16211,x16214,x16215),f440(x16213,x16212,x16214,x16215)) % 183.90/184.46 [1622]~E(x16221,x16222)+E(f440(x16223,x16224,x16221,x16225),f440(x16223,x16224,x16222,x16225)) % 183.90/184.46 [1623]~E(x16231,x16232)+E(f440(x16233,x16234,x16235,x16231),f440(x16233,x16234,x16235,x16232)) % 183.90/184.46 [1624]~E(x16241,x16242)+E(f705(x16241,x16243,x16244,x16245,x16246),f705(x16242,x16243,x16244,x16245,x16246)) % 183.90/184.46 [1625]~E(x16251,x16252)+E(f705(x16253,x16251,x16254,x16255,x16256),f705(x16253,x16252,x16254,x16255,x16256)) % 183.90/184.46 [1626]~E(x16261,x16262)+E(f705(x16263,x16264,x16261,x16265,x16266),f705(x16263,x16264,x16262,x16265,x16266)) % 183.90/184.46 [1627]~E(x16271,x16272)+E(f705(x16273,x16274,x16275,x16271,x16276),f705(x16273,x16274,x16275,x16272,x16276)) % 183.90/184.46 [1628]~E(x16281,x16282)+E(f705(x16283,x16284,x16285,x16286,x16281),f705(x16283,x16284,x16285,x16286,x16282)) % 183.90/184.46 [1629]~E(x16291,x16292)+E(f821(x16291,x16293),f821(x16292,x16293)) % 183.90/184.46 [1630]~E(x16301,x16302)+E(f821(x16303,x16301),f821(x16303,x16302)) % 183.90/184.46 [1631]~E(x16311,x16312)+E(f703(x16311,x16313,x16314,x16315),f703(x16312,x16313,x16314,x16315)) % 183.90/184.46 [1632]~E(x16321,x16322)+E(f703(x16323,x16321,x16324,x16325),f703(x16323,x16322,x16324,x16325)) % 183.90/184.46 [1633]~E(x16331,x16332)+E(f703(x16333,x16334,x16331,x16335),f703(x16333,x16334,x16332,x16335)) % 183.90/184.46 [1634]~E(x16341,x16342)+E(f703(x16343,x16344,x16345,x16341),f703(x16343,x16344,x16345,x16342)) % 183.90/184.46 [1635]~E(x16351,x16352)+E(f296(x16351,x16353,x16354),f296(x16352,x16353,x16354)) % 183.90/184.46 [1636]~E(x16361,x16362)+E(f296(x16363,x16361,x16364),f296(x16363,x16362,x16364)) % 183.90/184.46 [1637]~E(x16371,x16372)+E(f296(x16373,x16374,x16371),f296(x16373,x16374,x16372)) % 183.90/184.46 [1638]~E(x16381,x16382)+E(f123(x16381,x16383,x16384,x16385),f123(x16382,x16383,x16384,x16385)) % 183.90/184.46 [1639]~E(x16391,x16392)+E(f123(x16393,x16391,x16394,x16395),f123(x16393,x16392,x16394,x16395)) % 183.90/184.46 [1640]~E(x16401,x16402)+E(f123(x16403,x16404,x16401,x16405),f123(x16403,x16404,x16402,x16405)) % 183.90/184.46 [1641]~E(x16411,x16412)+E(f123(x16413,x16414,x16415,x16411),f123(x16413,x16414,x16415,x16412)) % 183.90/184.46 [1642]~E(x16421,x16422)+E(f675(x16421,x16423,x16424,x16425,x16426),f675(x16422,x16423,x16424,x16425,x16426)) % 183.90/184.46 [1643]~E(x16431,x16432)+E(f675(x16433,x16431,x16434,x16435,x16436),f675(x16433,x16432,x16434,x16435,x16436)) % 183.90/184.46 [1644]~E(x16441,x16442)+E(f675(x16443,x16444,x16441,x16445,x16446),f675(x16443,x16444,x16442,x16445,x16446)) % 183.90/184.46 [1645]~E(x16451,x16452)+E(f675(x16453,x16454,x16455,x16451,x16456),f675(x16453,x16454,x16455,x16452,x16456)) % 183.90/184.46 [1646]~E(x16461,x16462)+E(f675(x16463,x16464,x16465,x16466,x16461),f675(x16463,x16464,x16465,x16466,x16462)) % 183.90/184.46 [1647]~E(x16471,x16472)+E(f467(x16471,x16473,x16474,x16475,x16476),f467(x16472,x16473,x16474,x16475,x16476)) % 183.90/184.46 [1648]~E(x16481,x16482)+E(f467(x16483,x16481,x16484,x16485,x16486),f467(x16483,x16482,x16484,x16485,x16486)) % 183.90/184.46 [1649]~E(x16491,x16492)+E(f467(x16493,x16494,x16491,x16495,x16496),f467(x16493,x16494,x16492,x16495,x16496)) % 183.90/184.46 [1650]~E(x16501,x16502)+E(f467(x16503,x16504,x16505,x16501,x16506),f467(x16503,x16504,x16505,x16502,x16506)) % 183.90/184.46 [1651]~E(x16511,x16512)+E(f467(x16513,x16514,x16515,x16516,x16511),f467(x16513,x16514,x16515,x16516,x16512)) % 183.90/184.46 [1652]~E(x16521,x16522)+E(f493(x16521,x16523,x16524,x16525),f493(x16522,x16523,x16524,x16525)) % 183.90/184.46 [1653]~E(x16531,x16532)+E(f493(x16533,x16531,x16534,x16535),f493(x16533,x16532,x16534,x16535)) % 183.90/184.46 [1654]~E(x16541,x16542)+E(f493(x16543,x16544,x16541,x16545),f493(x16543,x16544,x16542,x16545)) % 183.90/184.46 [1655]~E(x16551,x16552)+E(f493(x16553,x16554,x16555,x16551),f493(x16553,x16554,x16555,x16552)) % 183.90/184.46 [1656]~E(x16561,x16562)+E(f512(x16561,x16563),f512(x16562,x16563)) % 183.90/184.46 [1657]~E(x16571,x16572)+E(f512(x16573,x16571),f512(x16573,x16572)) % 183.90/184.46 [1658]~E(x16581,x16582)+E(f208(x16581,x16583,x16584,x16585),f208(x16582,x16583,x16584,x16585)) % 183.90/184.46 [1659]~E(x16591,x16592)+E(f208(x16593,x16591,x16594,x16595),f208(x16593,x16592,x16594,x16595)) % 183.90/184.46 [1660]~E(x16601,x16602)+E(f208(x16603,x16604,x16601,x16605),f208(x16603,x16604,x16602,x16605)) % 183.90/184.46 [1661]~E(x16611,x16612)+E(f208(x16613,x16614,x16615,x16611),f208(x16613,x16614,x16615,x16612)) % 183.90/184.46 [1662]~E(x16621,x16622)+E(f259(x16621,x16623,x16624),f259(x16622,x16623,x16624)) % 183.90/184.46 [1663]~E(x16631,x16632)+E(f259(x16633,x16631,x16634),f259(x16633,x16632,x16634)) % 183.90/184.46 [1664]~E(x16641,x16642)+E(f259(x16643,x16644,x16641),f259(x16643,x16644,x16642)) % 183.90/184.46 [1665]~E(x16651,x16652)+E(f582(x16651,x16653,x16654),f582(x16652,x16653,x16654)) % 183.90/184.46 [1666]~E(x16661,x16662)+E(f582(x16663,x16661,x16664),f582(x16663,x16662,x16664)) % 183.90/184.46 [1667]~E(x16671,x16672)+E(f582(x16673,x16674,x16671),f582(x16673,x16674,x16672)) % 183.90/184.46 [1668]~E(x16681,x16682)+E(f130(x16681,x16683),f130(x16682,x16683)) % 183.90/184.46 [1669]~E(x16691,x16692)+E(f130(x16693,x16691),f130(x16693,x16692)) % 183.90/184.46 [1670]~E(x16701,x16702)+E(f714(x16701,x16703,x16704,x16705,x16706,x16707,x16708),f714(x16702,x16703,x16704,x16705,x16706,x16707,x16708)) % 183.90/184.46 [1671]~E(x16711,x16712)+E(f714(x16713,x16711,x16714,x16715,x16716,x16717,x16718),f714(x16713,x16712,x16714,x16715,x16716,x16717,x16718)) % 183.90/184.46 [1672]~E(x16721,x16722)+E(f714(x16723,x16724,x16721,x16725,x16726,x16727,x16728),f714(x16723,x16724,x16722,x16725,x16726,x16727,x16728)) % 183.90/184.46 [1673]~E(x16731,x16732)+E(f714(x16733,x16734,x16735,x16731,x16736,x16737,x16738),f714(x16733,x16734,x16735,x16732,x16736,x16737,x16738)) % 183.90/184.46 [1674]~E(x16741,x16742)+E(f714(x16743,x16744,x16745,x16746,x16741,x16747,x16748),f714(x16743,x16744,x16745,x16746,x16742,x16747,x16748)) % 183.90/184.46 [1675]~E(x16751,x16752)+E(f714(x16753,x16754,x16755,x16756,x16757,x16751,x16758),f714(x16753,x16754,x16755,x16756,x16757,x16752,x16758)) % 183.90/184.46 [1676]~E(x16761,x16762)+E(f714(x16763,x16764,x16765,x16766,x16767,x16768,x16761),f714(x16763,x16764,x16765,x16766,x16767,x16768,x16762)) % 183.90/184.46 [1677]~E(x16771,x16772)+E(f748(x16771,x16773,x16774),f748(x16772,x16773,x16774)) % 183.90/184.46 [1678]~E(x16781,x16782)+E(f748(x16783,x16781,x16784),f748(x16783,x16782,x16784)) % 183.90/184.46 [1679]~E(x16791,x16792)+E(f748(x16793,x16794,x16791),f748(x16793,x16794,x16792)) % 183.90/184.46 [1680]~E(x16801,x16802)+E(f605(x16801,x16803,x16804),f605(x16802,x16803,x16804)) % 183.90/184.46 [1681]~E(x16811,x16812)+E(f605(x16813,x16811,x16814),f605(x16813,x16812,x16814)) % 183.90/184.46 [1682]~E(x16821,x16822)+E(f605(x16823,x16824,x16821),f605(x16823,x16824,x16822)) % 183.90/184.46 [1683]~E(x16831,x16832)+E(f669(x16831,x16833),f669(x16832,x16833)) % 183.90/184.46 [1684]~E(x16841,x16842)+E(f669(x16843,x16841),f669(x16843,x16842)) % 183.90/184.46 [1685]~E(x16851,x16852)+E(f457(x16851,x16853,x16854,x16855),f457(x16852,x16853,x16854,x16855)) % 183.90/184.46 [1686]~E(x16861,x16862)+E(f457(x16863,x16861,x16864,x16865),f457(x16863,x16862,x16864,x16865)) % 183.90/184.46 [1687]~E(x16871,x16872)+E(f457(x16873,x16874,x16871,x16875),f457(x16873,x16874,x16872,x16875)) % 183.90/184.46 [1688]~E(x16881,x16882)+E(f457(x16883,x16884,x16885,x16881),f457(x16883,x16884,x16885,x16882)) % 183.90/184.46 [1689]~E(x16891,x16892)+E(f794(x16891,x16893,x16894),f794(x16892,x16893,x16894)) % 183.90/184.46 [1690]~E(x16901,x16902)+E(f794(x16903,x16901,x16904),f794(x16903,x16902,x16904)) % 183.90/184.46 [1691]~E(x16911,x16912)+E(f794(x16913,x16914,x16911),f794(x16913,x16914,x16912)) % 183.90/184.46 [1692]~E(x16921,x16922)+E(f773(x16921,x16923,x16924,x16925),f773(x16922,x16923,x16924,x16925)) % 183.90/184.46 [1693]~E(x16931,x16932)+E(f773(x16933,x16931,x16934,x16935),f773(x16933,x16932,x16934,x16935)) % 183.90/184.46 [1694]~E(x16941,x16942)+E(f773(x16943,x16944,x16941,x16945),f773(x16943,x16944,x16942,x16945)) % 183.90/184.46 [1695]~E(x16951,x16952)+E(f773(x16953,x16954,x16955,x16951),f773(x16953,x16954,x16955,x16952)) % 183.90/184.46 [1696]~E(x16961,x16962)+E(f437(x16961,x16963,x16964,x16965),f437(x16962,x16963,x16964,x16965)) % 183.90/184.46 [1697]~E(x16971,x16972)+E(f437(x16973,x16971,x16974,x16975),f437(x16973,x16972,x16974,x16975)) % 183.90/184.46 [1698]~E(x16981,x16982)+E(f437(x16983,x16984,x16981,x16985),f437(x16983,x16984,x16982,x16985)) % 183.90/184.46 [1699]~E(x16991,x16992)+E(f437(x16993,x16994,x16995,x16991),f437(x16993,x16994,x16995,x16992)) % 183.90/184.46 [1700]~E(x17001,x17002)+E(f382(x17001,x17003,x17004,x17005,x17006),f382(x17002,x17003,x17004,x17005,x17006)) % 183.90/184.46 [1701]~E(x17011,x17012)+E(f382(x17013,x17011,x17014,x17015,x17016),f382(x17013,x17012,x17014,x17015,x17016)) % 183.90/184.46 [1702]~E(x17021,x17022)+E(f382(x17023,x17024,x17021,x17025,x17026),f382(x17023,x17024,x17022,x17025,x17026)) % 183.90/184.46 [1703]~E(x17031,x17032)+E(f382(x17033,x17034,x17035,x17031,x17036),f382(x17033,x17034,x17035,x17032,x17036)) % 183.90/184.46 [1704]~E(x17041,x17042)+E(f382(x17043,x17044,x17045,x17046,x17041),f382(x17043,x17044,x17045,x17046,x17042)) % 183.90/184.46 [1705]~E(x17051,x17052)+E(f820(x17051,x17053,x17054),f820(x17052,x17053,x17054)) % 183.90/184.46 [1706]~E(x17061,x17062)+E(f820(x17063,x17061,x17064),f820(x17063,x17062,x17064)) % 183.90/184.46 [1707]~E(x17071,x17072)+E(f820(x17073,x17074,x17071),f820(x17073,x17074,x17072)) % 183.90/184.46 [1708]~E(x17081,x17082)+E(f612(x17081,x17083),f612(x17082,x17083)) % 183.90/184.46 [1709]~E(x17091,x17092)+E(f612(x17093,x17091),f612(x17093,x17092)) % 183.90/184.46 [1710]~E(x17101,x17102)+E(f600(x17101,x17103,x17104),f600(x17102,x17103,x17104)) % 183.90/184.46 [1711]~E(x17111,x17112)+E(f600(x17113,x17111,x17114),f600(x17113,x17112,x17114)) % 183.90/184.46 [1712]~E(x17121,x17122)+E(f600(x17123,x17124,x17121),f600(x17123,x17124,x17122)) % 183.90/184.46 [1713]~E(x17131,x17132)+E(f558(x17131,x17133,x17134,x17135,x17136),f558(x17132,x17133,x17134,x17135,x17136)) % 183.90/184.46 [1714]~E(x17141,x17142)+E(f558(x17143,x17141,x17144,x17145,x17146),f558(x17143,x17142,x17144,x17145,x17146)) % 183.90/184.46 [1715]~E(x17151,x17152)+E(f558(x17153,x17154,x17151,x17155,x17156),f558(x17153,x17154,x17152,x17155,x17156)) % 183.90/184.46 [1716]~E(x17161,x17162)+E(f558(x17163,x17164,x17165,x17161,x17166),f558(x17163,x17164,x17165,x17162,x17166)) % 183.90/184.46 [1717]~E(x17171,x17172)+E(f558(x17173,x17174,x17175,x17176,x17171),f558(x17173,x17174,x17175,x17176,x17172)) % 183.90/184.46 [1718]~E(x17181,x17182)+E(f427(x17181,x17183,x17184,x17185),f427(x17182,x17183,x17184,x17185)) % 183.90/184.46 [1719]~E(x17191,x17192)+E(f427(x17193,x17191,x17194,x17195),f427(x17193,x17192,x17194,x17195)) % 183.90/184.46 [1720]~E(x17201,x17202)+E(f427(x17203,x17204,x17201,x17205),f427(x17203,x17204,x17202,x17205)) % 183.90/184.46 [1721]~E(x17211,x17212)+E(f427(x17213,x17214,x17215,x17211),f427(x17213,x17214,x17215,x17212)) % 183.90/184.46 [1722]~E(x17221,x17222)+E(f400(x17221,x17223,x17224,x17225,x17226,x17227),f400(x17222,x17223,x17224,x17225,x17226,x17227)) % 183.90/184.46 [1723]~E(x17231,x17232)+E(f400(x17233,x17231,x17234,x17235,x17236,x17237),f400(x17233,x17232,x17234,x17235,x17236,x17237)) % 183.90/184.46 [1724]~E(x17241,x17242)+E(f400(x17243,x17244,x17241,x17245,x17246,x17247),f400(x17243,x17244,x17242,x17245,x17246,x17247)) % 183.90/184.46 [1725]~E(x17251,x17252)+E(f400(x17253,x17254,x17255,x17251,x17256,x17257),f400(x17253,x17254,x17255,x17252,x17256,x17257)) % 183.90/184.46 [1726]~E(x17261,x17262)+E(f400(x17263,x17264,x17265,x17266,x17261,x17267),f400(x17263,x17264,x17265,x17266,x17262,x17267)) % 183.90/184.46 [1727]~E(x17271,x17272)+E(f400(x17273,x17274,x17275,x17276,x17277,x17271),f400(x17273,x17274,x17275,x17276,x17277,x17272)) % 183.90/184.46 [1728]~E(x17281,x17282)+E(f661(x17281,x17283),f661(x17282,x17283)) % 183.90/184.46 [1729]~E(x17291,x17292)+E(f661(x17293,x17291),f661(x17293,x17292)) % 183.90/184.46 [1730]~E(x17301,x17302)+E(f176(x17301,x17303,x17304),f176(x17302,x17303,x17304)) % 183.90/184.46 [1731]~E(x17311,x17312)+E(f176(x17313,x17311,x17314),f176(x17313,x17312,x17314)) % 183.90/184.46 [1732]~E(x17321,x17322)+E(f176(x17323,x17324,x17321),f176(x17323,x17324,x17322)) % 183.90/184.46 [1733]~E(x17331,x17332)+E(f857(x17331,x17333,x17334,x17335,x17336),f857(x17332,x17333,x17334,x17335,x17336)) % 183.90/184.46 [1734]~E(x17341,x17342)+E(f857(x17343,x17341,x17344,x17345,x17346),f857(x17343,x17342,x17344,x17345,x17346)) % 183.90/184.46 [1735]~E(x17351,x17352)+E(f857(x17353,x17354,x17351,x17355,x17356),f857(x17353,x17354,x17352,x17355,x17356)) % 183.90/184.46 [1736]~E(x17361,x17362)+E(f857(x17363,x17364,x17365,x17361,x17366),f857(x17363,x17364,x17365,x17362,x17366)) % 183.90/184.46 [1737]~E(x17371,x17372)+E(f857(x17373,x17374,x17375,x17376,x17371),f857(x17373,x17374,x17375,x17376,x17372)) % 183.90/184.46 [1738]~E(x17381,x17382)+E(f653(x17381,x17383,x17384),f653(x17382,x17383,x17384)) % 183.90/184.46 [1739]~E(x17391,x17392)+E(f653(x17393,x17391,x17394),f653(x17393,x17392,x17394)) % 183.90/184.46 [1740]~E(x17401,x17402)+E(f653(x17403,x17404,x17401),f653(x17403,x17404,x17402)) % 183.90/184.46 [1741]~E(x17411,x17412)+E(f412(x17411,x17413),f412(x17412,x17413)) % 183.90/184.46 [1742]~E(x17421,x17422)+E(f412(x17423,x17421),f412(x17423,x17422)) % 183.90/184.46 [1743]~E(x17431,x17432)+E(f690(x17431,x17433),f690(x17432,x17433)) % 183.90/184.46 [1744]~E(x17441,x17442)+E(f690(x17443,x17441),f690(x17443,x17442)) % 183.90/184.46 [1745]~E(x17451,x17452)+E(f222(x17451,x17453,x17454,x17455),f222(x17452,x17453,x17454,x17455)) % 183.90/184.46 [1746]~E(x17461,x17462)+E(f222(x17463,x17461,x17464,x17465),f222(x17463,x17462,x17464,x17465)) % 183.90/184.46 [1747]~E(x17471,x17472)+E(f222(x17473,x17474,x17471,x17475),f222(x17473,x17474,x17472,x17475)) % 183.90/184.46 [1748]~E(x17481,x17482)+E(f222(x17483,x17484,x17485,x17481),f222(x17483,x17484,x17485,x17482)) % 183.90/184.46 [1749]~E(x17491,x17492)+E(f855(x17491,x17493),f855(x17492,x17493)) % 183.90/184.46 [1750]~E(x17501,x17502)+E(f855(x17503,x17501),f855(x17503,x17502)) % 183.90/184.46 [1751]~E(x17511,x17512)+E(f396(x17511,x17513,x17514),f396(x17512,x17513,x17514)) % 183.90/184.46 [1752]~E(x17521,x17522)+E(f396(x17523,x17521,x17524),f396(x17523,x17522,x17524)) % 183.90/184.46 [1753]~E(x17531,x17532)+E(f396(x17533,x17534,x17531),f396(x17533,x17534,x17532)) % 183.90/184.46 [1754]~E(x17541,x17542)+E(f571(x17541,x17543),f571(x17542,x17543)) % 183.90/184.46 [1755]~E(x17551,x17552)+E(f571(x17553,x17551),f571(x17553,x17552)) % 183.90/184.46 [1756]~E(x17561,x17562)+E(f532(x17561,x17563,x17564,x17565,x17566),f532(x17562,x17563,x17564,x17565,x17566)) % 183.90/184.46 [1757]~E(x17571,x17572)+E(f532(x17573,x17571,x17574,x17575,x17576),f532(x17573,x17572,x17574,x17575,x17576)) % 183.90/184.46 [1758]~E(x17581,x17582)+E(f532(x17583,x17584,x17581,x17585,x17586),f532(x17583,x17584,x17582,x17585,x17586)) % 183.90/184.46 [1759]~E(x17591,x17592)+E(f532(x17593,x17594,x17595,x17591,x17596),f532(x17593,x17594,x17595,x17592,x17596)) % 183.90/184.46 [1760]~E(x17601,x17602)+E(f532(x17603,x17604,x17605,x17606,x17601),f532(x17603,x17604,x17605,x17606,x17602)) % 183.90/184.46 [1761]~E(x17611,x17612)+E(f676(x17611,x17613,x17614,x17615),f676(x17612,x17613,x17614,x17615)) % 183.90/184.46 [1762]~E(x17621,x17622)+E(f676(x17623,x17621,x17624,x17625),f676(x17623,x17622,x17624,x17625)) % 183.90/184.46 [1763]~E(x17631,x17632)+E(f676(x17633,x17634,x17631,x17635),f676(x17633,x17634,x17632,x17635)) % 183.90/184.46 [1764]~E(x17641,x17642)+E(f676(x17643,x17644,x17645,x17641),f676(x17643,x17644,x17645,x17642)) % 183.90/184.46 [1765]~E(x17651,x17652)+E(f727(x17651,x17653,x17654),f727(x17652,x17653,x17654)) % 183.90/184.46 [1766]~E(x17661,x17662)+E(f727(x17663,x17661,x17664),f727(x17663,x17662,x17664)) % 183.90/184.46 [1767]~E(x17671,x17672)+E(f727(x17673,x17674,x17671),f727(x17673,x17674,x17672)) % 183.90/184.46 [1768]~E(x17681,x17682)+E(f650(x17681,x17683,x17684,x17685),f650(x17682,x17683,x17684,x17685)) % 183.90/184.46 [1769]~E(x17691,x17692)+E(f650(x17693,x17691,x17694,x17695),f650(x17693,x17692,x17694,x17695)) % 183.90/184.46 [1770]~E(x17701,x17702)+E(f650(x17703,x17704,x17701,x17705),f650(x17703,x17704,x17702,x17705)) % 183.90/184.46 [1771]~E(x17711,x17712)+E(f650(x17713,x17714,x17715,x17711),f650(x17713,x17714,x17715,x17712)) % 183.90/184.46 [1772]~E(x17721,x17722)+E(f124(x17721,x17723),f124(x17722,x17723)) % 183.90/184.46 [1773]~E(x17731,x17732)+E(f124(x17733,x17731),f124(x17733,x17732)) % 183.90/184.46 [1774]~E(x17741,x17742)+E(f341(x17741),f341(x17742)) % 183.90/184.46 [1775]~E(x17751,x17752)+E(f730(x17751,x17753),f730(x17752,x17753)) % 183.90/184.46 [1776]~E(x17761,x17762)+E(f730(x17763,x17761),f730(x17763,x17762)) % 183.90/184.46 [1777]~E(x17771,x17772)+E(f843(x17771,x17773,x17774,x17775,x17776),f843(x17772,x17773,x17774,x17775,x17776)) % 183.90/184.46 [1778]~E(x17781,x17782)+E(f843(x17783,x17781,x17784,x17785,x17786),f843(x17783,x17782,x17784,x17785,x17786)) % 183.90/184.46 [1779]~E(x17791,x17792)+E(f843(x17793,x17794,x17791,x17795,x17796),f843(x17793,x17794,x17792,x17795,x17796)) % 183.90/184.46 [1780]~E(x17801,x17802)+E(f843(x17803,x17804,x17805,x17801,x17806),f843(x17803,x17804,x17805,x17802,x17806)) % 183.90/184.46 [1781]~E(x17811,x17812)+E(f843(x17813,x17814,x17815,x17816,x17811),f843(x17813,x17814,x17815,x17816,x17812)) % 183.90/184.46 [1782]~E(x17821,x17822)+E(f359(x17821,x17823,x17824),f359(x17822,x17823,x17824)) % 183.90/184.46 [1783]~E(x17831,x17832)+E(f359(x17833,x17831,x17834),f359(x17833,x17832,x17834)) % 183.90/184.46 [1784]~E(x17841,x17842)+E(f359(x17843,x17844,x17841),f359(x17843,x17844,x17842)) % 183.90/184.46 [1785]~E(x17851,x17852)+E(f606(x17851,x17853,x17854,x17855),f606(x17852,x17853,x17854,x17855)) % 183.90/184.46 [1786]~E(x17861,x17862)+E(f606(x17863,x17861,x17864,x17865),f606(x17863,x17862,x17864,x17865)) % 183.90/184.46 [1787]~E(x17871,x17872)+E(f606(x17873,x17874,x17871,x17875),f606(x17873,x17874,x17872,x17875)) % 183.90/184.46 [1788]~E(x17881,x17882)+E(f606(x17883,x17884,x17885,x17881),f606(x17883,x17884,x17885,x17882)) % 183.90/184.46 [1789]~E(x17891,x17892)+E(f718(x17891,x17893),f718(x17892,x17893)) % 183.90/184.46 [1790]~E(x17901,x17902)+E(f718(x17903,x17901),f718(x17903,x17902)) % 183.90/184.46 [1791]~E(x17911,x17912)+E(f347(x17911,x17913,x17914,x17915,x17916),f347(x17912,x17913,x17914,x17915,x17916)) % 183.90/184.46 [1792]~E(x17921,x17922)+E(f347(x17923,x17921,x17924,x17925,x17926),f347(x17923,x17922,x17924,x17925,x17926)) % 183.90/184.46 [1793]~E(x17931,x17932)+E(f347(x17933,x17934,x17931,x17935,x17936),f347(x17933,x17934,x17932,x17935,x17936)) % 183.90/184.46 [1794]~E(x17941,x17942)+E(f347(x17943,x17944,x17945,x17941,x17946),f347(x17943,x17944,x17945,x17942,x17946)) % 183.90/184.46 [1795]~E(x17951,x17952)+E(f347(x17953,x17954,x17955,x17956,x17951),f347(x17953,x17954,x17955,x17956,x17952)) % 183.90/184.46 [1796]~E(x17961,x17962)+E(f505(x17961,x17963),f505(x17962,x17963)) % 183.90/184.46 [1797]~E(x17971,x17972)+E(f505(x17973,x17971),f505(x17973,x17972)) % 183.90/184.46 [1798]~E(x17981,x17982)+E(f299(x17981,x17983,x17984),f299(x17982,x17983,x17984)) % 183.90/184.46 [1799]~E(x17991,x17992)+E(f299(x17993,x17991,x17994),f299(x17993,x17992,x17994)) % 183.90/184.46 [1800]~E(x18001,x18002)+E(f299(x18003,x18004,x18001),f299(x18003,x18004,x18002)) % 183.90/184.46 [1801]~E(x18011,x18012)+E(f696(x18011,x18013,x18014),f696(x18012,x18013,x18014)) % 183.90/184.46 [1802]~E(x18021,x18022)+E(f696(x18023,x18021,x18024),f696(x18023,x18022,x18024)) % 183.90/184.46 [1803]~E(x18031,x18032)+E(f696(x18033,x18034,x18031),f696(x18033,x18034,x18032)) % 183.90/184.46 [1804]~E(x18041,x18042)+E(f622(x18041,x18043,x18044,x18045,x18046),f622(x18042,x18043,x18044,x18045,x18046)) % 183.90/184.46 [1805]~E(x18051,x18052)+E(f622(x18053,x18051,x18054,x18055,x18056),f622(x18053,x18052,x18054,x18055,x18056)) % 183.90/184.46 [1806]~E(x18061,x18062)+E(f622(x18063,x18064,x18061,x18065,x18066),f622(x18063,x18064,x18062,x18065,x18066)) % 183.90/184.46 [1807]~E(x18071,x18072)+E(f622(x18073,x18074,x18075,x18071,x18076),f622(x18073,x18074,x18075,x18072,x18076)) % 183.90/184.46 [1808]~E(x18081,x18082)+E(f622(x18083,x18084,x18085,x18086,x18081),f622(x18083,x18084,x18085,x18086,x18082)) % 183.90/184.46 [1809]~E(x18091,x18092)+E(f524(x18091,x18093,x18094,x18095),f524(x18092,x18093,x18094,x18095)) % 183.90/184.46 [1810]~E(x18101,x18102)+E(f524(x18103,x18101,x18104,x18105),f524(x18103,x18102,x18104,x18105)) % 183.90/184.46 [1811]~E(x18111,x18112)+E(f524(x18113,x18114,x18111,x18115),f524(x18113,x18114,x18112,x18115)) % 183.90/184.46 [1812]~E(x18121,x18122)+E(f524(x18123,x18124,x18125,x18121),f524(x18123,x18124,x18125,x18122)) % 183.90/184.46 [1813]~E(x18131,x18132)+E(f343(x18131),f343(x18132)) % 183.90/184.46 [1814]~E(x18141,x18142)+E(f516(x18141,x18143,x18144),f516(x18142,x18143,x18144)) % 183.90/184.46 [1815]~E(x18151,x18152)+E(f516(x18153,x18151,x18154),f516(x18153,x18152,x18154)) % 183.90/184.46 [1816]~E(x18161,x18162)+E(f516(x18163,x18164,x18161),f516(x18163,x18164,x18162)) % 183.90/184.46 [1817]~E(x18171,x18172)+E(f556(x18171,x18173,x18174),f556(x18172,x18173,x18174)) % 183.90/184.46 [1818]~E(x18181,x18182)+E(f556(x18183,x18181,x18184),f556(x18183,x18182,x18184)) % 183.90/184.46 [1819]~E(x18191,x18192)+E(f556(x18193,x18194,x18191),f556(x18193,x18194,x18192)) % 183.90/184.46 [1820]~E(x18201,x18202)+E(f557(x18201,x18203,x18204),f557(x18202,x18203,x18204)) % 183.90/184.46 [1821]~E(x18211,x18212)+E(f557(x18213,x18211,x18214),f557(x18213,x18212,x18214)) % 183.90/184.46 [1822]~E(x18221,x18222)+E(f557(x18223,x18224,x18221),f557(x18223,x18224,x18222)) % 183.90/184.46 [1823]~E(x18231,x18232)+E(f749(x18231,x18233,x18234),f749(x18232,x18233,x18234)) % 183.90/184.46 [1824]~E(x18241,x18242)+E(f749(x18243,x18241,x18244),f749(x18243,x18242,x18244)) % 183.90/184.46 [1825]~E(x18251,x18252)+E(f749(x18253,x18254,x18251),f749(x18253,x18254,x18252)) % 183.90/184.46 [1826]~E(x18261,x18262)+E(f861(x18261,x18263,x18264,x18265),f861(x18262,x18263,x18264,x18265)) % 183.90/184.46 [1827]~E(x18271,x18272)+E(f861(x18273,x18271,x18274,x18275),f861(x18273,x18272,x18274,x18275)) % 183.90/184.46 [1828]~E(x18281,x18282)+E(f861(x18283,x18284,x18281,x18285),f861(x18283,x18284,x18282,x18285)) % 183.90/184.46 [1829]~E(x18291,x18292)+E(f861(x18293,x18294,x18295,x18291),f861(x18293,x18294,x18295,x18292)) % 183.90/184.46 [1830]~E(x18301,x18302)+E(f829(x18301,x18303,x18304,x18305,x18306),f829(x18302,x18303,x18304,x18305,x18306)) % 183.90/184.46 [1831]~E(x18311,x18312)+E(f829(x18313,x18311,x18314,x18315,x18316),f829(x18313,x18312,x18314,x18315,x18316)) % 183.90/184.46 [1832]~E(x18321,x18322)+E(f829(x18323,x18324,x18321,x18325,x18326),f829(x18323,x18324,x18322,x18325,x18326)) % 183.90/184.46 [1833]~E(x18331,x18332)+E(f829(x18333,x18334,x18335,x18331,x18336),f829(x18333,x18334,x18335,x18332,x18336)) % 183.90/184.46 [1834]~E(x18341,x18342)+E(f829(x18343,x18344,x18345,x18346,x18341),f829(x18343,x18344,x18345,x18346,x18342)) % 183.90/184.46 [1835]~E(x18351,x18352)+E(f804(x18351,x18353),f804(x18352,x18353)) % 183.90/184.46 [1836]~E(x18361,x18362)+E(f804(x18363,x18361),f804(x18363,x18362)) % 183.90/184.46 [1837]~E(x18371,x18372)+E(f541(x18371,x18373,x18374,x18375),f541(x18372,x18373,x18374,x18375)) % 183.90/184.46 [1838]~E(x18381,x18382)+E(f541(x18383,x18381,x18384,x18385),f541(x18383,x18382,x18384,x18385)) % 183.90/184.46 [1839]~E(x18391,x18392)+E(f541(x18393,x18394,x18391,x18395),f541(x18393,x18394,x18392,x18395)) % 183.90/184.46 [1840]~E(x18401,x18402)+E(f541(x18403,x18404,x18405,x18401),f541(x18403,x18404,x18405,x18402)) % 183.90/184.46 [1841]~E(x18411,x18412)+E(f784(x18411,x18413,x18414,x18415,x18416),f784(x18412,x18413,x18414,x18415,x18416)) % 183.90/184.46 [1842]~E(x18421,x18422)+E(f784(x18423,x18421,x18424,x18425,x18426),f784(x18423,x18422,x18424,x18425,x18426)) % 183.90/184.46 [1843]~E(x18431,x18432)+E(f784(x18433,x18434,x18431,x18435,x18436),f784(x18433,x18434,x18432,x18435,x18436)) % 183.90/184.46 [1844]~E(x18441,x18442)+E(f784(x18443,x18444,x18445,x18441,x18446),f784(x18443,x18444,x18445,x18442,x18446)) % 183.90/184.46 [1845]~E(x18451,x18452)+E(f784(x18453,x18454,x18455,x18456,x18451),f784(x18453,x18454,x18455,x18456,x18452)) % 183.90/184.46 [1846]~E(x18461,x18462)+E(f422(x18461,x18463,x18464,x18465),f422(x18462,x18463,x18464,x18465)) % 183.90/184.46 [1847]~E(x18471,x18472)+E(f422(x18473,x18471,x18474,x18475),f422(x18473,x18472,x18474,x18475)) % 183.90/184.46 [1848]~E(x18481,x18482)+E(f422(x18483,x18484,x18481,x18485),f422(x18483,x18484,x18482,x18485)) % 183.90/184.46 [1849]~E(x18491,x18492)+E(f422(x18493,x18494,x18495,x18491),f422(x18493,x18494,x18495,x18492)) % 183.90/184.46 [1850]~E(x18501,x18502)+E(f295(x18501,x18503,x18504),f295(x18502,x18503,x18504)) % 183.90/184.46 [1851]~E(x18511,x18512)+E(f295(x18513,x18511,x18514),f295(x18513,x18512,x18514)) % 183.90/184.46 [1852]~E(x18521,x18522)+E(f295(x18523,x18524,x18521),f295(x18523,x18524,x18522)) % 183.90/184.46 [1853]~E(x18531,x18532)+E(f399(x18531,x18533,x18534,x18535,x18536),f399(x18532,x18533,x18534,x18535,x18536)) % 183.90/184.46 [1854]~E(x18541,x18542)+E(f399(x18543,x18541,x18544,x18545,x18546),f399(x18543,x18542,x18544,x18545,x18546)) % 183.90/184.46 [1855]~E(x18551,x18552)+E(f399(x18553,x18554,x18551,x18555,x18556),f399(x18553,x18554,x18552,x18555,x18556)) % 183.90/184.46 [1856]~E(x18561,x18562)+E(f399(x18563,x18564,x18565,x18561,x18566),f399(x18563,x18564,x18565,x18562,x18566)) % 183.90/184.46 [1857]~E(x18571,x18572)+E(f399(x18573,x18574,x18575,x18576,x18571),f399(x18573,x18574,x18575,x18576,x18572)) % 183.90/184.46 [1858]~E(x18581,x18582)+E(f575(x18581,x18583),f575(x18582,x18583)) % 183.90/184.46 [1859]~E(x18591,x18592)+E(f575(x18593,x18591),f575(x18593,x18592)) % 183.90/184.46 [1860]~E(x18601,x18602)+E(f485(x18601),f485(x18602)) % 183.90/184.46 [1861]~E(x18611,x18612)+E(f638(x18611,x18613,x18614,x18615,x18616),f638(x18612,x18613,x18614,x18615,x18616)) % 183.90/184.46 [1862]~E(x18621,x18622)+E(f638(x18623,x18621,x18624,x18625,x18626),f638(x18623,x18622,x18624,x18625,x18626)) % 183.90/184.46 [1863]~E(x18631,x18632)+E(f638(x18633,x18634,x18631,x18635,x18636),f638(x18633,x18634,x18632,x18635,x18636)) % 183.90/184.46 [1864]~E(x18641,x18642)+E(f638(x18643,x18644,x18645,x18641,x18646),f638(x18643,x18644,x18645,x18642,x18646)) % 183.90/184.46 [1865]~E(x18651,x18652)+E(f638(x18653,x18654,x18655,x18656,x18651),f638(x18653,x18654,x18655,x18656,x18652)) % 183.90/184.46 [1866]~E(x18661,x18662)+E(f477(x18661,x18663,x18664,x18665),f477(x18662,x18663,x18664,x18665)) % 183.90/184.46 [1867]~E(x18671,x18672)+E(f477(x18673,x18671,x18674,x18675),f477(x18673,x18672,x18674,x18675)) % 183.90/184.46 [1868]~E(x18681,x18682)+E(f477(x18683,x18684,x18681,x18685),f477(x18683,x18684,x18682,x18685)) % 183.90/184.46 [1869]~E(x18691,x18692)+E(f477(x18693,x18694,x18695,x18691),f477(x18693,x18694,x18695,x18692)) % 183.90/184.46 [1870]~E(x18701,x18702)+E(f816(x18701,x18703,x18704,x18705,x18706),f816(x18702,x18703,x18704,x18705,x18706)) % 183.90/184.46 [1871]~E(x18711,x18712)+E(f816(x18713,x18711,x18714,x18715,x18716),f816(x18713,x18712,x18714,x18715,x18716)) % 183.90/184.46 [1872]~E(x18721,x18722)+E(f816(x18723,x18724,x18721,x18725,x18726),f816(x18723,x18724,x18722,x18725,x18726)) % 183.90/184.46 [1873]~E(x18731,x18732)+E(f816(x18733,x18734,x18735,x18731,x18736),f816(x18733,x18734,x18735,x18732,x18736)) % 183.90/184.46 [1874]~E(x18741,x18742)+E(f816(x18743,x18744,x18745,x18746,x18741),f816(x18743,x18744,x18745,x18746,x18742)) % 183.90/184.46 [1875]~E(x18751,x18752)+E(f719(x18751,x18753,x18754),f719(x18752,x18753,x18754)) % 183.90/184.46 [1876]~E(x18761,x18762)+E(f719(x18763,x18761,x18764),f719(x18763,x18762,x18764)) % 183.90/184.46 [1877]~E(x18771,x18772)+E(f719(x18773,x18774,x18771),f719(x18773,x18774,x18772)) % 183.90/184.46 [1878]~E(x18781,x18782)+E(f644(x18781,x18783,x18784,x18785,x18786),f644(x18782,x18783,x18784,x18785,x18786)) % 183.90/184.46 [1879]~E(x18791,x18792)+E(f644(x18793,x18791,x18794,x18795,x18796),f644(x18793,x18792,x18794,x18795,x18796)) % 183.90/184.46 [1880]~E(x18801,x18802)+E(f644(x18803,x18804,x18801,x18805,x18806),f644(x18803,x18804,x18802,x18805,x18806)) % 183.90/184.46 [1881]~E(x18811,x18812)+E(f644(x18813,x18814,x18815,x18811,x18816),f644(x18813,x18814,x18815,x18812,x18816)) % 183.90/184.46 [1882]~E(x18821,x18822)+E(f644(x18823,x18824,x18825,x18826,x18821),f644(x18823,x18824,x18825,x18826,x18822)) % 183.90/184.46 [1883]~E(x18831,x18832)+E(f560(x18831,x18833,x18834,x18835),f560(x18832,x18833,x18834,x18835)) % 183.90/184.46 [1884]~E(x18841,x18842)+E(f560(x18843,x18841,x18844,x18845),f560(x18843,x18842,x18844,x18845)) % 183.90/184.46 [1885]~E(x18851,x18852)+E(f560(x18853,x18854,x18851,x18855),f560(x18853,x18854,x18852,x18855)) % 183.90/184.46 [1886]~E(x18861,x18862)+E(f560(x18863,x18864,x18865,x18861),f560(x18863,x18864,x18865,x18862)) % 183.90/184.46 [1887]~E(x18871,x18872)+E(f660(x18871,x18873,x18874,x18875),f660(x18872,x18873,x18874,x18875)) % 183.90/184.46 [1888]~E(x18881,x18882)+E(f660(x18883,x18881,x18884,x18885),f660(x18883,x18882,x18884,x18885)) % 183.90/184.46 [1889]~E(x18891,x18892)+E(f660(x18893,x18894,x18891,x18895),f660(x18893,x18894,x18892,x18895)) % 183.90/184.46 [1890]~E(x18901,x18902)+E(f660(x18903,x18904,x18905,x18901),f660(x18903,x18904,x18905,x18902)) % 183.90/184.46 [1891]~E(x18911,x18912)+E(f484(x18911,x18913,x18914,x18915,x18916),f484(x18912,x18913,x18914,x18915,x18916)) % 183.90/184.46 [1892]~E(x18921,x18922)+E(f484(x18923,x18921,x18924,x18925,x18926),f484(x18923,x18922,x18924,x18925,x18926)) % 183.90/184.46 [1893]~E(x18931,x18932)+E(f484(x18933,x18934,x18931,x18935,x18936),f484(x18933,x18934,x18932,x18935,x18936)) % 183.90/184.46 [1894]~E(x18941,x18942)+E(f484(x18943,x18944,x18945,x18941,x18946),f484(x18943,x18944,x18945,x18942,x18946)) % 183.90/184.46 [1895]~E(x18951,x18952)+E(f484(x18953,x18954,x18955,x18956,x18951),f484(x18953,x18954,x18955,x18956,x18952)) % 183.90/184.46 [1896]~E(x18961,x18962)+E(f837(x18961,x18963,x18964,x18965,x18966),f837(x18962,x18963,x18964,x18965,x18966)) % 183.90/184.46 [1897]~E(x18971,x18972)+E(f837(x18973,x18971,x18974,x18975,x18976),f837(x18973,x18972,x18974,x18975,x18976)) % 183.90/184.46 [1898]~E(x18981,x18982)+E(f837(x18983,x18984,x18981,x18985,x18986),f837(x18983,x18984,x18982,x18985,x18986)) % 183.90/184.46 [1899]~E(x18991,x18992)+E(f837(x18993,x18994,x18995,x18991,x18996),f837(x18993,x18994,x18995,x18992,x18996)) % 183.90/184.46 [1900]~E(x19001,x19002)+E(f837(x19003,x19004,x19005,x19006,x19001),f837(x19003,x19004,x19005,x19006,x19002)) % 183.90/184.46 [1901]~E(x19011,x19012)+E(f421(x19011,x19013,x19014,x19015),f421(x19012,x19013,x19014,x19015)) % 183.90/184.46 [1902]~E(x19021,x19022)+E(f421(x19023,x19021,x19024,x19025),f421(x19023,x19022,x19024,x19025)) % 183.90/184.46 [1903]~E(x19031,x19032)+E(f421(x19033,x19034,x19031,x19035),f421(x19033,x19034,x19032,x19035)) % 183.90/184.46 [1904]~E(x19041,x19042)+E(f421(x19043,x19044,x19045,x19041),f421(x19043,x19044,x19045,x19042)) % 183.90/184.46 [1905]~E(x19051,x19052)+E(f21(x19051,x19053),f21(x19052,x19053)) % 183.90/184.46 [1906]~E(x19061,x19062)+E(f21(x19063,x19061),f21(x19063,x19062)) % 183.90/184.46 [1907]~E(x19071,x19072)+E(f220(x19071),f220(x19072)) % 183.90/184.46 [1908]~E(x19081,x19082)+E(f513(x19081,x19083),f513(x19082,x19083)) % 183.90/184.46 [1909]~E(x19091,x19092)+E(f513(x19093,x19091),f513(x19093,x19092)) % 183.90/184.46 [1910]~E(x19101,x19102)+E(f527(x19101,x19103,x19104),f527(x19102,x19103,x19104)) % 183.90/184.46 [1911]~E(x19111,x19112)+E(f527(x19113,x19111,x19114),f527(x19113,x19112,x19114)) % 183.90/184.46 [1912]~E(x19121,x19122)+E(f527(x19123,x19124,x19121),f527(x19123,x19124,x19122)) % 183.90/184.46 [1913]~E(x19131,x19132)+E(f420(x19131,x19133,x19134),f420(x19132,x19133,x19134)) % 183.90/184.46 [1914]~E(x19141,x19142)+E(f420(x19143,x19141,x19144),f420(x19143,x19142,x19144)) % 183.90/184.46 [1915]~E(x19151,x19152)+E(f420(x19153,x19154,x19151),f420(x19153,x19154,x19152)) % 183.90/184.46 [1916]~E(x19161,x19162)+E(f624(x19161,x19163,x19164,x19165,x19166,x19167,x19168,x19169),f624(x19162,x19163,x19164,x19165,x19166,x19167,x19168,x19169)) % 183.90/184.46 [1917]~E(x19171,x19172)+E(f624(x19173,x19171,x19174,x19175,x19176,x19177,x19178,x19179),f624(x19173,x19172,x19174,x19175,x19176,x19177,x19178,x19179)) % 183.90/184.46 [1918]~E(x19181,x19182)+E(f624(x19183,x19184,x19181,x19185,x19186,x19187,x19188,x19189),f624(x19183,x19184,x19182,x19185,x19186,x19187,x19188,x19189)) % 183.90/184.46 [1919]~E(x19191,x19192)+E(f624(x19193,x19194,x19195,x19191,x19196,x19197,x19198,x19199),f624(x19193,x19194,x19195,x19192,x19196,x19197,x19198,x19199)) % 183.90/184.46 [1920]~E(x19201,x19202)+E(f624(x19203,x19204,x19205,x19206,x19201,x19207,x19208,x19209),f624(x19203,x19204,x19205,x19206,x19202,x19207,x19208,x19209)) % 183.90/184.46 [1921]~E(x19211,x19212)+E(f624(x19213,x19214,x19215,x19216,x19217,x19211,x19218,x19219),f624(x19213,x19214,x19215,x19216,x19217,x19212,x19218,x19219)) % 183.90/184.46 [1922]~E(x19221,x19222)+E(f624(x19223,x19224,x19225,x19226,x19227,x19228,x19221,x19229),f624(x19223,x19224,x19225,x19226,x19227,x19228,x19222,x19229)) % 183.90/184.46 [1923]~E(x19231,x19232)+E(f624(x19233,x19234,x19235,x19236,x19237,x19238,x19239,x19231),f624(x19233,x19234,x19235,x19236,x19237,x19238,x19239,x19232)) % 183.90/184.46 [1924]~E(x19241,x19242)+E(f449(x19241,x19243,x19244,x19245,x19246),f449(x19242,x19243,x19244,x19245,x19246)) % 183.90/184.46 [1925]~E(x19251,x19252)+E(f449(x19253,x19251,x19254,x19255,x19256),f449(x19253,x19252,x19254,x19255,x19256)) % 183.90/184.46 [1926]~E(x19261,x19262)+E(f449(x19263,x19264,x19261,x19265,x19266),f449(x19263,x19264,x19262,x19265,x19266)) % 183.90/184.46 [1927]~E(x19271,x19272)+E(f449(x19273,x19274,x19275,x19271,x19276),f449(x19273,x19274,x19275,x19272,x19276)) % 183.90/184.46 [1928]~E(x19281,x19282)+E(f449(x19283,x19284,x19285,x19286,x19281),f449(x19283,x19284,x19285,x19286,x19282)) % 183.90/184.46 [1929]~E(x19291,x19292)+E(f351(x19291,x19293,x19294,x19295,x19296),f351(x19292,x19293,x19294,x19295,x19296)) % 183.90/184.46 [1930]~E(x19301,x19302)+E(f351(x19303,x19301,x19304,x19305,x19306),f351(x19303,x19302,x19304,x19305,x19306)) % 183.90/184.46 [1931]~E(x19311,x19312)+E(f351(x19313,x19314,x19311,x19315,x19316),f351(x19313,x19314,x19312,x19315,x19316)) % 183.90/184.46 [1932]~E(x19321,x19322)+E(f351(x19323,x19324,x19325,x19321,x19326),f351(x19323,x19324,x19325,x19322,x19326)) % 183.90/184.46 [1933]~E(x19331,x19332)+E(f351(x19333,x19334,x19335,x19336,x19331),f351(x19333,x19334,x19335,x19336,x19332)) % 183.90/184.46 [1934]~E(x19341,x19342)+E(f613(x19341,x19343,x19344),f613(x19342,x19343,x19344)) % 183.90/184.46 [1935]~E(x19351,x19352)+E(f613(x19353,x19351,x19354),f613(x19353,x19352,x19354)) % 183.90/184.46 [1936]~E(x19361,x19362)+E(f613(x19363,x19364,x19361),f613(x19363,x19364,x19362)) % 183.90/184.46 [1937]~E(x19371,x19372)+E(f677(x19371,x19373,x19374,x19375),f677(x19372,x19373,x19374,x19375)) % 183.90/184.46 [1938]~E(x19381,x19382)+E(f677(x19383,x19381,x19384,x19385),f677(x19383,x19382,x19384,x19385)) % 183.90/184.46 [1939]~E(x19391,x19392)+E(f677(x19393,x19394,x19391,x19395),f677(x19393,x19394,x19392,x19395)) % 183.90/184.46 [1940]~E(x19401,x19402)+E(f677(x19403,x19404,x19405,x19401),f677(x19403,x19404,x19405,x19402)) % 183.90/184.46 [1941]~E(x19411,x19412)+E(f868(x19411,x19413,x19414,x19415,x19416),f868(x19412,x19413,x19414,x19415,x19416)) % 183.90/184.46 [1942]~E(x19421,x19422)+E(f868(x19423,x19421,x19424,x19425,x19426),f868(x19423,x19422,x19424,x19425,x19426)) % 183.90/184.46 [1943]~E(x19431,x19432)+E(f868(x19433,x19434,x19431,x19435,x19436),f868(x19433,x19434,x19432,x19435,x19436)) % 183.90/184.46 [1944]~E(x19441,x19442)+E(f868(x19443,x19444,x19445,x19441,x19446),f868(x19443,x19444,x19445,x19442,x19446)) % 183.90/184.46 [1945]~E(x19451,x19452)+E(f868(x19453,x19454,x19455,x19456,x19451),f868(x19453,x19454,x19455,x19456,x19452)) % 183.90/184.46 [1946]~E(x19461,x19462)+E(f583(x19461,x19463),f583(x19462,x19463)) % 183.90/184.46 [1947]~E(x19471,x19472)+E(f583(x19473,x19471),f583(x19473,x19472)) % 183.90/184.46 [1948]~E(x19481,x19482)+E(f434(x19481,x19483),f434(x19482,x19483)) % 183.90/184.46 [1949]~E(x19491,x19492)+E(f434(x19493,x19491),f434(x19493,x19492)) % 183.90/184.46 [1950]~E(x19501,x19502)+E(f601(x19501,x19503,x19504),f601(x19502,x19503,x19504)) % 183.90/184.46 [1951]~E(x19511,x19512)+E(f601(x19513,x19511,x19514),f601(x19513,x19512,x19514)) % 183.90/184.46 [1952]~E(x19521,x19522)+E(f601(x19523,x19524,x19521),f601(x19523,x19524,x19522)) % 183.90/184.46 [1953]~E(x19531,x19532)+E(f589(x19531),f589(x19532)) % 183.90/184.46 [1954]~E(x19541,x19542)+E(f783(x19541,x19543,x19544,x19545,x19546),f783(x19542,x19543,x19544,x19545,x19546)) % 183.90/184.46 [1955]~E(x19551,x19552)+E(f783(x19553,x19551,x19554,x19555,x19556),f783(x19553,x19552,x19554,x19555,x19556)) % 183.90/184.46 [1956]~E(x19561,x19562)+E(f783(x19563,x19564,x19561,x19565,x19566),f783(x19563,x19564,x19562,x19565,x19566)) % 183.90/184.46 [1957]~E(x19571,x19572)+E(f783(x19573,x19574,x19575,x19571,x19576),f783(x19573,x19574,x19575,x19572,x19576)) % 183.90/184.46 [1958]~E(x19581,x19582)+E(f783(x19583,x19584,x19585,x19586,x19581),f783(x19583,x19584,x19585,x19586,x19582)) % 183.90/184.46 [1959]~E(x19591,x19592)+E(f564(x19591,x19593),f564(x19592,x19593)) % 183.90/184.46 [1960]~E(x19601,x19602)+E(f564(x19603,x19601),f564(x19603,x19602)) % 183.90/184.46 [1961]~E(x19611,x19612)+E(f630(x19611,x19613),f630(x19612,x19613)) % 183.90/184.46 [1962]~E(x19621,x19622)+E(f630(x19623,x19621),f630(x19623,x19622)) % 183.90/184.46 [1963]~E(x19631,x19632)+E(f616(x19631,x19633,x19634),f616(x19632,x19633,x19634)) % 183.90/184.46 [1964]~E(x19641,x19642)+E(f616(x19643,x19641,x19644),f616(x19643,x19642,x19644)) % 183.90/184.46 [1965]~E(x19651,x19652)+E(f616(x19653,x19654,x19651),f616(x19653,x19654,x19652)) % 183.90/184.46 [1966]~E(x19661,x19662)+E(f97(x19661,x19663,x19664,x19665),f97(x19662,x19663,x19664,x19665)) % 183.90/184.46 [1967]~E(x19671,x19672)+E(f97(x19673,x19671,x19674,x19675),f97(x19673,x19672,x19674,x19675)) % 183.90/184.46 [1968]~E(x19681,x19682)+E(f97(x19683,x19684,x19681,x19685),f97(x19683,x19684,x19682,x19685)) % 183.90/184.46 [1969]~E(x19691,x19692)+E(f97(x19693,x19694,x19695,x19691),f97(x19693,x19694,x19695,x19692)) % 183.90/184.46 [1970]~E(x19701,x19702)+E(f234(x19701,x19703,x19704,x19705),f234(x19702,x19703,x19704,x19705)) % 183.90/184.46 [1971]~E(x19711,x19712)+E(f234(x19713,x19711,x19714,x19715),f234(x19713,x19712,x19714,x19715)) % 183.90/184.46 [1972]~E(x19721,x19722)+E(f234(x19723,x19724,x19721,x19725),f234(x19723,x19724,x19722,x19725)) % 183.90/184.46 [1973]~E(x19731,x19732)+E(f234(x19733,x19734,x19735,x19731),f234(x19733,x19734,x19735,x19732)) % 183.90/184.46 [1974]~E(x19741,x19742)+E(f761(x19741,x19743),f761(x19742,x19743)) % 183.90/184.46 [1975]~E(x19751,x19752)+E(f761(x19753,x19751),f761(x19753,x19752)) % 183.90/184.46 [1976]~E(x19761,x19762)+E(f358(x19761,x19763),f358(x19762,x19763)) % 183.90/184.46 [1977]~E(x19771,x19772)+E(f358(x19773,x19771),f358(x19773,x19772)) % 183.90/184.46 [1978]~E(x19781,x19782)+E(f549(x19781,x19783,x19784),f549(x19782,x19783,x19784)) % 183.90/184.46 [1979]~E(x19791,x19792)+E(f549(x19793,x19791,x19794),f549(x19793,x19792,x19794)) % 183.90/184.46 [1980]~E(x19801,x19802)+E(f549(x19803,x19804,x19801),f549(x19803,x19804,x19802)) % 183.90/184.46 [1981]~E(x19811,x19812)+E(f379(x19811,x19813,x19814,x19815,x19816),f379(x19812,x19813,x19814,x19815,x19816)) % 183.90/184.46 [1982]~E(x19821,x19822)+E(f379(x19823,x19821,x19824,x19825,x19826),f379(x19823,x19822,x19824,x19825,x19826)) % 183.90/184.46 [1983]~E(x19831,x19832)+E(f379(x19833,x19834,x19831,x19835,x19836),f379(x19833,x19834,x19832,x19835,x19836)) % 183.90/184.46 [1984]~E(x19841,x19842)+E(f379(x19843,x19844,x19845,x19841,x19846),f379(x19843,x19844,x19845,x19842,x19846)) % 183.90/184.46 [1985]~E(x19851,x19852)+E(f379(x19853,x19854,x19855,x19856,x19851),f379(x19853,x19854,x19855,x19856,x19852)) % 183.90/184.46 [1986]~E(x19861,x19862)+E(f693(x19861,x19863,x19864,x19865),f693(x19862,x19863,x19864,x19865)) % 183.90/184.46 [1987]~E(x19871,x19872)+E(f693(x19873,x19871,x19874,x19875),f693(x19873,x19872,x19874,x19875)) % 183.90/184.46 [1988]~E(x19881,x19882)+E(f693(x19883,x19884,x19881,x19885),f693(x19883,x19884,x19882,x19885)) % 183.90/184.46 [1989]~E(x19891,x19892)+E(f693(x19893,x19894,x19895,x19891),f693(x19893,x19894,x19895,x19892)) % 183.90/184.46 [1990]~E(x19901,x19902)+E(f611(x19901,x19903,x19904,x19905,x19906,x19907),f611(x19902,x19903,x19904,x19905,x19906,x19907)) % 183.90/184.46 [1991]~E(x19911,x19912)+E(f611(x19913,x19911,x19914,x19915,x19916,x19917),f611(x19913,x19912,x19914,x19915,x19916,x19917)) % 183.90/184.46 [1992]~E(x19921,x19922)+E(f611(x19923,x19924,x19921,x19925,x19926,x19927),f611(x19923,x19924,x19922,x19925,x19926,x19927)) % 183.90/184.46 [1993]~E(x19931,x19932)+E(f611(x19933,x19934,x19935,x19931,x19936,x19937),f611(x19933,x19934,x19935,x19932,x19936,x19937)) % 183.90/184.46 [1994]~E(x19941,x19942)+E(f611(x19943,x19944,x19945,x19946,x19941,x19947),f611(x19943,x19944,x19945,x19946,x19942,x19947)) % 183.90/184.46 [1995]~E(x19951,x19952)+E(f611(x19953,x19954,x19955,x19956,x19957,x19951),f611(x19953,x19954,x19955,x19956,x19957,x19952)) % 183.90/184.46 [1996]~E(x19961,x19962)+E(f772(x19961,x19963,x19964,x19965,x19966,x19967,x19968,x19969),f772(x19962,x19963,x19964,x19965,x19966,x19967,x19968,x19969)) % 183.90/184.46 [1997]~E(x19971,x19972)+E(f772(x19973,x19971,x19974,x19975,x19976,x19977,x19978,x19979),f772(x19973,x19972,x19974,x19975,x19976,x19977,x19978,x19979)) % 183.90/184.46 [1998]~E(x19981,x19982)+E(f772(x19983,x19984,x19981,x19985,x19986,x19987,x19988,x19989),f772(x19983,x19984,x19982,x19985,x19986,x19987,x19988,x19989)) % 183.90/184.46 [1999]~E(x19991,x19992)+E(f772(x19993,x19994,x19995,x19991,x19996,x19997,x19998,x19999),f772(x19993,x19994,x19995,x19992,x19996,x19997,x19998,x19999)) % 183.90/184.46 [2000]~E(x20001,x20002)+E(f772(x20003,x20004,x20005,x20006,x20001,x20007,x20008,x20009),f772(x20003,x20004,x20005,x20006,x20002,x20007,x20008,x20009)) % 183.90/184.46 [2001]~E(x20011,x20012)+E(f772(x20013,x20014,x20015,x20016,x20017,x20011,x20018,x20019),f772(x20013,x20014,x20015,x20016,x20017,x20012,x20018,x20019)) % 183.90/184.46 [2002]~E(x20021,x20022)+E(f772(x20023,x20024,x20025,x20026,x20027,x20028,x20021,x20029),f772(x20023,x20024,x20025,x20026,x20027,x20028,x20022,x20029)) % 183.90/184.46 [2003]~E(x20031,x20032)+E(f772(x20033,x20034,x20035,x20036,x20037,x20038,x20039,x20031),f772(x20033,x20034,x20035,x20036,x20037,x20038,x20039,x20032)) % 183.90/184.46 [2004]~E(x20041,x20042)+E(f132(x20041,x20043,x20044,x20045),f132(x20042,x20043,x20044,x20045)) % 183.90/184.46 [2005]~E(x20051,x20052)+E(f132(x20053,x20051,x20054,x20055),f132(x20053,x20052,x20054,x20055)) % 183.90/184.46 [2006]~E(x20061,x20062)+E(f132(x20063,x20064,x20061,x20065),f132(x20063,x20064,x20062,x20065)) % 183.90/184.46 [2007]~E(x20071,x20072)+E(f132(x20073,x20074,x20075,x20071),f132(x20073,x20074,x20075,x20072)) % 183.90/184.46 [2008]~E(x20081,x20082)+E(f639(x20081,x20083,x20084,x20085,x20086),f639(x20082,x20083,x20084,x20085,x20086)) % 183.90/184.46 [2009]~E(x20091,x20092)+E(f639(x20093,x20091,x20094,x20095,x20096),f639(x20093,x20092,x20094,x20095,x20096)) % 183.90/184.46 [2010]~E(x20101,x20102)+E(f639(x20103,x20104,x20101,x20105,x20106),f639(x20103,x20104,x20102,x20105,x20106)) % 183.90/184.46 [2011]~E(x20111,x20112)+E(f639(x20113,x20114,x20115,x20111,x20116),f639(x20113,x20114,x20115,x20112,x20116)) % 183.90/184.46 [2012]~E(x20121,x20122)+E(f639(x20123,x20124,x20125,x20126,x20121),f639(x20123,x20124,x20125,x20126,x20122)) % 183.90/184.46 [2013]~E(x20131,x20132)+E(f432(x20131,x20133,x20134),f432(x20132,x20133,x20134)) % 183.90/184.46 [2014]~E(x20141,x20142)+E(f432(x20143,x20141,x20144),f432(x20143,x20142,x20144)) % 183.90/184.46 [2015]~E(x20151,x20152)+E(f432(x20153,x20154,x20151),f432(x20153,x20154,x20152)) % 183.90/184.46 [2016]~E(x20161,x20162)+E(f243(x20161,x20163,x20164,x20165,x20166),f243(x20162,x20163,x20164,x20165,x20166)) % 183.90/184.46 [2017]~E(x20171,x20172)+E(f243(x20173,x20171,x20174,x20175,x20176),f243(x20173,x20172,x20174,x20175,x20176)) % 183.90/184.46 [2018]~E(x20181,x20182)+E(f243(x20183,x20184,x20181,x20185,x20186),f243(x20183,x20184,x20182,x20185,x20186)) % 183.90/184.46 [2019]~E(x20191,x20192)+E(f243(x20193,x20194,x20195,x20191,x20196),f243(x20193,x20194,x20195,x20192,x20196)) % 183.90/184.46 [2020]~E(x20201,x20202)+E(f243(x20203,x20204,x20205,x20206,x20201),f243(x20203,x20204,x20205,x20206,x20202)) % 183.90/184.46 [2021]~E(x20211,x20212)+E(f539(x20211,x20213,x20214),f539(x20212,x20213,x20214)) % 183.90/184.46 [2022]~E(x20221,x20222)+E(f539(x20223,x20221,x20224),f539(x20223,x20222,x20224)) % 183.90/184.46 [2023]~E(x20231,x20232)+E(f539(x20233,x20234,x20231),f539(x20233,x20234,x20232)) % 183.90/184.46 [2024]~E(x20241,x20242)+E(f586(x20241,x20243,x20244,x20245,x20246,x20247,x20248,x20249),f586(x20242,x20243,x20244,x20245,x20246,x20247,x20248,x20249)) % 183.90/184.46 [2025]~E(x20251,x20252)+E(f586(x20253,x20251,x20254,x20255,x20256,x20257,x20258,x20259),f586(x20253,x20252,x20254,x20255,x20256,x20257,x20258,x20259)) % 183.90/184.46 [2026]~E(x20261,x20262)+E(f586(x20263,x20264,x20261,x20265,x20266,x20267,x20268,x20269),f586(x20263,x20264,x20262,x20265,x20266,x20267,x20268,x20269)) % 183.90/184.46 [2027]~E(x20271,x20272)+E(f586(x20273,x20274,x20275,x20271,x20276,x20277,x20278,x20279),f586(x20273,x20274,x20275,x20272,x20276,x20277,x20278,x20279)) % 183.90/184.46 [2028]~E(x20281,x20282)+E(f586(x20283,x20284,x20285,x20286,x20281,x20287,x20288,x20289),f586(x20283,x20284,x20285,x20286,x20282,x20287,x20288,x20289)) % 183.90/184.46 [2029]~E(x20291,x20292)+E(f586(x20293,x20294,x20295,x20296,x20297,x20291,x20298,x20299),f586(x20293,x20294,x20295,x20296,x20297,x20292,x20298,x20299)) % 183.90/184.46 [2030]~E(x20301,x20302)+E(f586(x20303,x20304,x20305,x20306,x20307,x20308,x20301,x20309),f586(x20303,x20304,x20305,x20306,x20307,x20308,x20302,x20309)) % 183.90/184.46 [2031]~E(x20311,x20312)+E(f586(x20313,x20314,x20315,x20316,x20317,x20318,x20319,x20311),f586(x20313,x20314,x20315,x20316,x20317,x20318,x20319,x20312)) % 183.90/184.46 [2032]~E(x20321,x20322)+E(f439(x20321,x20323,x20324,x20325),f439(x20322,x20323,x20324,x20325)) % 183.90/184.46 [2033]~E(x20331,x20332)+E(f439(x20333,x20331,x20334,x20335),f439(x20333,x20332,x20334,x20335)) % 183.90/184.46 [2034]~E(x20341,x20342)+E(f439(x20343,x20344,x20341,x20345),f439(x20343,x20344,x20342,x20345)) % 183.90/184.46 [2035]~E(x20351,x20352)+E(f439(x20353,x20354,x20355,x20351),f439(x20353,x20354,x20355,x20352)) % 183.90/184.46 [2036]~E(x20361,x20362)+E(f441(x20361,x20363),f441(x20362,x20363)) % 183.90/184.46 [2037]~E(x20371,x20372)+E(f441(x20373,x20371),f441(x20373,x20372)) % 183.90/184.46 [2038]~E(x20381,x20382)+E(f465(x20381,x20383,x20384),f465(x20382,x20383,x20384)) % 183.90/184.46 [2039]~E(x20391,x20392)+E(f465(x20393,x20391,x20394),f465(x20393,x20392,x20394)) % 183.90/184.46 [2040]~E(x20401,x20402)+E(f465(x20403,x20404,x20401),f465(x20403,x20404,x20402)) % 183.90/184.46 [2041]~E(x20411,x20412)+E(f402(x20411),f402(x20412)) % 183.90/184.46 [2042]~E(x20421,x20422)+E(f98(x20421,x20423,x20424,x20425),f98(x20422,x20423,x20424,x20425)) % 183.90/184.46 [2043]~E(x20431,x20432)+E(f98(x20433,x20431,x20434,x20435),f98(x20433,x20432,x20434,x20435)) % 183.90/184.46 [2044]~E(x20441,x20442)+E(f98(x20443,x20444,x20441,x20445),f98(x20443,x20444,x20442,x20445)) % 183.90/184.46 [2045]~E(x20451,x20452)+E(f98(x20453,x20454,x20455,x20451),f98(x20453,x20454,x20455,x20452)) % 183.90/184.46 [2046]~E(x20461,x20462)+E(f350(x20461,x20463,x20464,x20465,x20466),f350(x20462,x20463,x20464,x20465,x20466)) % 183.90/184.46 [2047]~E(x20471,x20472)+E(f350(x20473,x20471,x20474,x20475,x20476),f350(x20473,x20472,x20474,x20475,x20476)) % 183.90/184.46 [2048]~E(x20481,x20482)+E(f350(x20483,x20484,x20481,x20485,x20486),f350(x20483,x20484,x20482,x20485,x20486)) % 183.90/184.46 [2049]~E(x20491,x20492)+E(f350(x20493,x20494,x20495,x20491,x20496),f350(x20493,x20494,x20495,x20492,x20496)) % 183.90/184.46 [2050]~E(x20501,x20502)+E(f350(x20503,x20504,x20505,x20506,x20501),f350(x20503,x20504,x20505,x20506,x20502)) % 183.90/184.46 [2051]~E(x20511,x20512)+E(f594(x20511,x20513,x20514),f594(x20512,x20513,x20514)) % 183.90/184.46 [2052]~E(x20521,x20522)+E(f594(x20523,x20521,x20524),f594(x20523,x20522,x20524)) % 183.90/184.46 [2053]~E(x20531,x20532)+E(f594(x20533,x20534,x20531),f594(x20533,x20534,x20532)) % 183.90/184.46 [2054]~E(x20541,x20542)+E(f701(x20541,x20543,x20544,x20545),f701(x20542,x20543,x20544,x20545)) % 183.90/184.46 [2055]~E(x20551,x20552)+E(f701(x20553,x20551,x20554,x20555),f701(x20553,x20552,x20554,x20555)) % 183.90/184.46 [2056]~E(x20561,x20562)+E(f701(x20563,x20564,x20561,x20565),f701(x20563,x20564,x20562,x20565)) % 183.90/184.46 [2057]~E(x20571,x20572)+E(f701(x20573,x20574,x20575,x20571),f701(x20573,x20574,x20575,x20572)) % 183.90/184.46 [2058]~E(x20581,x20582)+E(f411(x20581,x20583),f411(x20582,x20583)) % 183.90/184.46 [2059]~E(x20591,x20592)+E(f411(x20593,x20591),f411(x20593,x20592)) % 183.90/184.46 [2060]~E(x20601,x20602)+E(f410(x20601,x20603),f410(x20602,x20603)) % 183.90/184.46 [2061]~E(x20611,x20612)+E(f410(x20613,x20611),f410(x20613,x20612)) % 183.90/184.46 [2062]~E(x20621,x20622)+E(f810(x20621,x20623,x20624,x20625),f810(x20622,x20623,x20624,x20625)) % 183.90/184.46 [2063]~E(x20631,x20632)+E(f810(x20633,x20631,x20634,x20635),f810(x20633,x20632,x20634,x20635)) % 183.90/184.46 [2064]~E(x20641,x20642)+E(f810(x20643,x20644,x20641,x20645),f810(x20643,x20644,x20642,x20645)) % 183.90/184.46 [2065]~E(x20651,x20652)+E(f810(x20653,x20654,x20655,x20651),f810(x20653,x20654,x20655,x20652)) % 183.90/184.46 [2066]~E(x20661,x20662)+E(f654(x20661,x20663,x20664),f654(x20662,x20663,x20664)) % 183.90/184.46 [2067]~E(x20671,x20672)+E(f654(x20673,x20671,x20674),f654(x20673,x20672,x20674)) % 183.90/184.46 [2068]~E(x20681,x20682)+E(f654(x20683,x20684,x20681),f654(x20683,x20684,x20682)) % 183.90/184.46 [2069]~E(x20691,x20692)+E(f559(x20691,x20693),f559(x20692,x20693)) % 183.90/184.46 [2070]~E(x20701,x20702)+E(f559(x20703,x20701),f559(x20703,x20702)) % 183.90/184.46 [2071]~E(x20711,x20712)+E(f750(x20711,x20713,x20714,x20715,x20716),f750(x20712,x20713,x20714,x20715,x20716)) % 183.90/184.46 [2072]~E(x20721,x20722)+E(f750(x20723,x20721,x20724,x20725,x20726),f750(x20723,x20722,x20724,x20725,x20726)) % 183.90/184.46 [2073]~E(x20731,x20732)+E(f750(x20733,x20734,x20731,x20735,x20736),f750(x20733,x20734,x20732,x20735,x20736)) % 183.90/184.46 [2074]~E(x20741,x20742)+E(f750(x20743,x20744,x20745,x20741,x20746),f750(x20743,x20744,x20745,x20742,x20746)) % 183.90/184.46 [2075]~E(x20751,x20752)+E(f750(x20753,x20754,x20755,x20756,x20751),f750(x20753,x20754,x20755,x20756,x20752)) % 183.90/184.46 [2076]~E(x20761,x20762)+E(f649(x20761,x20763,x20764,x20765,x20766),f649(x20762,x20763,x20764,x20765,x20766)) % 183.90/184.46 [2077]~E(x20771,x20772)+E(f649(x20773,x20771,x20774,x20775,x20776),f649(x20773,x20772,x20774,x20775,x20776)) % 183.90/184.46 [2078]~E(x20781,x20782)+E(f649(x20783,x20784,x20781,x20785,x20786),f649(x20783,x20784,x20782,x20785,x20786)) % 183.90/184.46 [2079]~E(x20791,x20792)+E(f649(x20793,x20794,x20795,x20791,x20796),f649(x20793,x20794,x20795,x20792,x20796)) % 183.90/184.46 [2080]~E(x20801,x20802)+E(f649(x20803,x20804,x20805,x20806,x20801),f649(x20803,x20804,x20805,x20806,x20802)) % 183.90/184.46 [2081]~E(x20811,x20812)+E(f577(x20811,x20813,x20814,x20815),f577(x20812,x20813,x20814,x20815)) % 183.90/184.46 [2082]~E(x20821,x20822)+E(f577(x20823,x20821,x20824,x20825),f577(x20823,x20822,x20824,x20825)) % 183.90/184.46 [2083]~E(x20831,x20832)+E(f577(x20833,x20834,x20831,x20835),f577(x20833,x20834,x20832,x20835)) % 183.90/184.46 [2084]~E(x20841,x20842)+E(f577(x20843,x20844,x20845,x20841),f577(x20843,x20844,x20845,x20842)) % 183.90/184.46 [2085]~E(x20851,x20852)+E(f741(x20851,x20853,x20854),f741(x20852,x20853,x20854)) % 183.90/184.46 [2086]~E(x20861,x20862)+E(f741(x20863,x20861,x20864),f741(x20863,x20862,x20864)) % 183.90/184.46 [2087]~E(x20871,x20872)+E(f741(x20873,x20874,x20871),f741(x20873,x20874,x20872)) % 183.90/184.46 [2088]~E(x20881,x20882)+E(f579(x20881,x20883,x20884,x20885,x20886,x20887),f579(x20882,x20883,x20884,x20885,x20886,x20887)) % 183.90/184.46 [2089]~E(x20891,x20892)+E(f579(x20893,x20891,x20894,x20895,x20896,x20897),f579(x20893,x20892,x20894,x20895,x20896,x20897)) % 183.90/184.46 [2090]~E(x20901,x20902)+E(f579(x20903,x20904,x20901,x20905,x20906,x20907),f579(x20903,x20904,x20902,x20905,x20906,x20907)) % 183.90/184.46 [2091]~E(x20911,x20912)+E(f579(x20913,x20914,x20915,x20911,x20916,x20917),f579(x20913,x20914,x20915,x20912,x20916,x20917)) % 183.90/184.46 [2092]~E(x20921,x20922)+E(f579(x20923,x20924,x20925,x20926,x20921,x20927),f579(x20923,x20924,x20925,x20926,x20922,x20927)) % 183.90/184.46 [2093]~E(x20931,x20932)+E(f579(x20933,x20934,x20935,x20936,x20937,x20931),f579(x20933,x20934,x20935,x20936,x20937,x20932)) % 183.90/184.46 [2094]~E(x20941,x20942)+E(f642(x20941,x20943,x20944,x20945),f642(x20942,x20943,x20944,x20945)) % 183.90/184.46 [2095]~E(x20951,x20952)+E(f642(x20953,x20951,x20954,x20955),f642(x20953,x20952,x20954,x20955)) % 183.90/184.46 [2096]~E(x20961,x20962)+E(f642(x20963,x20964,x20961,x20965),f642(x20963,x20964,x20962,x20965)) % 183.90/184.46 [2097]~E(x20971,x20972)+E(f642(x20973,x20974,x20975,x20971),f642(x20973,x20974,x20975,x20972)) % 183.90/184.46 [2098]~E(x20981,x20982)+E(f260(x20981,x20983,x20984),f260(x20982,x20983,x20984)) % 183.90/184.46 [2099]~E(x20991,x20992)+E(f260(x20993,x20991,x20994),f260(x20993,x20992,x20994)) % 183.90/184.46 [2100]~E(x21001,x21002)+E(f260(x21003,x21004,x21001),f260(x21003,x21004,x21002)) % 183.90/184.46 [2101]~E(x21011,x21012)+E(f782(x21011,x21013,x21014,x21015,x21016),f782(x21012,x21013,x21014,x21015,x21016)) % 183.90/184.46 [2102]~E(x21021,x21022)+E(f782(x21023,x21021,x21024,x21025,x21026),f782(x21023,x21022,x21024,x21025,x21026)) % 183.90/184.46 [2103]~E(x21031,x21032)+E(f782(x21033,x21034,x21031,x21035,x21036),f782(x21033,x21034,x21032,x21035,x21036)) % 183.90/184.46 [2104]~E(x21041,x21042)+E(f782(x21043,x21044,x21045,x21041,x21046),f782(x21043,x21044,x21045,x21042,x21046)) % 183.90/184.46 [2105]~E(x21051,x21052)+E(f782(x21053,x21054,x21055,x21056,x21051),f782(x21053,x21054,x21055,x21056,x21052)) % 183.90/184.46 [2106]~E(x21061,x21062)+E(f699(x21061,x21063,x21064,x21065,x21066),f699(x21062,x21063,x21064,x21065,x21066)) % 183.90/184.46 [2107]~E(x21071,x21072)+E(f699(x21073,x21071,x21074,x21075,x21076),f699(x21073,x21072,x21074,x21075,x21076)) % 183.90/184.46 [2108]~E(x21081,x21082)+E(f699(x21083,x21084,x21081,x21085,x21086),f699(x21083,x21084,x21082,x21085,x21086)) % 183.90/184.46 [2109]~E(x21091,x21092)+E(f699(x21093,x21094,x21095,x21091,x21096),f699(x21093,x21094,x21095,x21092,x21096)) % 183.90/184.46 [2110]~E(x21101,x21102)+E(f699(x21103,x21104,x21105,x21106,x21101),f699(x21103,x21104,x21105,x21106,x21102)) % 183.90/184.46 [2111]~E(x21111,x21112)+E(f95(x21111,x21113,x21114,x21115),f95(x21112,x21113,x21114,x21115)) % 183.90/184.46 [2112]~E(x21121,x21122)+E(f95(x21123,x21121,x21124,x21125),f95(x21123,x21122,x21124,x21125)) % 183.90/184.46 [2113]~E(x21131,x21132)+E(f95(x21133,x21134,x21131,x21135),f95(x21133,x21134,x21132,x21135)) % 183.90/184.46 [2114]~E(x21141,x21142)+E(f95(x21143,x21144,x21145,x21141),f95(x21143,x21144,x21145,x21142)) % 183.90/184.46 [2115]~E(x21151,x21152)+E(f691(x21151,x21153),f691(x21152,x21153)) % 183.90/184.46 [2116]~E(x21161,x21162)+E(f691(x21163,x21161),f691(x21163,x21162)) % 183.90/184.46 [2117]~E(x21171,x21172)+E(f698(x21171,x21173,x21174,x21175,x21176),f698(x21172,x21173,x21174,x21175,x21176)) % 183.90/184.46 [2118]~E(x21181,x21182)+E(f698(x21183,x21181,x21184,x21185,x21186),f698(x21183,x21182,x21184,x21185,x21186)) % 183.90/184.46 [2119]~E(x21191,x21192)+E(f698(x21193,x21194,x21191,x21195,x21196),f698(x21193,x21194,x21192,x21195,x21196)) % 183.90/184.46 [2120]~E(x21201,x21202)+E(f698(x21203,x21204,x21205,x21201,x21206),f698(x21203,x21204,x21205,x21202,x21206)) % 183.90/184.46 [2121]~E(x21211,x21212)+E(f698(x21213,x21214,x21215,x21216,x21211),f698(x21213,x21214,x21215,x21216,x21212)) % 183.90/184.46 [2122]~E(x21221,x21222)+E(f67(x21221,x21223,x21224),f67(x21222,x21223,x21224)) % 183.90/184.46 [2123]~E(x21231,x21232)+E(f67(x21233,x21231,x21234),f67(x21233,x21232,x21234)) % 183.90/184.46 [2124]~E(x21241,x21242)+E(f67(x21243,x21244,x21241),f67(x21243,x21244,x21242)) % 183.90/184.46 [2125]~E(x21251,x21252)+E(f607(x21251,x21253,x21254),f607(x21252,x21253,x21254)) % 183.90/184.46 [2126]~E(x21261,x21262)+E(f607(x21263,x21261,x21264),f607(x21263,x21262,x21264)) % 183.90/184.46 [2127]~E(x21271,x21272)+E(f607(x21273,x21274,x21271),f607(x21273,x21274,x21272)) % 183.90/184.46 [2128]~E(x21281,x21282)+E(f488(x21281,x21283,x21284),f488(x21282,x21283,x21284)) % 183.90/184.46 [2129]~E(x21291,x21292)+E(f488(x21293,x21291,x21294),f488(x21293,x21292,x21294)) % 183.90/184.46 [2130]~E(x21301,x21302)+E(f488(x21303,x21304,x21301),f488(x21303,x21304,x21302)) % 183.90/184.46 [2131]~E(x21311,x21312)+E(f729(x21311,x21313),f729(x21312,x21313)) % 183.90/184.46 [2132]~E(x21321,x21322)+E(f729(x21323,x21321),f729(x21323,x21322)) % 183.90/184.46 [2133]~E(x21331,x21332)+E(f370(x21331,x21333,x21334,x21335,x21336),f370(x21332,x21333,x21334,x21335,x21336)) % 183.90/184.46 [2134]~E(x21341,x21342)+E(f370(x21343,x21341,x21344,x21345,x21346),f370(x21343,x21342,x21344,x21345,x21346)) % 183.90/184.46 [2135]~E(x21351,x21352)+E(f370(x21353,x21354,x21351,x21355,x21356),f370(x21353,x21354,x21352,x21355,x21356)) % 183.90/184.46 [2136]~E(x21361,x21362)+E(f370(x21363,x21364,x21365,x21361,x21366),f370(x21363,x21364,x21365,x21362,x21366)) % 183.90/184.46 [2137]~E(x21371,x21372)+E(f370(x21373,x21374,x21375,x21376,x21371),f370(x21373,x21374,x21375,x21376,x21372)) % 183.90/184.46 [2138]~E(x21381,x21382)+E(f538(x21381,x21383),f538(x21382,x21383)) % 183.90/184.46 [2139]~E(x21391,x21392)+E(f538(x21393,x21391),f538(x21393,x21392)) % 183.90/184.46 [2140]~E(x21401,x21402)+E(f417(x21401,x21403,x21404),f417(x21402,x21403,x21404)) % 183.90/184.46 [2141]~E(x21411,x21412)+E(f417(x21413,x21411,x21414),f417(x21413,x21412,x21414)) % 183.90/184.46 [2142]~E(x21421,x21422)+E(f417(x21423,x21424,x21421),f417(x21423,x21424,x21422)) % 183.90/184.46 [2143]~E(x21431,x21432)+E(f619(x21431,x21433,x21434),f619(x21432,x21433,x21434)) % 183.90/184.46 [2144]~E(x21441,x21442)+E(f619(x21443,x21441,x21444),f619(x21443,x21442,x21444)) % 183.90/184.46 [2145]~E(x21451,x21452)+E(f619(x21453,x21454,x21451),f619(x21453,x21454,x21452)) % 183.90/184.46 [2146]~E(x21461,x21462)+E(f811(x21461,x21463,x21464,x21465),f811(x21462,x21463,x21464,x21465)) % 183.90/184.46 [2147]~E(x21471,x21472)+E(f811(x21473,x21471,x21474,x21475),f811(x21473,x21472,x21474,x21475)) % 183.90/184.46 [2148]~E(x21481,x21482)+E(f811(x21483,x21484,x21481,x21485),f811(x21483,x21484,x21482,x21485)) % 183.90/184.46 [2149]~E(x21491,x21492)+E(f811(x21493,x21494,x21495,x21491),f811(x21493,x21494,x21495,x21492)) % 183.90/184.46 [2150]~E(x21501,x21502)+E(f670(x21501,x21503,x21504,x21505,x21506),f670(x21502,x21503,x21504,x21505,x21506)) % 183.90/184.46 [2151]~E(x21511,x21512)+E(f670(x21513,x21511,x21514,x21515,x21516),f670(x21513,x21512,x21514,x21515,x21516)) % 183.90/184.46 [2152]~E(x21521,x21522)+E(f670(x21523,x21524,x21521,x21525,x21526),f670(x21523,x21524,x21522,x21525,x21526)) % 183.90/184.46 [2153]~E(x21531,x21532)+E(f670(x21533,x21534,x21535,x21531,x21536),f670(x21533,x21534,x21535,x21532,x21536)) % 183.90/184.46 [2154]~E(x21541,x21542)+E(f670(x21543,x21544,x21545,x21546,x21541),f670(x21543,x21544,x21545,x21546,x21542)) % 183.90/184.46 [2155]~E(x21551,x21552)+E(f456(x21551,x21553,x21554,x21555),f456(x21552,x21553,x21554,x21555)) % 183.90/184.46 [2156]~E(x21561,x21562)+E(f456(x21563,x21561,x21564,x21565),f456(x21563,x21562,x21564,x21565)) % 183.90/184.46 [2157]~E(x21571,x21572)+E(f456(x21573,x21574,x21571,x21575),f456(x21573,x21574,x21572,x21575)) % 183.90/184.46 [2158]~E(x21581,x21582)+E(f456(x21583,x21584,x21585,x21581),f456(x21583,x21584,x21585,x21582)) % 183.90/184.46 [2159]~E(x21591,x21592)+E(f373(x21591),f373(x21592)) % 183.90/184.46 [2160]~E(x21601,x21602)+E(f450(x21601,x21603,x21604,x21605,x21606),f450(x21602,x21603,x21604,x21605,x21606)) % 183.90/184.46 [2161]~E(x21611,x21612)+E(f450(x21613,x21611,x21614,x21615,x21616),f450(x21613,x21612,x21614,x21615,x21616)) % 183.90/184.46 [2162]~E(x21621,x21622)+E(f450(x21623,x21624,x21621,x21625,x21626),f450(x21623,x21624,x21622,x21625,x21626)) % 183.90/184.46 [2163]~E(x21631,x21632)+E(f450(x21633,x21634,x21635,x21631,x21636),f450(x21633,x21634,x21635,x21632,x21636)) % 183.90/184.46 [2164]~E(x21641,x21642)+E(f450(x21643,x21644,x21645,x21646,x21641),f450(x21643,x21644,x21645,x21646,x21642)) % 183.90/184.46 [2165]~E(x21651,x21652)+E(f393(x21651,x21653,x21654),f393(x21652,x21653,x21654)) % 183.90/184.46 [2166]~E(x21661,x21662)+E(f393(x21663,x21661,x21664),f393(x21663,x21662,x21664)) % 183.90/184.46 [2167]~E(x21671,x21672)+E(f393(x21673,x21674,x21671),f393(x21673,x21674,x21672)) % 183.90/184.46 [2168]~E(x21681,x21682)+E(f561(x21681,x21683,x21684,x21685,x21686),f561(x21682,x21683,x21684,x21685,x21686)) % 183.90/184.46 [2169]~E(x21691,x21692)+E(f561(x21693,x21691,x21694,x21695,x21696),f561(x21693,x21692,x21694,x21695,x21696)) % 183.90/184.46 [2170]~E(x21701,x21702)+E(f561(x21703,x21704,x21701,x21705,x21706),f561(x21703,x21704,x21702,x21705,x21706)) % 183.90/184.46 [2171]~E(x21711,x21712)+E(f561(x21713,x21714,x21715,x21711,x21716),f561(x21713,x21714,x21715,x21712,x21716)) % 183.90/184.46 [2172]~E(x21721,x21722)+E(f561(x21723,x21724,x21725,x21726,x21721),f561(x21723,x21724,x21725,x21726,x21722)) % 183.90/184.46 [2173]~E(x21731,x21732)+E(f349(x21731,x21733,x21734,x21735),f349(x21732,x21733,x21734,x21735)) % 183.90/184.46 [2174]~E(x21741,x21742)+E(f349(x21743,x21741,x21744,x21745),f349(x21743,x21742,x21744,x21745)) % 183.90/184.46 [2175]~E(x21751,x21752)+E(f349(x21753,x21754,x21751,x21755),f349(x21753,x21754,x21752,x21755)) % 183.90/184.46 [2176]~E(x21761,x21762)+E(f349(x21763,x21764,x21765,x21761),f349(x21763,x21764,x21765,x21762)) % 183.90/184.46 [2177]~E(x21771,x21772)+E(f550(x21771,x21773,x21774),f550(x21772,x21773,x21774)) % 183.90/184.46 [2178]~E(x21781,x21782)+E(f550(x21783,x21781,x21784),f550(x21783,x21782,x21784)) % 183.90/184.46 [2179]~E(x21791,x21792)+E(f550(x21793,x21794,x21791),f550(x21793,x21794,x21792)) % 183.90/184.46 [2180]~E(x21801,x21802)+E(f731(x21801,x21803,x21804,x21805),f731(x21802,x21803,x21804,x21805)) % 183.90/184.46 [2181]~E(x21811,x21812)+E(f731(x21813,x21811,x21814,x21815),f731(x21813,x21812,x21814,x21815)) % 183.90/184.46 [2182]~E(x21821,x21822)+E(f731(x21823,x21824,x21821,x21825),f731(x21823,x21824,x21822,x21825)) % 183.90/184.46 [2183]~E(x21831,x21832)+E(f731(x21833,x21834,x21835,x21831),f731(x21833,x21834,x21835,x21832)) % 183.90/184.46 [2184]~E(x21841,x21842)+E(f618(x21841,x21843,x21844,x21845,x21846,x21847),f618(x21842,x21843,x21844,x21845,x21846,x21847)) % 183.90/184.46 [2185]~E(x21851,x21852)+E(f618(x21853,x21851,x21854,x21855,x21856,x21857),f618(x21853,x21852,x21854,x21855,x21856,x21857)) % 183.90/184.46 [2186]~E(x21861,x21862)+E(f618(x21863,x21864,x21861,x21865,x21866,x21867),f618(x21863,x21864,x21862,x21865,x21866,x21867)) % 183.90/184.46 [2187]~E(x21871,x21872)+E(f618(x21873,x21874,x21875,x21871,x21876,x21877),f618(x21873,x21874,x21875,x21872,x21876,x21877)) % 183.90/184.46 [2188]~E(x21881,x21882)+E(f618(x21883,x21884,x21885,x21886,x21881,x21887),f618(x21883,x21884,x21885,x21886,x21882,x21887)) % 183.90/184.46 [2189]~E(x21891,x21892)+E(f618(x21893,x21894,x21895,x21896,x21897,x21891),f618(x21893,x21894,x21895,x21896,x21897,x21892)) % 183.90/184.46 [2190]~E(x21901,x21902)+E(f767(x21901,x21903,x21904,x21905,x21906,x21907),f767(x21902,x21903,x21904,x21905,x21906,x21907)) % 183.90/184.46 [2191]~E(x21911,x21912)+E(f767(x21913,x21911,x21914,x21915,x21916,x21917),f767(x21913,x21912,x21914,x21915,x21916,x21917)) % 183.90/184.46 [2192]~E(x21921,x21922)+E(f767(x21923,x21924,x21921,x21925,x21926,x21927),f767(x21923,x21924,x21922,x21925,x21926,x21927)) % 183.90/184.46 [2193]~E(x21931,x21932)+E(f767(x21933,x21934,x21935,x21931,x21936,x21937),f767(x21933,x21934,x21935,x21932,x21936,x21937)) % 183.90/184.46 [2194]~E(x21941,x21942)+E(f767(x21943,x21944,x21945,x21946,x21941,x21947),f767(x21943,x21944,x21945,x21946,x21942,x21947)) % 183.90/184.46 [2195]~E(x21951,x21952)+E(f767(x21953,x21954,x21955,x21956,x21957,x21951),f767(x21953,x21954,x21955,x21956,x21957,x21952)) % 183.90/184.46 [2196]~E(x21961,x21962)+E(f428(x21961,x21963,x21964,x21965),f428(x21962,x21963,x21964,x21965)) % 183.90/184.46 [2197]~E(x21971,x21972)+E(f428(x21973,x21971,x21974,x21975),f428(x21973,x21972,x21974,x21975)) % 183.90/184.46 [2198]~E(x21981,x21982)+E(f428(x21983,x21984,x21981,x21985),f428(x21983,x21984,x21982,x21985)) % 183.90/184.46 [2199]~E(x21991,x21992)+E(f428(x21993,x21994,x21995,x21991),f428(x21993,x21994,x21995,x21992)) % 183.90/184.46 [2200]~E(x22001,x22002)+E(f514(x22001,x22003,x22004),f514(x22002,x22003,x22004)) % 183.90/184.46 [2201]~E(x22011,x22012)+E(f514(x22013,x22011,x22014),f514(x22013,x22012,x22014)) % 183.90/184.46 [2202]~E(x22021,x22022)+E(f514(x22023,x22024,x22021),f514(x22023,x22024,x22022)) % 183.90/184.46 [2203]~E(x22031,x22032)+E(f709(x22031,x22033,x22034),f709(x22032,x22033,x22034)) % 183.90/184.46 [2204]~E(x22041,x22042)+E(f709(x22043,x22041,x22044),f709(x22043,x22042,x22044)) % 183.90/184.46 [2205]~E(x22051,x22052)+E(f709(x22053,x22054,x22051),f709(x22053,x22054,x22052)) % 183.90/184.46 [2206]~E(x22061,x22062)+E(f791(x22061,x22063,x22064),f791(x22062,x22063,x22064)) % 183.90/184.46 [2207]~E(x22071,x22072)+E(f791(x22073,x22071,x22074),f791(x22073,x22072,x22074)) % 183.90/184.46 [2208]~E(x22081,x22082)+E(f791(x22083,x22084,x22081),f791(x22083,x22084,x22082)) % 183.90/184.46 [2209]~E(x22091,x22092)+E(f425(x22091,x22093,x22094,x22095),f425(x22092,x22093,x22094,x22095)) % 183.90/184.46 [2210]~E(x22101,x22102)+E(f425(x22103,x22101,x22104,x22105),f425(x22103,x22102,x22104,x22105)) % 183.90/184.46 [2211]~E(x22111,x22112)+E(f425(x22113,x22114,x22111,x22115),f425(x22113,x22114,x22112,x22115)) % 183.90/184.46 [2212]~E(x22121,x22122)+E(f425(x22123,x22124,x22125,x22121),f425(x22123,x22124,x22125,x22122)) % 183.90/184.46 [2213]~E(x22131,x22132)+E(f596(x22131),f596(x22132)) % 183.90/184.46 [2214]~E(x22141,x22142)+E(f301(x22141,x22143,x22144,x22145,x22146),f301(x22142,x22143,x22144,x22145,x22146)) % 183.90/184.46 [2215]~E(x22151,x22152)+E(f301(x22153,x22151,x22154,x22155,x22156),f301(x22153,x22152,x22154,x22155,x22156)) % 183.90/184.46 [2216]~E(x22161,x22162)+E(f301(x22163,x22164,x22161,x22165,x22166),f301(x22163,x22164,x22162,x22165,x22166)) % 183.90/184.46 [2217]~E(x22171,x22172)+E(f301(x22173,x22174,x22175,x22171,x22176),f301(x22173,x22174,x22175,x22172,x22176)) % 183.90/184.46 [2218]~E(x22181,x22182)+E(f301(x22183,x22184,x22185,x22186,x22181),f301(x22183,x22184,x22185,x22186,x22182)) % 183.90/184.46 [2219]~E(x22191,x22192)+E(f480(x22191,x22193,x22194,x22195,x22196),f480(x22192,x22193,x22194,x22195,x22196)) % 183.90/184.46 [2220]~E(x22201,x22202)+E(f480(x22203,x22201,x22204,x22205,x22206),f480(x22203,x22202,x22204,x22205,x22206)) % 183.90/184.46 [2221]~E(x22211,x22212)+E(f480(x22213,x22214,x22211,x22215,x22216),f480(x22213,x22214,x22212,x22215,x22216)) % 183.90/184.46 [2222]~E(x22221,x22222)+E(f480(x22223,x22224,x22225,x22221,x22226),f480(x22223,x22224,x22225,x22222,x22226)) % 183.90/184.46 [2223]~E(x22231,x22232)+E(f480(x22233,x22234,x22235,x22236,x22231),f480(x22233,x22234,x22235,x22236,x22232)) % 183.90/184.46 [2224]~E(x22241,x22242)+E(f758(x22241,x22243,x22244,x22245,x22246),f758(x22242,x22243,x22244,x22245,x22246)) % 183.90/184.46 [2225]~E(x22251,x22252)+E(f758(x22253,x22251,x22254,x22255,x22256),f758(x22253,x22252,x22254,x22255,x22256)) % 183.90/184.46 [2226]~E(x22261,x22262)+E(f758(x22263,x22264,x22261,x22265,x22266),f758(x22263,x22264,x22262,x22265,x22266)) % 183.90/184.46 [2227]~E(x22271,x22272)+E(f758(x22273,x22274,x22275,x22271,x22276),f758(x22273,x22274,x22275,x22272,x22276)) % 183.90/184.46 [2228]~E(x22281,x22282)+E(f758(x22283,x22284,x22285,x22286,x22281),f758(x22283,x22284,x22285,x22286,x22282)) % 183.90/184.46 [2229]~E(x22291,x22292)+E(f768(x22291,x22293,x22294,x22295,x22296,x22297,x22298),f768(x22292,x22293,x22294,x22295,x22296,x22297,x22298)) % 183.90/184.46 [2230]~E(x22301,x22302)+E(f768(x22303,x22301,x22304,x22305,x22306,x22307,x22308),f768(x22303,x22302,x22304,x22305,x22306,x22307,x22308)) % 183.90/184.46 [2231]~E(x22311,x22312)+E(f768(x22313,x22314,x22311,x22315,x22316,x22317,x22318),f768(x22313,x22314,x22312,x22315,x22316,x22317,x22318)) % 183.90/184.46 [2232]~E(x22321,x22322)+E(f768(x22323,x22324,x22325,x22321,x22326,x22327,x22328),f768(x22323,x22324,x22325,x22322,x22326,x22327,x22328)) % 183.90/184.46 [2233]~E(x22331,x22332)+E(f768(x22333,x22334,x22335,x22336,x22331,x22337,x22338),f768(x22333,x22334,x22335,x22336,x22332,x22337,x22338)) % 183.90/184.46 [2234]~E(x22341,x22342)+E(f768(x22343,x22344,x22345,x22346,x22347,x22341,x22348),f768(x22343,x22344,x22345,x22346,x22347,x22342,x22348)) % 183.90/184.46 [2235]~E(x22351,x22352)+E(f768(x22353,x22354,x22355,x22356,x22357,x22358,x22351),f768(x22353,x22354,x22355,x22356,x22357,x22358,x22352)) % 183.90/184.46 [2236]~E(x22361,x22362)+E(f721(x22361,x22363,x22364,x22365),f721(x22362,x22363,x22364,x22365)) % 183.90/184.46 [2237]~E(x22371,x22372)+E(f721(x22373,x22371,x22374,x22375),f721(x22373,x22372,x22374,x22375)) % 183.90/184.46 [2238]~E(x22381,x22382)+E(f721(x22383,x22384,x22381,x22385),f721(x22383,x22384,x22382,x22385)) % 183.90/184.46 [2239]~E(x22391,x22392)+E(f721(x22393,x22394,x22395,x22391),f721(x22393,x22394,x22395,x22392)) % 183.90/184.46 [2240]~E(x22401,x22402)+E(f445(x22401,x22403,x22404,x22405),f445(x22402,x22403,x22404,x22405)) % 183.90/184.46 [2241]~E(x22411,x22412)+E(f445(x22413,x22411,x22414,x22415),f445(x22413,x22412,x22414,x22415)) % 183.90/184.46 [2242]~E(x22421,x22422)+E(f445(x22423,x22424,x22421,x22425),f445(x22423,x22424,x22422,x22425)) % 183.90/184.46 [2243]~E(x22431,x22432)+E(f445(x22433,x22434,x22435,x22431),f445(x22433,x22434,x22435,x22432)) % 183.90/184.46 [2244]~E(x22441,x22442)+E(f521(x22441,x22443),f521(x22442,x22443)) % 183.90/184.46 [2245]~E(x22451,x22452)+E(f521(x22453,x22451),f521(x22453,x22452)) % 183.90/184.46 [2246]~E(x22461,x22462)+E(f585(x22461,x22463,x22464,x22465,x22466),f585(x22462,x22463,x22464,x22465,x22466)) % 183.90/184.46 [2247]~E(x22471,x22472)+E(f585(x22473,x22471,x22474,x22475,x22476),f585(x22473,x22472,x22474,x22475,x22476)) % 183.90/184.46 [2248]~E(x22481,x22482)+E(f585(x22483,x22484,x22481,x22485,x22486),f585(x22483,x22484,x22482,x22485,x22486)) % 183.90/184.46 [2249]~E(x22491,x22492)+E(f585(x22493,x22494,x22495,x22491,x22496),f585(x22493,x22494,x22495,x22492,x22496)) % 183.90/184.46 [2250]~E(x22501,x22502)+E(f585(x22503,x22504,x22505,x22506,x22501),f585(x22503,x22504,x22505,x22506,x22502)) % 183.90/184.46 [2251]~E(x22511,x22512)+E(f444(x22511,x22513),f444(x22512,x22513)) % 183.90/184.46 [2252]~E(x22521,x22522)+E(f444(x22523,x22521),f444(x22523,x22522)) % 183.90/184.46 [2253]~E(x22531,x22532)+E(f469(x22531,x22533,x22534),f469(x22532,x22533,x22534)) % 183.90/184.46 [2254]~E(x22541,x22542)+E(f469(x22543,x22541,x22544),f469(x22543,x22542,x22544)) % 183.90/184.46 [2255]~E(x22551,x22552)+E(f469(x22553,x22554,x22551),f469(x22553,x22554,x22552)) % 183.90/184.46 [2256]~E(x22561,x22562)+E(f841(x22561,x22563,x22564,x22565,x22566,x22567,x22568),f841(x22562,x22563,x22564,x22565,x22566,x22567,x22568)) % 183.90/184.46 [2257]~E(x22571,x22572)+E(f841(x22573,x22571,x22574,x22575,x22576,x22577,x22578),f841(x22573,x22572,x22574,x22575,x22576,x22577,x22578)) % 183.90/184.46 [2258]~E(x22581,x22582)+E(f841(x22583,x22584,x22581,x22585,x22586,x22587,x22588),f841(x22583,x22584,x22582,x22585,x22586,x22587,x22588)) % 183.90/184.46 [2259]~E(x22591,x22592)+E(f841(x22593,x22594,x22595,x22591,x22596,x22597,x22598),f841(x22593,x22594,x22595,x22592,x22596,x22597,x22598)) % 183.90/184.46 [2260]~E(x22601,x22602)+E(f841(x22603,x22604,x22605,x22606,x22601,x22607,x22608),f841(x22603,x22604,x22605,x22606,x22602,x22607,x22608)) % 183.90/184.46 [2261]~E(x22611,x22612)+E(f841(x22613,x22614,x22615,x22616,x22617,x22611,x22618),f841(x22613,x22614,x22615,x22616,x22617,x22612,x22618)) % 183.90/184.46 [2262]~E(x22621,x22622)+E(f841(x22623,x22624,x22625,x22626,x22627,x22628,x22621),f841(x22623,x22624,x22625,x22626,x22627,x22628,x22622)) % 183.90/184.46 [2263]~E(x22631,x22632)+E(f371(x22631,x22633,x22634,x22635,x22636),f371(x22632,x22633,x22634,x22635,x22636)) % 183.90/184.46 [2264]~E(x22641,x22642)+E(f371(x22643,x22641,x22644,x22645,x22646),f371(x22643,x22642,x22644,x22645,x22646)) % 183.90/184.46 [2265]~E(x22651,x22652)+E(f371(x22653,x22654,x22651,x22655,x22656),f371(x22653,x22654,x22652,x22655,x22656)) % 183.90/184.46 [2266]~E(x22661,x22662)+E(f371(x22663,x22664,x22665,x22661,x22666),f371(x22663,x22664,x22665,x22662,x22666)) % 183.90/184.46 [2267]~E(x22671,x22672)+E(f371(x22673,x22674,x22675,x22676,x22671),f371(x22673,x22674,x22675,x22676,x22672)) % 183.90/184.46 [2268]~E(x22681,x22682)+E(f716(x22681,x22683),f716(x22682,x22683)) % 183.90/184.46 [2269]~E(x22691,x22692)+E(f716(x22693,x22691),f716(x22693,x22692)) % 183.90/184.46 [2270]~E(x22701,x22702)+E(f136(x22701),f136(x22702)) % 183.90/184.46 [2271]~E(x22711,x22712)+E(f830(x22711,x22713,x22714,x22715,x22716,x22717),f830(x22712,x22713,x22714,x22715,x22716,x22717)) % 183.90/184.46 [2272]~E(x22721,x22722)+E(f830(x22723,x22721,x22724,x22725,x22726,x22727),f830(x22723,x22722,x22724,x22725,x22726,x22727)) % 183.90/184.46 [2273]~E(x22731,x22732)+E(f830(x22733,x22734,x22731,x22735,x22736,x22737),f830(x22733,x22734,x22732,x22735,x22736,x22737)) % 183.90/184.46 [2274]~E(x22741,x22742)+E(f830(x22743,x22744,x22745,x22741,x22746,x22747),f830(x22743,x22744,x22745,x22742,x22746,x22747)) % 183.90/184.46 [2275]~E(x22751,x22752)+E(f830(x22753,x22754,x22755,x22756,x22751,x22757),f830(x22753,x22754,x22755,x22756,x22752,x22757)) % 183.90/184.46 [2276]~E(x22761,x22762)+E(f830(x22763,x22764,x22765,x22766,x22767,x22761),f830(x22763,x22764,x22765,x22766,x22767,x22762)) % 183.90/184.46 [2277]~E(x22771,x22772)+E(f504(x22771,x22773),f504(x22772,x22773)) % 183.90/184.46 [2278]~E(x22781,x22782)+E(f504(x22783,x22781),f504(x22783,x22782)) % 183.90/184.46 [2279]~E(x22791,x22792)+E(f570(x22791,x22793,x22794,x22795),f570(x22792,x22793,x22794,x22795)) % 183.90/184.46 [2280]~E(x22801,x22802)+E(f570(x22803,x22801,x22804,x22805),f570(x22803,x22802,x22804,x22805)) % 183.90/184.46 [2281]~E(x22811,x22812)+E(f570(x22813,x22814,x22811,x22815),f570(x22813,x22814,x22812,x22815)) % 183.90/184.46 [2282]~E(x22821,x22822)+E(f570(x22823,x22824,x22825,x22821),f570(x22823,x22824,x22825,x22822)) % 183.90/184.46 [2283]~E(x22831,x22832)+E(f466(x22831,x22833,x22834),f466(x22832,x22833,x22834)) % 183.90/184.46 [2284]~E(x22841,x22842)+E(f466(x22843,x22841,x22844),f466(x22843,x22842,x22844)) % 183.90/184.46 [2285]~E(x22851,x22852)+E(f466(x22853,x22854,x22851),f466(x22853,x22854,x22852)) % 183.90/184.46 [2286]~E(x22861,x22862)+E(f598(x22861),f598(x22862)) % 183.90/184.46 [2287]~E(x22871,x22872)+E(f540(x22871,x22873,x22874),f540(x22872,x22873,x22874)) % 183.90/184.46 [2288]~E(x22881,x22882)+E(f540(x22883,x22881,x22884),f540(x22883,x22882,x22884)) % 183.90/184.46 [2289]~E(x22891,x22892)+E(f540(x22893,x22894,x22891),f540(x22893,x22894,x22892)) % 183.90/184.46 [2290]~E(x22901,x22902)+E(f340(x22901),f340(x22902)) % 183.90/184.46 [2291]~E(x22911,x22912)+E(f249(x22911,x22913),f249(x22912,x22913)) % 183.90/184.46 [2292]~E(x22921,x22922)+E(f249(x22923,x22921),f249(x22923,x22922)) % 183.90/184.46 [2293]~E(x22931,x22932)+E(f367(x22931,x22933,x22934,x22935),f367(x22932,x22933,x22934,x22935)) % 183.90/184.46 [2294]~E(x22941,x22942)+E(f367(x22943,x22941,x22944,x22945),f367(x22943,x22942,x22944,x22945)) % 183.90/184.46 [2295]~E(x22951,x22952)+E(f367(x22953,x22954,x22951,x22955),f367(x22953,x22954,x22952,x22955)) % 183.90/184.46 [2296]~E(x22961,x22962)+E(f367(x22963,x22964,x22965,x22961),f367(x22963,x22964,x22965,x22962)) % 183.90/184.46 [2297]~E(x22971,x22972)+E(f499(x22971,x22973,x22974),f499(x22972,x22973,x22974)) % 183.90/184.46 [2298]~E(x22981,x22982)+E(f499(x22983,x22981,x22984),f499(x22983,x22982,x22984)) % 183.90/184.46 [2299]~E(x22991,x22992)+E(f499(x22993,x22994,x22991),f499(x22993,x22994,x22992)) % 183.90/184.46 [2300]~E(x23001,x23002)+E(f339(x23001),f339(x23002)) % 183.90/184.46 [2301]~E(x23011,x23012)+E(f368(x23011,x23013,x23014),f368(x23012,x23013,x23014)) % 183.90/184.46 [2302]~E(x23021,x23022)+E(f368(x23023,x23021,x23024),f368(x23023,x23022,x23024)) % 183.90/184.46 [2303]~E(x23031,x23032)+E(f368(x23033,x23034,x23031),f368(x23033,x23034,x23032)) % 183.90/184.46 [2304]~E(x23041,x23042)+E(f713(x23041,x23043,x23044,x23045,x23046),f713(x23042,x23043,x23044,x23045,x23046)) % 183.90/184.46 [2305]~E(x23051,x23052)+E(f713(x23053,x23051,x23054,x23055,x23056),f713(x23053,x23052,x23054,x23055,x23056)) % 183.90/184.46 [2306]~E(x23061,x23062)+E(f713(x23063,x23064,x23061,x23065,x23066),f713(x23063,x23064,x23062,x23065,x23066)) % 183.90/184.46 [2307]~E(x23071,x23072)+E(f713(x23073,x23074,x23075,x23071,x23076),f713(x23073,x23074,x23075,x23072,x23076)) % 183.90/184.46 [2308]~E(x23081,x23082)+E(f713(x23083,x23084,x23085,x23086,x23081),f713(x23083,x23084,x23085,x23086,x23082)) % 183.90/184.46 [2309]~E(x23091,x23092)+E(f762(x23091,x23093,x23094),f762(x23092,x23093,x23094)) % 183.90/184.46 [2310]~E(x23101,x23102)+E(f762(x23103,x23101,x23104),f762(x23103,x23102,x23104)) % 183.90/184.46 [2311]~E(x23111,x23112)+E(f762(x23113,x23114,x23111),f762(x23113,x23114,x23112)) % 183.90/184.46 [2312]~E(x23121,x23122)+E(f147(x23121,x23123),f147(x23122,x23123)) % 183.90/184.46 [2313]~E(x23131,x23132)+E(f147(x23133,x23131),f147(x23133,x23132)) % 183.90/184.46 [2314]~E(x23141,x23142)+E(f533(x23141,x23143,x23144,x23145,x23146,x23147,x23148),f533(x23142,x23143,x23144,x23145,x23146,x23147,x23148)) % 183.90/184.46 [2315]~E(x23151,x23152)+E(f533(x23153,x23151,x23154,x23155,x23156,x23157,x23158),f533(x23153,x23152,x23154,x23155,x23156,x23157,x23158)) % 183.90/184.46 [2316]~E(x23161,x23162)+E(f533(x23163,x23164,x23161,x23165,x23166,x23167,x23168),f533(x23163,x23164,x23162,x23165,x23166,x23167,x23168)) % 183.90/184.46 [2317]~E(x23171,x23172)+E(f533(x23173,x23174,x23175,x23171,x23176,x23177,x23178),f533(x23173,x23174,x23175,x23172,x23176,x23177,x23178)) % 183.90/184.46 [2318]~E(x23181,x23182)+E(f533(x23183,x23184,x23185,x23186,x23181,x23187,x23188),f533(x23183,x23184,x23185,x23186,x23182,x23187,x23188)) % 183.90/184.46 [2319]~E(x23191,x23192)+E(f533(x23193,x23194,x23195,x23196,x23197,x23191,x23198),f533(x23193,x23194,x23195,x23196,x23197,x23192,x23198)) % 183.90/184.46 [2320]~E(x23201,x23202)+E(f533(x23203,x23204,x23205,x23206,x23207,x23208,x23201),f533(x23203,x23204,x23205,x23206,x23207,x23208,x23202)) % 183.90/184.46 [2321]~E(x23211,x23212)+E(f487(x23211,x23213,x23214),f487(x23212,x23213,x23214)) % 183.90/184.46 [2322]~E(x23221,x23222)+E(f487(x23223,x23221,x23224),f487(x23223,x23222,x23224)) % 183.90/184.46 [2323]~E(x23231,x23232)+E(f487(x23233,x23234,x23231),f487(x23233,x23234,x23232)) % 183.90/184.46 [2324]~E(x23241,x23242)+E(f828(x23241,x23243,x23244,x23245),f828(x23242,x23243,x23244,x23245)) % 183.90/184.46 [2325]~E(x23251,x23252)+E(f828(x23253,x23251,x23254,x23255),f828(x23253,x23252,x23254,x23255)) % 183.90/184.46 [2326]~E(x23261,x23262)+E(f828(x23263,x23264,x23261,x23265),f828(x23263,x23264,x23262,x23265)) % 183.90/184.46 [2327]~E(x23271,x23272)+E(f828(x23273,x23274,x23275,x23271),f828(x23273,x23274,x23275,x23272)) % 183.90/184.46 [2328]~E(x23281,x23282)+E(f775(x23281,x23283),f775(x23282,x23283)) % 183.90/184.46 [2329]~E(x23291,x23292)+E(f775(x23293,x23291),f775(x23293,x23292)) % 183.90/184.46 [2330]~E(x23301,x23302)+E(f390(x23301,x23303),f390(x23302,x23303)) % 183.90/184.46 [2331]~E(x23311,x23312)+E(f390(x23313,x23311),f390(x23313,x23312)) % 183.90/184.46 [2332]~E(x23321,x23322)+E(f752(x23321,x23323,x23324),f752(x23322,x23323,x23324)) % 183.90/184.46 [2333]~E(x23331,x23332)+E(f752(x23333,x23331,x23334),f752(x23333,x23332,x23334)) % 183.90/184.46 [2334]~E(x23341,x23342)+E(f752(x23343,x23344,x23341),f752(x23343,x23344,x23342)) % 183.90/184.46 [2335]~E(x23351,x23352)+E(f805(x23351,x23353),f805(x23352,x23353)) % 183.90/184.46 [2336]~E(x23361,x23362)+E(f805(x23363,x23361),f805(x23363,x23362)) % 183.90/184.46 [2337]~E(x23371,x23372)+E(f656(x23371,x23373,x23374),f656(x23372,x23373,x23374)) % 183.90/184.46 [2338]~E(x23381,x23382)+E(f656(x23383,x23381,x23384),f656(x23383,x23382,x23384)) % 183.90/184.46 [2339]~E(x23391,x23392)+E(f656(x23393,x23394,x23391),f656(x23393,x23394,x23392)) % 183.90/184.46 [2340]~E(x23401,x23402)+E(f641(x23401,x23403,x23404,x23405,x23406,x23407,x23408),f641(x23402,x23403,x23404,x23405,x23406,x23407,x23408)) % 183.90/184.46 [2341]~E(x23411,x23412)+E(f641(x23413,x23411,x23414,x23415,x23416,x23417,x23418),f641(x23413,x23412,x23414,x23415,x23416,x23417,x23418)) % 183.90/184.46 [2342]~E(x23421,x23422)+E(f641(x23423,x23424,x23421,x23425,x23426,x23427,x23428),f641(x23423,x23424,x23422,x23425,x23426,x23427,x23428)) % 183.90/184.46 [2343]~E(x23431,x23432)+E(f641(x23433,x23434,x23435,x23431,x23436,x23437,x23438),f641(x23433,x23434,x23435,x23432,x23436,x23437,x23438)) % 183.90/184.46 [2344]~E(x23441,x23442)+E(f641(x23443,x23444,x23445,x23446,x23441,x23447,x23448),f641(x23443,x23444,x23445,x23446,x23442,x23447,x23448)) % 183.90/184.46 [2345]~E(x23451,x23452)+E(f641(x23453,x23454,x23455,x23456,x23457,x23451,x23458),f641(x23453,x23454,x23455,x23456,x23457,x23452,x23458)) % 183.90/184.46 [2346]~E(x23461,x23462)+E(f641(x23463,x23464,x23465,x23466,x23467,x23468,x23461),f641(x23463,x23464,x23465,x23466,x23467,x23468,x23462)) % 183.90/184.46 [2347]~E(x23471,x23472)+E(f847(x23471,x23473,x23474),f847(x23472,x23473,x23474)) % 183.90/184.46 [2348]~E(x23481,x23482)+E(f847(x23483,x23481,x23484),f847(x23483,x23482,x23484)) % 183.90/184.46 [2349]~E(x23491,x23492)+E(f847(x23493,x23494,x23491),f847(x23493,x23494,x23492)) % 183.90/184.46 [2350]~E(x23501,x23502)+E(f520(x23501,x23503,x23504),f520(x23502,x23503,x23504)) % 183.90/184.46 [2351]~E(x23511,x23512)+E(f520(x23513,x23511,x23514),f520(x23513,x23512,x23514)) % 183.90/184.46 [2352]~E(x23521,x23522)+E(f520(x23523,x23524,x23521),f520(x23523,x23524,x23522)) % 183.90/184.46 [2353]~E(x23531,x23532)+E(f623(x23531,x23533,x23534),f623(x23532,x23533,x23534)) % 183.90/184.46 [2354]~E(x23541,x23542)+E(f623(x23543,x23541,x23544),f623(x23543,x23542,x23544)) % 183.90/184.46 [2355]~E(x23551,x23552)+E(f623(x23553,x23554,x23551),f623(x23553,x23554,x23552)) % 183.90/184.46 [2356]~E(x23561,x23562)+E(f826(x23561,x23563,x23564,x23565),f826(x23562,x23563,x23564,x23565)) % 183.90/184.46 [2357]~E(x23571,x23572)+E(f826(x23573,x23571,x23574,x23575),f826(x23573,x23572,x23574,x23575)) % 183.90/184.46 [2358]~E(x23581,x23582)+E(f826(x23583,x23584,x23581,x23585),f826(x23583,x23584,x23582,x23585)) % 183.90/184.46 [2359]~E(x23591,x23592)+E(f826(x23593,x23594,x23595,x23591),f826(x23593,x23594,x23595,x23592)) % 183.90/184.46 [2360]~E(x23601,x23602)+E(f486(x23601),f486(x23602)) % 183.90/184.46 [2361]~E(x23611,x23612)+E(f454(x23611,x23613),f454(x23612,x23613)) % 183.90/184.46 [2362]~E(x23621,x23622)+E(f454(x23623,x23621),f454(x23623,x23622)) % 183.90/184.46 [2363]~E(x23631,x23632)+E(f354(x23631,x23633),f354(x23632,x23633)) % 183.90/184.46 [2364]~E(x23641,x23642)+E(f354(x23643,x23641),f354(x23643,x23642)) % 183.90/184.46 [2365]~E(x23651,x23652)+E(f125(x23651),f125(x23652)) % 183.90/184.46 [2366]~E(x23661,x23662)+E(f275(x23661,x23663,x23664,x23665,x23666),f275(x23662,x23663,x23664,x23665,x23666)) % 183.90/184.46 [2367]~E(x23671,x23672)+E(f275(x23673,x23671,x23674,x23675,x23676),f275(x23673,x23672,x23674,x23675,x23676)) % 183.90/184.46 [2368]~E(x23681,x23682)+E(f275(x23683,x23684,x23681,x23685,x23686),f275(x23683,x23684,x23682,x23685,x23686)) % 183.90/184.46 [2369]~E(x23691,x23692)+E(f275(x23693,x23694,x23695,x23691,x23696),f275(x23693,x23694,x23695,x23692,x23696)) % 183.90/184.46 [2370]~E(x23701,x23702)+E(f275(x23703,x23704,x23705,x23706,x23701),f275(x23703,x23704,x23705,x23706,x23702)) % 183.90/184.46 [2371]~E(x23711,x23712)+E(f759(x23711,x23713,x23714,x23715),f759(x23712,x23713,x23714,x23715)) % 183.90/184.46 [2372]~E(x23721,x23722)+E(f759(x23723,x23721,x23724,x23725),f759(x23723,x23722,x23724,x23725)) % 183.90/184.46 [2373]~E(x23731,x23732)+E(f759(x23733,x23734,x23731,x23735),f759(x23733,x23734,x23732,x23735)) % 183.90/184.46 [2374]~E(x23741,x23742)+E(f759(x23743,x23744,x23745,x23741),f759(x23743,x23744,x23745,x23742)) % 183.90/184.46 [2375]~E(x23751,x23752)+E(f237(x23751,x23753,x23754),f237(x23752,x23753,x23754)) % 183.90/184.46 [2376]~E(x23761,x23762)+E(f237(x23763,x23761,x23764),f237(x23763,x23762,x23764)) % 183.90/184.46 [2377]~E(x23771,x23772)+E(f237(x23773,x23774,x23771),f237(x23773,x23774,x23772)) % 183.90/184.46 [2378]~E(x23781,x23782)+E(f511(x23781,x23783,x23784),f511(x23782,x23783,x23784)) % 183.90/184.46 [2379]~E(x23791,x23792)+E(f511(x23793,x23791,x23794),f511(x23793,x23792,x23794)) % 183.90/184.46 [2380]~E(x23801,x23802)+E(f511(x23803,x23804,x23801),f511(x23803,x23804,x23802)) % 183.90/184.46 [2381]~E(x23811,x23812)+E(f726(x23811,x23813),f726(x23812,x23813)) % 183.90/184.46 [2382]~E(x23821,x23822)+E(f726(x23823,x23821),f726(x23823,x23822)) % 183.90/184.46 [2383]~E(x23831,x23832)+E(f96(x23831,x23833,x23834),f96(x23832,x23833,x23834)) % 183.90/184.46 [2384]~E(x23841,x23842)+E(f96(x23843,x23841,x23844),f96(x23843,x23842,x23844)) % 183.90/184.46 [2385]~E(x23851,x23852)+E(f96(x23853,x23854,x23851),f96(x23853,x23854,x23852)) % 183.90/184.46 [2386]~E(x23861,x23862)+E(f567(x23861,x23863,x23864),f567(x23862,x23863,x23864)) % 183.90/184.46 [2387]~E(x23871,x23872)+E(f567(x23873,x23871,x23874),f567(x23873,x23872,x23874)) % 183.90/184.46 [2388]~E(x23881,x23882)+E(f567(x23883,x23884,x23881),f567(x23883,x23884,x23882)) % 183.90/184.46 [2389]~E(x23891,x23892)+E(f438(x23891,x23893,x23894,x23895),f438(x23892,x23893,x23894,x23895)) % 183.90/184.46 [2390]~E(x23901,x23902)+E(f438(x23903,x23901,x23904,x23905),f438(x23903,x23902,x23904,x23905)) % 183.90/184.46 [2391]~E(x23911,x23912)+E(f438(x23913,x23914,x23911,x23915),f438(x23913,x23914,x23912,x23915)) % 183.90/184.46 [2392]~E(x23921,x23922)+E(f438(x23923,x23924,x23925,x23921),f438(x23923,x23924,x23925,x23922)) % 183.90/184.46 [2393]~E(x23931,x23932)+E(f786(x23931,x23933,x23934,x23935,x23936,x23937),f786(x23932,x23933,x23934,x23935,x23936,x23937)) % 183.90/184.46 [2394]~E(x23941,x23942)+E(f786(x23943,x23941,x23944,x23945,x23946,x23947),f786(x23943,x23942,x23944,x23945,x23946,x23947)) % 183.90/184.46 [2395]~E(x23951,x23952)+E(f786(x23953,x23954,x23951,x23955,x23956,x23957),f786(x23953,x23954,x23952,x23955,x23956,x23957)) % 183.90/184.46 [2396]~E(x23961,x23962)+E(f786(x23963,x23964,x23965,x23961,x23966,x23967),f786(x23963,x23964,x23965,x23962,x23966,x23967)) % 183.90/184.46 [2397]~E(x23971,x23972)+E(f786(x23973,x23974,x23975,x23976,x23971,x23977),f786(x23973,x23974,x23975,x23976,x23972,x23977)) % 183.90/184.46 [2398]~E(x23981,x23982)+E(f786(x23983,x23984,x23985,x23986,x23987,x23981),f786(x23983,x23984,x23985,x23986,x23987,x23982)) % 183.90/184.46 [2399]~E(x23991,x23992)+E(f414(x23991,x23993,x23994),f414(x23992,x23993,x23994)) % 183.90/184.46 [2400]~E(x24001,x24002)+E(f414(x24003,x24001,x24004),f414(x24003,x24002,x24004)) % 183.90/184.46 [2401]~E(x24011,x24012)+E(f414(x24013,x24014,x24011),f414(x24013,x24014,x24012)) % 183.90/184.46 [2402]~E(x24021,x24022)+E(f610(x24021,x24023,x24024,x24025,x24026,x24027),f610(x24022,x24023,x24024,x24025,x24026,x24027)) % 183.90/184.46 [2403]~E(x24031,x24032)+E(f610(x24033,x24031,x24034,x24035,x24036,x24037),f610(x24033,x24032,x24034,x24035,x24036,x24037)) % 183.90/184.46 [2404]~E(x24041,x24042)+E(f610(x24043,x24044,x24041,x24045,x24046,x24047),f610(x24043,x24044,x24042,x24045,x24046,x24047)) % 183.90/184.46 [2405]~E(x24051,x24052)+E(f610(x24053,x24054,x24055,x24051,x24056,x24057),f610(x24053,x24054,x24055,x24052,x24056,x24057)) % 183.90/184.46 [2406]~E(x24061,x24062)+E(f610(x24063,x24064,x24065,x24066,x24061,x24067),f610(x24063,x24064,x24065,x24066,x24062,x24067)) % 183.90/184.46 [2407]~E(x24071,x24072)+E(f610(x24073,x24074,x24075,x24076,x24077,x24071),f610(x24073,x24074,x24075,x24076,x24077,x24072)) % 183.90/184.46 [2408]~E(x24081,x24082)+E(f864(x24081,x24083,x24084),f864(x24082,x24083,x24084)) % 183.90/184.46 [2409]~E(x24091,x24092)+E(f864(x24093,x24091,x24094),f864(x24093,x24092,x24094)) % 183.90/184.46 [2410]~E(x24101,x24102)+E(f864(x24103,x24104,x24101),f864(x24103,x24104,x24102)) % 183.90/184.46 [2411]~E(x24111,x24112)+E(f555(x24111),f555(x24112)) % 183.90/184.46 [2412]~E(x24121,x24122)+E(f833(x24121,x24123,x24124,x24125,x24126,x24127,x24128,x24129),f833(x24122,x24123,x24124,x24125,x24126,x24127,x24128,x24129)) % 183.90/184.46 [2413]~E(x24131,x24132)+E(f833(x24133,x24131,x24134,x24135,x24136,x24137,x24138,x24139),f833(x24133,x24132,x24134,x24135,x24136,x24137,x24138,x24139)) % 183.90/184.46 [2414]~E(x24141,x24142)+E(f833(x24143,x24144,x24141,x24145,x24146,x24147,x24148,x24149),f833(x24143,x24144,x24142,x24145,x24146,x24147,x24148,x24149)) % 183.90/184.46 [2415]~E(x24151,x24152)+E(f833(x24153,x24154,x24155,x24151,x24156,x24157,x24158,x24159),f833(x24153,x24154,x24155,x24152,x24156,x24157,x24158,x24159)) % 183.90/184.46 [2416]~E(x24161,x24162)+E(f833(x24163,x24164,x24165,x24166,x24161,x24167,x24168,x24169),f833(x24163,x24164,x24165,x24166,x24162,x24167,x24168,x24169)) % 183.90/184.46 [2417]~E(x24171,x24172)+E(f833(x24173,x24174,x24175,x24176,x24177,x24171,x24178,x24179),f833(x24173,x24174,x24175,x24176,x24177,x24172,x24178,x24179)) % 183.90/184.46 [2418]~E(x24181,x24182)+E(f833(x24183,x24184,x24185,x24186,x24187,x24188,x24181,x24189),f833(x24183,x24184,x24185,x24186,x24187,x24188,x24182,x24189)) % 183.90/184.46 [2419]~E(x24191,x24192)+E(f833(x24193,x24194,x24195,x24196,x24197,x24198,x24199,x24191),f833(x24193,x24194,x24195,x24196,x24197,x24198,x24199,x24192)) % 183.90/184.46 [2420]~E(x24201,x24202)+E(f429(x24201,x24203,x24204,x24205),f429(x24202,x24203,x24204,x24205)) % 183.90/184.46 [2421]~E(x24211,x24212)+E(f429(x24213,x24211,x24214,x24215),f429(x24213,x24212,x24214,x24215)) % 183.90/184.46 [2422]~E(x24221,x24222)+E(f429(x24223,x24224,x24221,x24225),f429(x24223,x24224,x24222,x24225)) % 183.90/184.46 [2423]~E(x24231,x24232)+E(f429(x24233,x24234,x24235,x24231),f429(x24233,x24234,x24235,x24232)) % 183.90/184.46 [2424]~E(x24241,x24242)+E(f674(x24241,x24243,x24244,x24245,x24246),f674(x24242,x24243,x24244,x24245,x24246)) % 183.90/184.46 [2425]~E(x24251,x24252)+E(f674(x24253,x24251,x24254,x24255,x24256),f674(x24253,x24252,x24254,x24255,x24256)) % 183.90/184.46 [2426]~E(x24261,x24262)+E(f674(x24263,x24264,x24261,x24265,x24266),f674(x24263,x24264,x24262,x24265,x24266)) % 183.90/184.46 [2427]~E(x24271,x24272)+E(f674(x24273,x24274,x24275,x24271,x24276),f674(x24273,x24274,x24275,x24272,x24276)) % 183.90/184.46 [2428]~E(x24281,x24282)+E(f674(x24283,x24284,x24285,x24286,x24281),f674(x24283,x24284,x24285,x24286,x24282)) % 183.90/184.46 [2429]~E(x24291,x24292)+E(f629(x24291,x24293),f629(x24292,x24293)) % 183.90/184.46 [2430]~E(x24301,x24302)+E(f629(x24303,x24301),f629(x24303,x24302)) % 183.90/184.46 [2431]~E(x24311,x24312)+E(f337(x24311,x24313,x24314,x24315),f337(x24312,x24313,x24314,x24315)) % 183.90/184.46 [2432]~E(x24321,x24322)+E(f337(x24323,x24321,x24324,x24325),f337(x24323,x24322,x24324,x24325)) % 183.90/184.46 [2433]~E(x24331,x24332)+E(f337(x24333,x24334,x24331,x24335),f337(x24333,x24334,x24332,x24335)) % 183.90/184.46 [2434]~E(x24341,x24342)+E(f337(x24343,x24344,x24345,x24341),f337(x24343,x24344,x24345,x24342)) % 183.90/184.46 [2435]~E(x24351,x24352)+E(f463(x24351,x24353,x24354,x24355,x24356),f463(x24352,x24353,x24354,x24355,x24356)) % 183.90/184.46 [2436]~E(x24361,x24362)+E(f463(x24363,x24361,x24364,x24365,x24366),f463(x24363,x24362,x24364,x24365,x24366)) % 183.90/184.46 [2437]~E(x24371,x24372)+E(f463(x24373,x24374,x24371,x24375,x24376),f463(x24373,x24374,x24372,x24375,x24376)) % 183.90/184.46 [2438]~E(x24381,x24382)+E(f463(x24383,x24384,x24385,x24381,x24386),f463(x24383,x24384,x24385,x24382,x24386)) % 183.90/184.46 [2439]~E(x24391,x24392)+E(f463(x24393,x24394,x24395,x24396,x24391),f463(x24393,x24394,x24395,x24396,x24392)) % 183.90/184.46 [2440]~E(x24401,x24402)+E(f490(x24401,x24403),f490(x24402,x24403)) % 183.90/184.46 [2441]~E(x24411,x24412)+E(f490(x24413,x24411),f490(x24413,x24412)) % 183.90/184.46 [2442]~E(x24421,x24422)+E(f643(x24421,x24423,x24424,x24425,x24426),f643(x24422,x24423,x24424,x24425,x24426)) % 183.90/184.46 [2443]~E(x24431,x24432)+E(f643(x24433,x24431,x24434,x24435,x24436),f643(x24433,x24432,x24434,x24435,x24436)) % 183.90/184.46 [2444]~E(x24441,x24442)+E(f643(x24443,x24444,x24441,x24445,x24446),f643(x24443,x24444,x24442,x24445,x24446)) % 183.90/184.46 [2445]~E(x24451,x24452)+E(f643(x24453,x24454,x24455,x24451,x24456),f643(x24453,x24454,x24455,x24452,x24456)) % 183.90/184.46 [2446]~E(x24461,x24462)+E(f643(x24463,x24464,x24465,x24466,x24461),f643(x24463,x24464,x24465,x24466,x24462)) % 183.90/184.46 [2447]~E(x24471,x24472)+E(f636(x24471,x24473),f636(x24472,x24473)) % 183.90/184.46 [2448]~E(x24481,x24482)+E(f636(x24483,x24481),f636(x24483,x24482)) % 183.90/184.46 [2449]~E(x24491,x24492)+E(f416(x24491,x24493,x24494),f416(x24492,x24493,x24494)) % 183.90/184.46 [2450]~E(x24501,x24502)+E(f416(x24503,x24501,x24504),f416(x24503,x24502,x24504)) % 183.90/184.46 [2451]~E(x24511,x24512)+E(f416(x24513,x24514,x24511),f416(x24513,x24514,x24512)) % 183.90/184.46 [2452]~E(x24521,x24522)+E(f795(x24521,x24523,x24524),f795(x24522,x24523,x24524)) % 183.90/184.46 [2453]~E(x24531,x24532)+E(f795(x24533,x24531,x24534),f795(x24533,x24532,x24534)) % 183.90/184.46 [2454]~E(x24541,x24542)+E(f795(x24543,x24544,x24541),f795(x24543,x24544,x24542)) % 183.90/184.46 [2455]~E(x24551,x24552)+E(f385(x24551),f385(x24552)) % 183.90/184.46 [2456]~E(x24561,x24562)+E(f840(x24561,x24563,x24564,x24565,x24566,x24567),f840(x24562,x24563,x24564,x24565,x24566,x24567)) % 183.90/184.46 [2457]~E(x24571,x24572)+E(f840(x24573,x24571,x24574,x24575,x24576,x24577),f840(x24573,x24572,x24574,x24575,x24576,x24577)) % 183.90/184.46 [2458]~E(x24581,x24582)+E(f840(x24583,x24584,x24581,x24585,x24586,x24587),f840(x24583,x24584,x24582,x24585,x24586,x24587)) % 183.90/184.46 [2459]~E(x24591,x24592)+E(f840(x24593,x24594,x24595,x24591,x24596,x24597),f840(x24593,x24594,x24595,x24592,x24596,x24597)) % 183.90/184.46 [2460]~E(x24601,x24602)+E(f840(x24603,x24604,x24605,x24606,x24601,x24607),f840(x24603,x24604,x24605,x24606,x24602,x24607)) % 183.90/184.46 [2461]~E(x24611,x24612)+E(f840(x24613,x24614,x24615,x24616,x24617,x24611),f840(x24613,x24614,x24615,x24616,x24617,x24612)) % 183.90/184.46 [2462]~E(x24621,x24622)+E(f238(x24621,x24623,x24624,x24625),f238(x24622,x24623,x24624,x24625)) % 183.90/184.46 [2463]~E(x24631,x24632)+E(f238(x24633,x24631,x24634,x24635),f238(x24633,x24632,x24634,x24635)) % 183.90/184.46 [2464]~E(x24641,x24642)+E(f238(x24643,x24644,x24641,x24645),f238(x24643,x24644,x24642,x24645)) % 183.90/184.46 [2465]~E(x24651,x24652)+E(f238(x24653,x24654,x24655,x24651),f238(x24653,x24654,x24655,x24652)) % 183.90/184.46 [2466]~E(x24661,x24662)+E(f708(x24661,x24663,x24664),f708(x24662,x24663,x24664)) % 183.90/184.46 [2467]~E(x24671,x24672)+E(f708(x24673,x24671,x24674),f708(x24673,x24672,x24674)) % 183.90/184.46 [2468]~E(x24681,x24682)+E(f708(x24683,x24684,x24681),f708(x24683,x24684,x24682)) % 183.90/184.46 [2469]~E(x24691,x24692)+E(f221(x24691,x24693,x24694,x24695),f221(x24692,x24693,x24694,x24695)) % 183.90/184.46 [2470]~E(x24701,x24702)+E(f221(x24703,x24701,x24704,x24705),f221(x24703,x24702,x24704,x24705)) % 183.90/184.46 [2471]~E(x24711,x24712)+E(f221(x24713,x24714,x24711,x24715),f221(x24713,x24714,x24712,x24715)) % 183.90/184.46 [2472]~E(x24721,x24722)+E(f221(x24723,x24724,x24725,x24721),f221(x24723,x24724,x24725,x24722)) % 183.90/184.46 [2473]~E(x24731,x24732)+E(f565(x24731,x24733,x24734,x24735),f565(x24732,x24733,x24734,x24735)) % 183.90/184.46 [2474]~E(x24741,x24742)+E(f565(x24743,x24741,x24744,x24745),f565(x24743,x24742,x24744,x24745)) % 183.90/184.46 [2475]~E(x24751,x24752)+E(f565(x24753,x24754,x24751,x24755),f565(x24753,x24754,x24752,x24755)) % 183.90/184.46 [2476]~E(x24761,x24762)+E(f565(x24763,x24764,x24765,x24761),f565(x24763,x24764,x24765,x24762)) % 183.90/184.46 [2477]~E(x24771,x24772)+E(f509(x24771,x24773,x24774),f509(x24772,x24773,x24774)) % 183.90/184.46 [2478]~E(x24781,x24782)+E(f509(x24783,x24781,x24784),f509(x24783,x24782,x24784)) % 183.90/184.46 [2479]~E(x24791,x24792)+E(f509(x24793,x24794,x24791),f509(x24793,x24794,x24792)) % 183.90/184.46 [2480]~E(x24801,x24802)+E(f451(x24801,x24803),f451(x24802,x24803)) % 183.90/184.46 [2481]~E(x24811,x24812)+E(f451(x24813,x24811),f451(x24813,x24812)) % 183.90/184.46 [2482]~E(x24821,x24822)+E(f476(x24821,x24823,x24824,x24825),f476(x24822,x24823,x24824,x24825)) % 183.90/184.46 [2483]~E(x24831,x24832)+E(f476(x24833,x24831,x24834,x24835),f476(x24833,x24832,x24834,x24835)) % 183.90/184.46 [2484]~E(x24841,x24842)+E(f476(x24843,x24844,x24841,x24845),f476(x24843,x24844,x24842,x24845)) % 183.90/184.46 [2485]~E(x24851,x24852)+E(f476(x24853,x24854,x24855,x24851),f476(x24853,x24854,x24855,x24852)) % 183.90/184.46 [2486]~E(x24861,x24862)+E(f715(x24861,x24863,x24864,x24865,x24866),f715(x24862,x24863,x24864,x24865,x24866)) % 183.90/184.46 [2487]~E(x24871,x24872)+E(f715(x24873,x24871,x24874,x24875,x24876),f715(x24873,x24872,x24874,x24875,x24876)) % 183.90/184.46 [2488]~E(x24881,x24882)+E(f715(x24883,x24884,x24881,x24885,x24886),f715(x24883,x24884,x24882,x24885,x24886)) % 183.90/184.46 [2489]~E(x24891,x24892)+E(f715(x24893,x24894,x24895,x24891,x24896),f715(x24893,x24894,x24895,x24892,x24896)) % 183.90/184.46 [2490]~E(x24901,x24902)+E(f715(x24903,x24904,x24905,x24906,x24901),f715(x24903,x24904,x24905,x24906,x24902)) % 183.90/184.46 [2491]~E(x24911,x24912)+E(f603(x24911,x24913,x24914),f603(x24912,x24913,x24914)) % 183.90/184.46 [2492]~E(x24921,x24922)+E(f603(x24923,x24921,x24924),f603(x24923,x24922,x24924)) % 183.90/184.46 [2493]~E(x24931,x24932)+E(f603(x24933,x24934,x24931),f603(x24933,x24934,x24932)) % 183.90/184.46 [2494]~E(x24941,x24942)+E(f542(x24941,x24943,x24944,x24945,x24946,x24947,x24948),f542(x24942,x24943,x24944,x24945,x24946,x24947,x24948)) % 183.90/184.46 [2495]~E(x24951,x24952)+E(f542(x24953,x24951,x24954,x24955,x24956,x24957,x24958),f542(x24953,x24952,x24954,x24955,x24956,x24957,x24958)) % 183.90/184.46 [2496]~E(x24961,x24962)+E(f542(x24963,x24964,x24961,x24965,x24966,x24967,x24968),f542(x24963,x24964,x24962,x24965,x24966,x24967,x24968)) % 183.90/184.46 [2497]~E(x24971,x24972)+E(f542(x24973,x24974,x24975,x24971,x24976,x24977,x24978),f542(x24973,x24974,x24975,x24972,x24976,x24977,x24978)) % 183.90/184.46 [2498]~E(x24981,x24982)+E(f542(x24983,x24984,x24985,x24986,x24981,x24987,x24988),f542(x24983,x24984,x24985,x24986,x24982,x24987,x24988)) % 183.90/184.46 [2499]~E(x24991,x24992)+E(f542(x24993,x24994,x24995,x24996,x24997,x24991,x24998),f542(x24993,x24994,x24995,x24996,x24997,x24992,x24998)) % 183.90/184.46 [2500]~E(x25001,x25002)+E(f542(x25003,x25004,x25005,x25006,x25007,x25008,x25001),f542(x25003,x25004,x25005,x25006,x25007,x25008,x25002)) % 183.90/184.46 [2501]~E(x25011,x25012)+E(f378(x25011,x25013,x25014,x25015),f378(x25012,x25013,x25014,x25015)) % 183.90/184.46 [2502]~E(x25021,x25022)+E(f378(x25023,x25021,x25024,x25025),f378(x25023,x25022,x25024,x25025)) % 183.90/184.46 [2503]~E(x25031,x25032)+E(f378(x25033,x25034,x25031,x25035),f378(x25033,x25034,x25032,x25035)) % 183.90/184.46 [2504]~E(x25041,x25042)+E(f378(x25043,x25044,x25045,x25041),f378(x25043,x25044,x25045,x25042)) % 183.90/184.46 [2505]~E(x25051,x25052)+E(f360(x25051,x25053,x25054),f360(x25052,x25053,x25054)) % 183.90/184.46 [2506]~E(x25061,x25062)+E(f360(x25063,x25061,x25064),f360(x25063,x25062,x25064)) % 183.90/184.46 [2507]~E(x25071,x25072)+E(f360(x25073,x25074,x25071),f360(x25073,x25074,x25072)) % 183.90/184.46 [2508]~E(x25081,x25082)+E(f503(x25081,x25083),f503(x25082,x25083)) % 183.90/184.46 [2509]~E(x25091,x25092)+E(f503(x25093,x25091),f503(x25093,x25092)) % 183.90/184.46 [2510]~E(x25101,x25102)+E(f711(x25101,x25103,x25104,x25105,x25106),f711(x25102,x25103,x25104,x25105,x25106)) % 183.90/184.46 [2511]~E(x25111,x25112)+E(f711(x25113,x25111,x25114,x25115,x25116),f711(x25113,x25112,x25114,x25115,x25116)) % 183.90/184.46 [2512]~E(x25121,x25122)+E(f711(x25123,x25124,x25121,x25125,x25126),f711(x25123,x25124,x25122,x25125,x25126)) % 183.90/184.46 [2513]~E(x25131,x25132)+E(f711(x25133,x25134,x25135,x25131,x25136),f711(x25133,x25134,x25135,x25132,x25136)) % 183.90/184.46 [2514]~E(x25141,x25142)+E(f711(x25143,x25144,x25145,x25146,x25141),f711(x25143,x25144,x25145,x25146,x25142)) % 183.90/184.46 [2515]~E(x25151,x25152)+E(f433(x25151,x25153,x25154),f433(x25152,x25153,x25154)) % 183.90/184.46 [2516]~E(x25161,x25162)+E(f433(x25163,x25161,x25164),f433(x25163,x25162,x25164)) % 183.90/184.46 [2517]~E(x25171,x25172)+E(f433(x25173,x25174,x25171),f433(x25173,x25174,x25172)) % 183.90/184.46 [2518]~E(x25181,x25182)+E(f353(x25181,x25183,x25184,x25185),f353(x25182,x25183,x25184,x25185)) % 183.90/184.46 [2519]~E(x25191,x25192)+E(f353(x25193,x25191,x25194,x25195),f353(x25193,x25192,x25194,x25195)) % 183.90/184.46 [2520]~E(x25201,x25202)+E(f353(x25203,x25204,x25201,x25205),f353(x25203,x25204,x25202,x25205)) % 183.90/184.46 [2521]~E(x25211,x25212)+E(f353(x25213,x25214,x25215,x25211),f353(x25213,x25214,x25215,x25212)) % 183.90/184.46 [2522]~E(x25221,x25222)+E(f464(x25221,x25223,x25224),f464(x25222,x25223,x25224)) % 183.90/184.46 [2523]~E(x25231,x25232)+E(f464(x25233,x25231,x25234),f464(x25233,x25232,x25234)) % 183.90/184.46 [2524]~E(x25241,x25242)+E(f464(x25243,x25244,x25241),f464(x25243,x25244,x25242)) % 183.90/184.46 [2525]~E(x25251,x25252)+E(f798(x25251,x25253,x25254),f798(x25252,x25253,x25254)) % 183.90/184.46 [2526]~E(x25261,x25262)+E(f798(x25263,x25261,x25264),f798(x25263,x25262,x25264)) % 183.90/184.46 [2527]~E(x25271,x25272)+E(f798(x25273,x25274,x25271),f798(x25273,x25274,x25272)) % 183.90/184.46 [2528]~E(x25281,x25282)+E(f839(x25281,x25283,x25284,x25285,x25286),f839(x25282,x25283,x25284,x25285,x25286)) % 183.90/184.46 [2529]~E(x25291,x25292)+E(f839(x25293,x25291,x25294,x25295,x25296),f839(x25293,x25292,x25294,x25295,x25296)) % 183.90/184.46 [2530]~E(x25301,x25302)+E(f839(x25303,x25304,x25301,x25305,x25306),f839(x25303,x25304,x25302,x25305,x25306)) % 183.90/184.46 [2531]~E(x25311,x25312)+E(f839(x25313,x25314,x25315,x25311,x25316),f839(x25313,x25314,x25315,x25312,x25316)) % 183.90/184.46 [2532]~E(x25321,x25322)+E(f839(x25323,x25324,x25325,x25326,x25321),f839(x25323,x25324,x25325,x25326,x25322)) % 183.90/184.46 [2533]~E(x25331,x25332)+E(f219(x25331,x25333,x25334,x25335,x25336,x25337,x25338),f219(x25332,x25333,x25334,x25335,x25336,x25337,x25338)) % 183.90/184.46 [2534]~E(x25341,x25342)+E(f219(x25343,x25341,x25344,x25345,x25346,x25347,x25348),f219(x25343,x25342,x25344,x25345,x25346,x25347,x25348)) % 183.90/184.46 [2535]~E(x25351,x25352)+E(f219(x25353,x25354,x25351,x25355,x25356,x25357,x25358),f219(x25353,x25354,x25352,x25355,x25356,x25357,x25358)) % 183.90/184.46 [2536]~E(x25361,x25362)+E(f219(x25363,x25364,x25365,x25361,x25366,x25367,x25368),f219(x25363,x25364,x25365,x25362,x25366,x25367,x25368)) % 183.90/184.46 [2537]~E(x25371,x25372)+E(f219(x25373,x25374,x25375,x25376,x25371,x25377,x25378),f219(x25373,x25374,x25375,x25376,x25372,x25377,x25378)) % 183.90/184.46 [2538]~E(x25381,x25382)+E(f219(x25383,x25384,x25385,x25386,x25387,x25381,x25388),f219(x25383,x25384,x25385,x25386,x25387,x25382,x25388)) % 183.90/184.46 [2539]~E(x25391,x25392)+E(f219(x25393,x25394,x25395,x25396,x25397,x25398,x25391),f219(x25393,x25394,x25395,x25396,x25397,x25398,x25392)) % 183.90/184.46 [2540]~E(x25401,x25402)+E(f212(x25401),f212(x25402)) % 183.90/184.46 [2541]~E(x25411,x25412)+E(f423(x25411,x25413,x25414,x25415),f423(x25412,x25413,x25414,x25415)) % 183.90/184.46 [2542]~E(x25421,x25422)+E(f423(x25423,x25421,x25424,x25425),f423(x25423,x25422,x25424,x25425)) % 183.90/184.46 [2543]~E(x25431,x25432)+E(f423(x25433,x25434,x25431,x25435),f423(x25433,x25434,x25432,x25435)) % 183.90/184.46 [2544]~E(x25441,x25442)+E(f423(x25443,x25444,x25445,x25441),f423(x25443,x25444,x25445,x25442)) % 183.90/184.46 [2545]~E(x25451,x25452)+E(f566(x25451,x25453),f566(x25452,x25453)) % 183.90/184.46 [2546]~E(x25461,x25462)+E(f566(x25463,x25461),f566(x25463,x25462)) % 183.90/184.46 [2547]~E(x25471,x25472)+E(f223(x25471,x25473,x25474,x25475,x25476,x25477,x25478),f223(x25472,x25473,x25474,x25475,x25476,x25477,x25478)) % 183.90/184.46 [2548]~E(x25481,x25482)+E(f223(x25483,x25481,x25484,x25485,x25486,x25487,x25488),f223(x25483,x25482,x25484,x25485,x25486,x25487,x25488)) % 183.90/184.46 [2549]~E(x25491,x25492)+E(f223(x25493,x25494,x25491,x25495,x25496,x25497,x25498),f223(x25493,x25494,x25492,x25495,x25496,x25497,x25498)) % 183.90/184.46 [2550]~E(x25501,x25502)+E(f223(x25503,x25504,x25505,x25501,x25506,x25507,x25508),f223(x25503,x25504,x25505,x25502,x25506,x25507,x25508)) % 183.90/184.46 [2551]~E(x25511,x25512)+E(f223(x25513,x25514,x25515,x25516,x25511,x25517,x25518),f223(x25513,x25514,x25515,x25516,x25512,x25517,x25518)) % 183.90/184.46 [2552]~E(x25521,x25522)+E(f223(x25523,x25524,x25525,x25526,x25527,x25521,x25528),f223(x25523,x25524,x25525,x25526,x25527,x25522,x25528)) % 183.90/184.46 [2553]~E(x25531,x25532)+E(f223(x25533,x25534,x25535,x25536,x25537,x25538,x25531),f223(x25533,x25534,x25535,x25536,x25537,x25538,x25532)) % 183.90/184.46 [2554]~E(x25541,x25542)+E(f733(x25541,x25543,x25544,x25545,x25546),f733(x25542,x25543,x25544,x25545,x25546)) % 183.90/184.46 [2555]~E(x25551,x25552)+E(f733(x25553,x25551,x25554,x25555,x25556),f733(x25553,x25552,x25554,x25555,x25556)) % 183.90/184.46 [2556]~E(x25561,x25562)+E(f733(x25563,x25564,x25561,x25565,x25566),f733(x25563,x25564,x25562,x25565,x25566)) % 183.90/184.46 [2557]~E(x25571,x25572)+E(f733(x25573,x25574,x25575,x25571,x25576),f733(x25573,x25574,x25575,x25572,x25576)) % 183.90/184.46 [2558]~E(x25581,x25582)+E(f733(x25583,x25584,x25585,x25586,x25581),f733(x25583,x25584,x25585,x25586,x25582)) % 183.90/184.46 [2559]~E(x25591,x25592)+E(f518(x25591,x25593,x25594),f518(x25592,x25593,x25594)) % 183.90/184.46 [2560]~E(x25601,x25602)+E(f518(x25603,x25601,x25604),f518(x25603,x25602,x25604)) % 183.90/184.46 [2561]~E(x25611,x25612)+E(f518(x25613,x25614,x25611),f518(x25613,x25614,x25612)) % 183.90/184.46 [2562]~E(x25621,x25622)+E(f207(x25621,x25623,x25624,x25625),f207(x25622,x25623,x25624,x25625)) % 183.90/184.46 [2563]~E(x25631,x25632)+E(f207(x25633,x25631,x25634,x25635),f207(x25633,x25632,x25634,x25635)) % 183.90/184.46 [2564]~E(x25641,x25642)+E(f207(x25643,x25644,x25641,x25645),f207(x25643,x25644,x25642,x25645)) % 183.90/184.46 [2565]~E(x25651,x25652)+E(f207(x25653,x25654,x25655,x25651),f207(x25653,x25654,x25655,x25652)) % 183.90/184.46 [2566]~E(x25661,x25662)+E(f459(x25661,x25663,x25664,x25665,x25666),f459(x25662,x25663,x25664,x25665,x25666)) % 183.90/184.46 [2567]~E(x25671,x25672)+E(f459(x25673,x25671,x25674,x25675,x25676),f459(x25673,x25672,x25674,x25675,x25676)) % 183.90/184.46 [2568]~E(x25681,x25682)+E(f459(x25683,x25684,x25681,x25685,x25686),f459(x25683,x25684,x25682,x25685,x25686)) % 183.90/184.46 [2569]~E(x25691,x25692)+E(f459(x25693,x25694,x25695,x25691,x25696),f459(x25693,x25694,x25695,x25692,x25696)) % 183.90/184.46 [2570]~E(x25701,x25702)+E(f459(x25703,x25704,x25705,x25706,x25701),f459(x25703,x25704,x25705,x25706,x25702)) % 183.90/184.46 [2571]~E(x25711,x25712)+E(f666(x25711,x25713,x25714,x25715),f666(x25712,x25713,x25714,x25715)) % 183.90/184.46 [2572]~E(x25721,x25722)+E(f666(x25723,x25721,x25724,x25725),f666(x25723,x25722,x25724,x25725)) % 183.90/184.46 [2573]~E(x25731,x25732)+E(f666(x25733,x25734,x25731,x25735),f666(x25733,x25734,x25732,x25735)) % 183.90/184.46 [2574]~E(x25741,x25742)+E(f666(x25743,x25744,x25745,x25741),f666(x25743,x25744,x25745,x25742)) % 183.90/184.46 [2575]~E(x25751,x25752)+E(f685(x25751,x25753),f685(x25752,x25753)) % 183.90/184.46 [2576]~E(x25761,x25762)+E(f685(x25763,x25761),f685(x25763,x25762)) % 183.90/184.46 [2577]~E(x25771,x25772)+E(f554(x25771,x25773,x25774,x25775,x25776),f554(x25772,x25773,x25774,x25775,x25776)) % 183.90/184.46 [2578]~E(x25781,x25782)+E(f554(x25783,x25781,x25784,x25785,x25786),f554(x25783,x25782,x25784,x25785,x25786)) % 183.90/184.46 [2579]~E(x25791,x25792)+E(f554(x25793,x25794,x25791,x25795,x25796),f554(x25793,x25794,x25792,x25795,x25796)) % 183.90/184.46 [2580]~E(x25801,x25802)+E(f554(x25803,x25804,x25805,x25801,x25806),f554(x25803,x25804,x25805,x25802,x25806)) % 183.90/184.46 [2581]~E(x25811,x25812)+E(f554(x25813,x25814,x25815,x25816,x25811),f554(x25813,x25814,x25815,x25816,x25812)) % 183.90/184.46 [2582]~E(x25821,x25822)+E(f435(x25821,x25823,x25824,x25825),f435(x25822,x25823,x25824,x25825)) % 183.90/184.46 [2583]~E(x25831,x25832)+E(f435(x25833,x25831,x25834,x25835),f435(x25833,x25832,x25834,x25835)) % 183.90/184.46 [2584]~E(x25841,x25842)+E(f435(x25843,x25844,x25841,x25845),f435(x25843,x25844,x25842,x25845)) % 183.90/184.46 [2585]~E(x25851,x25852)+E(f435(x25853,x25854,x25855,x25851),f435(x25853,x25854,x25855,x25852)) % 183.90/184.46 [2586]~E(x25861,x25862)+E(f519(x25861,x25863,x25864,x25865),f519(x25862,x25863,x25864,x25865)) % 183.90/184.46 [2587]~E(x25871,x25872)+E(f519(x25873,x25871,x25874,x25875),f519(x25873,x25872,x25874,x25875)) % 183.90/184.46 [2588]~E(x25881,x25882)+E(f519(x25883,x25884,x25881,x25885),f519(x25883,x25884,x25882,x25885)) % 183.90/184.46 [2589]~E(x25891,x25892)+E(f519(x25893,x25894,x25895,x25891),f519(x25893,x25894,x25895,x25892)) % 183.90/184.46 [2590]~E(x25901,x25902)+E(f218(x25901,x25903,x25904,x25905),f218(x25902,x25903,x25904,x25905)) % 183.90/184.46 [2591]~E(x25911,x25912)+E(f218(x25913,x25911,x25914,x25915),f218(x25913,x25912,x25914,x25915)) % 183.90/184.46 [2592]~E(x25921,x25922)+E(f218(x25923,x25924,x25921,x25925),f218(x25923,x25924,x25922,x25925)) % 183.90/184.46 [2593]~E(x25931,x25932)+E(f218(x25933,x25934,x25935,x25931),f218(x25933,x25934,x25935,x25932)) % 183.90/184.46 [2594]~E(x25941,x25942)+E(f376(x25941),f376(x25942)) % 183.90/184.46 [2595]~E(x25951,x25952)+E(f591(x25951,x25953),f591(x25952,x25953)) % 183.90/184.46 [2596]~E(x25961,x25962)+E(f591(x25963,x25961),f591(x25963,x25962)) % 183.90/184.46 [2597]~E(x25971,x25972)+E(f621(x25971,x25973,x25974,x25975),f621(x25972,x25973,x25974,x25975)) % 183.90/184.46 [2598]~E(x25981,x25982)+E(f621(x25983,x25981,x25984,x25985),f621(x25983,x25982,x25984,x25985)) % 183.90/184.46 [2599]~E(x25991,x25992)+E(f621(x25993,x25994,x25991,x25995),f621(x25993,x25994,x25992,x25995)) % 183.90/184.46 [2600]~E(x26001,x26002)+E(f621(x26003,x26004,x26005,x26001),f621(x26003,x26004,x26005,x26002)) % 183.90/184.46 [2601]~E(x26011,x26012)+E(f233(x26011,x26013,x26014),f233(x26012,x26013,x26014)) % 183.90/184.46 [2602]~E(x26021,x26022)+E(f233(x26023,x26021,x26024),f233(x26023,x26022,x26024)) % 183.90/184.46 [2603]~E(x26031,x26032)+E(f233(x26033,x26034,x26031),f233(x26033,x26034,x26032)) % 183.90/184.46 [2604]~E(x26041,x26042)+E(f455(x26041,x26043,x26044),f455(x26042,x26043,x26044)) % 183.90/184.46 [2605]~E(x26051,x26052)+E(f455(x26053,x26051,x26054),f455(x26053,x26052,x26054)) % 183.90/184.46 [2606]~E(x26061,x26062)+E(f455(x26063,x26064,x26061),f455(x26063,x26064,x26062)) % 183.90/184.46 [2607]~E(x26071,x26072)+E(f215(x26071,x26073,x26074),f215(x26072,x26073,x26074)) % 183.90/184.46 [2608]~E(x26081,x26082)+E(f215(x26083,x26081,x26084),f215(x26083,x26082,x26084)) % 183.90/184.46 [2609]~E(x26091,x26092)+E(f215(x26093,x26094,x26091),f215(x26093,x26094,x26092)) % 183.90/184.46 [2610]~E(x26101,x26102)+E(f316(x26101,x26103,x26104),f316(x26102,x26103,x26104)) % 183.90/184.46 [2611]~E(x26111,x26112)+E(f316(x26113,x26111,x26114),f316(x26113,x26112,x26114)) % 183.90/184.46 [2612]~E(x26121,x26122)+E(f316(x26123,x26124,x26121),f316(x26123,x26124,x26122)) % 183.90/184.46 [2613]~E(x26131,x26132)+E(f317(x26131,x26133,x26134),f317(x26132,x26133,x26134)) % 183.90/184.46 [2614]~E(x26141,x26142)+E(f317(x26143,x26141,x26144),f317(x26143,x26142,x26144)) % 183.90/184.46 [2615]~E(x26151,x26152)+E(f317(x26153,x26154,x26151),f317(x26153,x26154,x26152)) % 183.90/184.46 [2616]~E(x26161,x26162)+E(f707(x26161,x26163,x26164),f707(x26162,x26163,x26164)) % 183.90/184.46 [2617]~E(x26171,x26172)+E(f707(x26173,x26171,x26174),f707(x26173,x26172,x26174)) % 183.90/184.46 [2618]~E(x26181,x26182)+E(f707(x26183,x26184,x26181),f707(x26183,x26184,x26182)) % 183.90/184.46 [2619]~E(x26191,x26192)+E(f369(x26191,x26193,x26194),f369(x26192,x26193,x26194)) % 183.90/184.46 [2620]~E(x26201,x26202)+E(f369(x26203,x26201,x26204),f369(x26203,x26202,x26204)) % 183.90/184.46 [2621]~E(x26211,x26212)+E(f369(x26213,x26214,x26211),f369(x26213,x26214,x26212)) % 183.90/184.46 [2622]~P1(x26221)+P1(x26222)+~E(x26221,x26222) % 183.90/184.46 [2623]~P2(x26231)+P2(x26232)+~E(x26231,x26232) % 183.90/184.46 [2624]~P106(x26241)+P106(x26242)+~E(x26241,x26242) % 183.90/184.46 [2625]~P3(x26251)+P3(x26252)+~E(x26251,x26252) % 183.90/184.46 [2626]P143(x26262,x26263,x26264)+~E(x26261,x26262)+~P143(x26261,x26263,x26264) % 183.90/184.46 [2627]P143(x26273,x26272,x26274)+~E(x26271,x26272)+~P143(x26273,x26271,x26274) % 183.90/184.46 [2628]P143(x26283,x26284,x26282)+~E(x26281,x26282)+~P143(x26283,x26284,x26281) % 183.90/184.46 [2629]~P62(x26291)+P62(x26292)+~E(x26291,x26292) % 183.90/184.46 [2630]~P107(x26301)+P107(x26302)+~E(x26301,x26302) % 183.90/184.46 [2631]P144(x26312,x26313,x26314)+~E(x26311,x26312)+~P144(x26311,x26313,x26314) % 183.90/184.46 [2632]P144(x26323,x26322,x26324)+~E(x26321,x26322)+~P144(x26323,x26321,x26324) % 183.90/184.46 [2633]P144(x26333,x26334,x26332)+~E(x26331,x26332)+~P144(x26333,x26334,x26331) % 183.90/184.46 [2634]~P63(x26341)+P63(x26342)+~E(x26341,x26342) % 183.90/184.46 [2635]~P98(x26351)+P98(x26352)+~E(x26351,x26352) % 183.90/184.46 [2636]~P138(x26361)+P138(x26362)+~E(x26361,x26362) % 183.90/184.46 [2637]P27(x26372,x26373,x26374)+~E(x26371,x26372)+~P27(x26371,x26373,x26374) % 183.90/184.46 [2638]P27(x26383,x26382,x26384)+~E(x26381,x26382)+~P27(x26383,x26381,x26384) % 183.90/184.46 [2639]P27(x26393,x26394,x26392)+~E(x26391,x26392)+~P27(x26393,x26394,x26391) % 183.90/184.46 [2640]~P99(x26401)+P99(x26402)+~E(x26401,x26402) % 183.90/184.46 [2641]~P109(x26411)+P109(x26412)+~E(x26411,x26412) % 183.90/184.46 [2642]~P91(x26421)+P91(x26422)+~E(x26421,x26422) % 183.90/184.46 [2643]~P64(x26431)+P64(x26432)+~E(x26431,x26432) % 183.90/184.46 [2644]~P61(x26441)+P61(x26442)+~E(x26441,x26442) % 183.90/184.46 [2645]~P122(x26451)+P122(x26452)+~E(x26451,x26452) % 183.90/184.46 [2646]~P114(x26461)+P114(x26462)+~E(x26461,x26462) % 183.90/184.46 [2647]~P96(x26471)+P96(x26472)+~E(x26471,x26472) % 183.90/184.46 [2648]~P4(x26481)+P4(x26482)+~E(x26481,x26482) % 183.90/184.46 [2649]P28(x26492,x26493,x26494)+~E(x26491,x26492)+~P28(x26491,x26493,x26494) % 183.90/184.46 [2650]P28(x26503,x26502,x26504)+~E(x26501,x26502)+~P28(x26503,x26501,x26504) % 183.90/184.46 [2651]P28(x26513,x26514,x26512)+~E(x26511,x26512)+~P28(x26513,x26514,x26511) % 183.90/184.46 [2652]~P103(x26521)+P103(x26522)+~E(x26521,x26522) % 183.90/184.46 [2653]~P65(x26531)+P65(x26532)+~E(x26531,x26532) % 183.90/184.46 [2654]P14(x26542,x26543)+~E(x26541,x26542)+~P14(x26541,x26543) % 183.90/184.46 [2655]P14(x26553,x26552)+~E(x26551,x26552)+~P14(x26553,x26551) % 183.90/184.46 [2656]~P66(x26561)+P66(x26562)+~E(x26561,x26562) % 183.90/184.46 [2657]~P60(x26571)+P60(x26572)+~E(x26571,x26572) % 183.90/184.46 [2658]~P132(x26581)+P132(x26582)+~E(x26581,x26582) % 183.90/184.46 [2659]~P104(x26591)+P104(x26592)+~E(x26591,x26592) % 183.90/184.46 [2660]~P97(x26601)+P97(x26602)+~E(x26601,x26602) % 183.90/184.46 [2661]~P72(x26611)+P72(x26612)+~E(x26611,x26612) % 183.90/184.46 [2662]~P67(x26621)+P67(x26622)+~E(x26621,x26622) % 183.90/184.46 [2663]P34(x26632,x26633,x26634,x26635,x26636)+~E(x26631,x26632)+~P34(x26631,x26633,x26634,x26635,x26636) % 183.90/184.46 [2664]P34(x26643,x26642,x26644,x26645,x26646)+~E(x26641,x26642)+~P34(x26643,x26641,x26644,x26645,x26646) % 183.90/184.46 [2665]P34(x26653,x26654,x26652,x26655,x26656)+~E(x26651,x26652)+~P34(x26653,x26654,x26651,x26655,x26656) % 183.90/184.46 [2666]P34(x26663,x26664,x26665,x26662,x26666)+~E(x26661,x26662)+~P34(x26663,x26664,x26665,x26661,x26666) % 183.90/184.46 [2667]P34(x26673,x26674,x26675,x26676,x26672)+~E(x26671,x26672)+~P34(x26673,x26674,x26675,x26676,x26671) % 183.90/184.46 [2668]~P38(x26681)+P38(x26682)+~E(x26681,x26682) % 183.90/184.46 [2669]~P134(x26691)+P134(x26692)+~E(x26691,x26692) % 183.90/184.46 [2670]P18(x26702,x26703,x26704)+~E(x26701,x26702)+~P18(x26701,x26703,x26704) % 183.90/184.46 [2671]P18(x26713,x26712,x26714)+~E(x26711,x26712)+~P18(x26713,x26711,x26714) % 183.90/184.46 [2672]P18(x26723,x26724,x26722)+~E(x26721,x26722)+~P18(x26723,x26724,x26721) % 183.90/184.46 [2673]~P80(x26731)+P80(x26732)+~E(x26731,x26732) % 183.90/184.46 [2674]~P68(x26741)+P68(x26742)+~E(x26741,x26742) % 183.90/184.46 [2675]P7(x26752,x26753,x26754)+~E(x26751,x26752)+~P7(x26751,x26753,x26754) % 183.90/184.46 [2676]P7(x26763,x26762,x26764)+~E(x26761,x26762)+~P7(x26763,x26761,x26764) % 183.90/184.46 [2677]P7(x26773,x26774,x26772)+~E(x26771,x26772)+~P7(x26773,x26774,x26771) % 183.90/184.46 [2678]P16(x26782,x26783,x26784)+~E(x26781,x26782)+~P16(x26781,x26783,x26784) % 183.90/184.46 [2679]P16(x26793,x26792,x26794)+~E(x26791,x26792)+~P16(x26793,x26791,x26794) % 183.90/184.46 [2680]P16(x26803,x26804,x26802)+~E(x26801,x26802)+~P16(x26803,x26804,x26801) % 183.90/184.46 [2681]~P69(x26811)+P69(x26812)+~E(x26811,x26812) % 183.90/184.46 [2682]~P5(x26821)+P5(x26822)+~E(x26821,x26822) % 183.90/184.46 [2683]P25(x26832,x26833,x26834,x26835)+~E(x26831,x26832)+~P25(x26831,x26833,x26834,x26835) % 183.90/184.46 [2684]P25(x26843,x26842,x26844,x26845)+~E(x26841,x26842)+~P25(x26843,x26841,x26844,x26845) % 183.90/184.46 [2685]P25(x26853,x26854,x26852,x26855)+~E(x26851,x26852)+~P25(x26853,x26854,x26851,x26855) % 183.90/184.46 [2686]P25(x26863,x26864,x26865,x26862)+~E(x26861,x26862)+~P25(x26863,x26864,x26865,x26861) % 183.90/184.46 [2687]~P70(x26871)+P70(x26872)+~E(x26871,x26872) % 183.90/184.46 [2688]~P120(x26881)+P120(x26882)+~E(x26881,x26882) % 183.90/184.46 [2689]~P58(x26891)+P58(x26892)+~E(x26891,x26892) % 183.90/184.46 [2690]~P74(x26901)+P74(x26902)+~E(x26901,x26902) % 183.90/184.46 [2691]~P55(x26911)+P55(x26912)+~E(x26911,x26912) % 183.90/184.46 [2692]~P85(x26921)+P85(x26922)+~E(x26921,x26922) % 183.90/184.46 [2693]~P139(x26931)+P139(x26932)+~E(x26931,x26932) % 183.90/184.46 [2694]P24(x26942,x26943,x26944)+~E(x26941,x26942)+~P24(x26941,x26943,x26944) % 183.90/184.46 [2695]P24(x26953,x26952,x26954)+~E(x26951,x26952)+~P24(x26953,x26951,x26954) % 183.90/184.46 [2696]P24(x26963,x26964,x26962)+~E(x26961,x26962)+~P24(x26963,x26964,x26961) % 183.90/184.46 [2697]~P135(x26971)+P135(x26972)+~E(x26971,x26972) % 183.90/184.46 [2698]~P82(x26981)+P82(x26982)+~E(x26981,x26982) % 183.90/184.46 [2699]~P73(x26991)+P73(x26992)+~E(x26991,x26992) % 183.90/184.46 [2700]~P110(x27001)+P110(x27002)+~E(x27001,x27002) % 183.90/184.46 [2701]~P90(x27011)+P90(x27012)+~E(x27011,x27012) % 183.90/184.46 [2702]~P83(x27021)+P83(x27022)+~E(x27021,x27022) % 183.90/184.46 [2703]~P108(x27031)+P108(x27032)+~E(x27031,x27032) % 183.90/184.46 [2704]~P59(x27041)+P59(x27042)+~E(x27041,x27042) % 183.90/184.46 [2705]P23(x27052,x27053,x27054,x27055,x27056,x27057)+~E(x27051,x27052)+~P23(x27051,x27053,x27054,x27055,x27056,x27057) % 183.90/184.46 [2706]P23(x27063,x27062,x27064,x27065,x27066,x27067)+~E(x27061,x27062)+~P23(x27063,x27061,x27064,x27065,x27066,x27067) % 183.90/184.46 [2707]P23(x27073,x27074,x27072,x27075,x27076,x27077)+~E(x27071,x27072)+~P23(x27073,x27074,x27071,x27075,x27076,x27077) % 183.90/184.46 [2708]P23(x27083,x27084,x27085,x27082,x27086,x27087)+~E(x27081,x27082)+~P23(x27083,x27084,x27085,x27081,x27086,x27087) % 183.90/184.46 [2709]P23(x27093,x27094,x27095,x27096,x27092,x27097)+~E(x27091,x27092)+~P23(x27093,x27094,x27095,x27096,x27091,x27097) % 183.90/184.46 [2710]P23(x27103,x27104,x27105,x27106,x27107,x27102)+~E(x27101,x27102)+~P23(x27103,x27104,x27105,x27106,x27107,x27101) % 183.90/184.46 [2711]~P76(x27111)+P76(x27112)+~E(x27111,x27112) % 183.90/184.46 [2712]~P113(x27121)+P113(x27122)+~E(x27121,x27122) % 183.90/184.46 [2713]P19(x27132,x27133,x27134,x27135)+~E(x27131,x27132)+~P19(x27131,x27133,x27134,x27135) % 183.90/184.46 [2714]P19(x27143,x27142,x27144,x27145)+~E(x27141,x27142)+~P19(x27143,x27141,x27144,x27145) % 183.90/184.46 [2715]P19(x27153,x27154,x27152,x27155)+~E(x27151,x27152)+~P19(x27153,x27154,x27151,x27155) % 183.90/184.46 [2716]P19(x27163,x27164,x27165,x27162)+~E(x27161,x27162)+~P19(x27163,x27164,x27165,x27161) % 183.90/184.46 [2717]~P77(x27171)+P77(x27172)+~E(x27171,x27172) % 183.90/184.46 [2718]P37(x27182,x27183)+~E(x27181,x27182)+~P37(x27181,x27183) % 183.90/184.46 [2719]P37(x27193,x27192)+~E(x27191,x27192)+~P37(x27193,x27191) % 183.90/184.46 [2720]P54(x27202,x27203)+~E(x27201,x27202)+~P54(x27201,x27203) % 183.90/184.46 [2721]P54(x27213,x27212)+~E(x27211,x27212)+~P54(x27213,x27211) % 183.90/184.46 [2722]~P105(x27221)+P105(x27222)+~E(x27221,x27222) % 183.90/184.46 [2723]P52(x27232,x27233)+~E(x27231,x27232)+~P52(x27231,x27233) % 183.90/184.46 [2724]P52(x27243,x27242)+~E(x27241,x27242)+~P52(x27243,x27241) % 183.90/184.46 [2725]P10(x27252,x27253,x27254)+~E(x27251,x27252)+~P10(x27251,x27253,x27254) % 183.90/184.46 [2726]P10(x27263,x27262,x27264)+~E(x27261,x27262)+~P10(x27263,x27261,x27264) % 183.90/184.46 [2727]P10(x27273,x27274,x27272)+~E(x27271,x27272)+~P10(x27273,x27274,x27271) % 183.90/184.46 [2728]~P141(x27281)+P141(x27282)+~E(x27281,x27282) % 183.90/184.46 [2729]~P125(x27291)+P125(x27292)+~E(x27291,x27292) % 183.90/184.46 [2730]P39(x27302,x27303,x27304)+~E(x27301,x27302)+~P39(x27301,x27303,x27304) % 183.90/184.46 [2731]P39(x27313,x27312,x27314)+~E(x27311,x27312)+~P39(x27313,x27311,x27314) % 183.90/184.46 [2732]P39(x27323,x27324,x27322)+~E(x27321,x27322)+~P39(x27323,x27324,x27321) % 183.90/184.46 [2733]~P87(x27331)+P87(x27332)+~E(x27331,x27332) % 183.90/184.46 [2734]P50(x27342,x27343,x27344)+~E(x27341,x27342)+~P50(x27341,x27343,x27344) % 183.90/184.46 [2735]P50(x27353,x27352,x27354)+~E(x27351,x27352)+~P50(x27353,x27351,x27354) % 183.90/184.46 [2736]P50(x27363,x27364,x27362)+~E(x27361,x27362)+~P50(x27363,x27364,x27361) % 183.90/184.46 [2737]~P137(x27371)+P137(x27372)+~E(x27371,x27372) % 183.90/184.46 [2738]~P123(x27381)+P123(x27382)+~E(x27381,x27382) % 183.90/184.46 [2739]P33(x27392,x27393,x27394)+~E(x27391,x27392)+~P33(x27391,x27393,x27394) % 183.90/184.46 [2740]P33(x27403,x27402,x27404)+~E(x27401,x27402)+~P33(x27403,x27401,x27404) % 183.90/184.46 [2741]P33(x27413,x27414,x27412)+~E(x27411,x27412)+~P33(x27413,x27414,x27411) % 183.90/184.46 [2742]~P57(x27421)+P57(x27422)+~E(x27421,x27422) % 183.90/184.46 [2743]P35(x27432,x27433,x27434)+~E(x27431,x27432)+~P35(x27431,x27433,x27434) % 183.90/184.46 [2744]P35(x27443,x27442,x27444)+~E(x27441,x27442)+~P35(x27443,x27441,x27444) % 183.90/184.46 [2745]P35(x27453,x27454,x27452)+~E(x27451,x27452)+~P35(x27453,x27454,x27451) % 183.90/184.46 [2746]~P79(x27461)+P79(x27462)+~E(x27461,x27462) % 183.90/184.46 [2747]P15(x27472,x27473,x27474)+~E(x27471,x27472)+~P15(x27471,x27473,x27474) % 183.90/184.46 [2748]P15(x27483,x27482,x27484)+~E(x27481,x27482)+~P15(x27483,x27481,x27484) % 183.90/184.46 [2749]P15(x27493,x27494,x27492)+~E(x27491,x27492)+~P15(x27493,x27494,x27491) % 183.90/184.46 [2750]~P89(x27501)+P89(x27502)+~E(x27501,x27502) % 183.90/184.46 [2751]P49(x27512,x27513,x27514)+~E(x27511,x27512)+~P49(x27511,x27513,x27514) % 183.90/184.46 [2752]P49(x27523,x27522,x27524)+~E(x27521,x27522)+~P49(x27523,x27521,x27524) % 183.90/184.46 [2753]P49(x27533,x27534,x27532)+~E(x27531,x27532)+~P49(x27533,x27534,x27531) % 183.90/184.46 [2754]P31(x27542,x27543,x27544)+~E(x27541,x27542)+~P31(x27541,x27543,x27544) % 183.90/184.46 [2755]P31(x27553,x27552,x27554)+~E(x27551,x27552)+~P31(x27553,x27551,x27554) % 183.90/184.46 [2756]P31(x27563,x27564,x27562)+~E(x27561,x27562)+~P31(x27563,x27564,x27561) % 183.90/184.46 [2757]~P78(x27571)+P78(x27572)+~E(x27571,x27572) % 183.90/184.46 [2758]~P129(x27581)+P129(x27582)+~E(x27581,x27582) % 183.90/184.46 [2759]P30(x27592,x27593)+~E(x27591,x27592)+~P30(x27591,x27593) % 183.90/184.46 [2760]P30(x27603,x27602)+~E(x27601,x27602)+~P30(x27603,x27601) % 183.90/184.46 [2761]~P93(x27611)+P93(x27612)+~E(x27611,x27612) % 183.90/184.46 [2762]~P81(x27621)+P81(x27622)+~E(x27621,x27622) % 183.90/184.46 [2763]P20(x27632,x27633,x27634,x27635)+~E(x27631,x27632)+~P20(x27631,x27633,x27634,x27635) % 183.90/184.46 [2764]P20(x27643,x27642,x27644,x27645)+~E(x27641,x27642)+~P20(x27643,x27641,x27644,x27645) % 183.90/184.46 [2765]P20(x27653,x27654,x27652,x27655)+~E(x27651,x27652)+~P20(x27653,x27654,x27651,x27655) % 183.90/184.46 [2766]P20(x27663,x27664,x27665,x27662)+~E(x27661,x27662)+~P20(x27663,x27664,x27665,x27661) % 183.90/184.46 [2767]~P100(x27671)+P100(x27672)+~E(x27671,x27672) % 183.90/184.46 [2768]~P121(x27681)+P121(x27682)+~E(x27681,x27682) % 183.90/184.46 [2769]P32(x27692,x27693,x27694,x27695)+~E(x27691,x27692)+~P32(x27691,x27693,x27694,x27695) % 183.90/184.46 [2770]P32(x27703,x27702,x27704,x27705)+~E(x27701,x27702)+~P32(x27703,x27701,x27704,x27705) % 183.90/184.46 [2771]P32(x27713,x27714,x27712,x27715)+~E(x27711,x27712)+~P32(x27713,x27714,x27711,x27715) % 183.90/184.46 [2772]P32(x27723,x27724,x27725,x27722)+~E(x27721,x27722)+~P32(x27723,x27724,x27725,x27721) % 183.90/184.46 [2773]~P130(x27731)+P130(x27732)+~E(x27731,x27732) % 183.90/184.46 [2774]~P101(x27741)+P101(x27742)+~E(x27741,x27742) % 183.90/184.46 [2775]~P117(x27751)+P117(x27752)+~E(x27751,x27752) % 183.90/184.46 [2776]~P111(x27761)+P111(x27762)+~E(x27761,x27762) % 183.90/184.46 [2777]P53(x27772,x27773,x27774,x27775)+~E(x27771,x27772)+~P53(x27771,x27773,x27774,x27775) % 183.90/184.46 [2778]P53(x27783,x27782,x27784,x27785)+~E(x27781,x27782)+~P53(x27783,x27781,x27784,x27785) % 183.90/184.46 [2779]P53(x27793,x27794,x27792,x27795)+~E(x27791,x27792)+~P53(x27793,x27794,x27791,x27795) % 183.90/184.46 [2780]P53(x27803,x27804,x27805,x27802)+~E(x27801,x27802)+~P53(x27803,x27804,x27805,x27801) % 183.90/184.46 [2781]P12(x27812,x27813,x27814,x27815)+~E(x27811,x27812)+~P12(x27811,x27813,x27814,x27815) % 183.90/184.46 [2782]P12(x27823,x27822,x27824,x27825)+~E(x27821,x27822)+~P12(x27823,x27821,x27824,x27825) % 183.90/184.46 [2783]P12(x27833,x27834,x27832,x27835)+~E(x27831,x27832)+~P12(x27833,x27834,x27831,x27835) % 183.90/184.46 [2784]P12(x27843,x27844,x27845,x27842)+~E(x27841,x27842)+~P12(x27843,x27844,x27845,x27841) % 183.90/184.46 [2785]~P84(x27851)+P84(x27852)+~E(x27851,x27852) % 183.90/184.46 [2786]~P94(x27861)+P94(x27862)+~E(x27861,x27862) % 183.90/184.46 [2787]P26(x27872,x27873)+~E(x27871,x27872)+~P26(x27871,x27873) % 183.90/184.46 [2788]P26(x27883,x27882)+~E(x27881,x27882)+~P26(x27883,x27881) % 183.90/184.46 [2789]~P124(x27891)+P124(x27892)+~E(x27891,x27892) % 183.90/184.46 [2790]~P133(x27901)+P133(x27902)+~E(x27901,x27902) % 183.90/184.46 [2791]P42(x27912,x27913,x27914,x27915,x27916,x27917)+~E(x27911,x27912)+~P42(x27911,x27913,x27914,x27915,x27916,x27917) % 183.90/184.46 [2792]P42(x27923,x27922,x27924,x27925,x27926,x27927)+~E(x27921,x27922)+~P42(x27923,x27921,x27924,x27925,x27926,x27927) % 183.90/184.46 [2793]P42(x27933,x27934,x27932,x27935,x27936,x27937)+~E(x27931,x27932)+~P42(x27933,x27934,x27931,x27935,x27936,x27937) % 183.90/184.46 [2794]P42(x27943,x27944,x27945,x27942,x27946,x27947)+~E(x27941,x27942)+~P42(x27943,x27944,x27945,x27941,x27946,x27947) % 183.90/184.46 [2795]P42(x27953,x27954,x27955,x27956,x27952,x27957)+~E(x27951,x27952)+~P42(x27953,x27954,x27955,x27956,x27951,x27957) % 183.90/184.46 [2796]P42(x27963,x27964,x27965,x27966,x27967,x27962)+~E(x27961,x27962)+~P42(x27963,x27964,x27965,x27966,x27967,x27961) % 183.90/184.46 [2797]P51(x27972,x27973,x27974,x27975,x27976)+~E(x27971,x27972)+~P51(x27971,x27973,x27974,x27975,x27976) % 183.90/184.46 [2798]P51(x27983,x27982,x27984,x27985,x27986)+~E(x27981,x27982)+~P51(x27983,x27981,x27984,x27985,x27986) % 183.90/184.46 [2799]P51(x27993,x27994,x27992,x27995,x27996)+~E(x27991,x27992)+~P51(x27993,x27994,x27991,x27995,x27996) % 183.90/184.46 [2800]P51(x28003,x28004,x28005,x28002,x28006)+~E(x28001,x28002)+~P51(x28003,x28004,x28005,x28001,x28006) % 183.90/184.46 [2801]P51(x28013,x28014,x28015,x28016,x28012)+~E(x28011,x28012)+~P51(x28013,x28014,x28015,x28016,x28011) % 183.90/184.46 [2802]P6(x28022,x28023)+~E(x28021,x28022)+~P6(x28021,x28023) % 183.90/184.46 [2803]P6(x28033,x28032)+~E(x28031,x28032)+~P6(x28033,x28031) % 183.90/184.46 [2804]P22(x28042,x28043,x28044,x28045,x28046,x28047)+~E(x28041,x28042)+~P22(x28041,x28043,x28044,x28045,x28046,x28047) % 183.90/184.46 [2805]P22(x28053,x28052,x28054,x28055,x28056,x28057)+~E(x28051,x28052)+~P22(x28053,x28051,x28054,x28055,x28056,x28057) % 183.90/184.46 [2806]P22(x28063,x28064,x28062,x28065,x28066,x28067)+~E(x28061,x28062)+~P22(x28063,x28064,x28061,x28065,x28066,x28067) % 183.90/184.46 [2807]P22(x28073,x28074,x28075,x28072,x28076,x28077)+~E(x28071,x28072)+~P22(x28073,x28074,x28075,x28071,x28076,x28077) % 183.90/184.46 [2808]P22(x28083,x28084,x28085,x28086,x28082,x28087)+~E(x28081,x28082)+~P22(x28083,x28084,x28085,x28086,x28081,x28087) % 183.90/184.46 [2809]P22(x28093,x28094,x28095,x28096,x28097,x28092)+~E(x28091,x28092)+~P22(x28093,x28094,x28095,x28096,x28097,x28091) % 183.90/184.46 [2810]~P140(x28101)+P140(x28102)+~E(x28101,x28102) % 183.90/184.46 [2811]~P128(x28111)+P128(x28112)+~E(x28111,x28112) % 183.90/184.46 [2812]~P116(x28121)+P116(x28122)+~E(x28121,x28122) % 183.90/184.46 [2813]~P131(x28131)+P131(x28132)+~E(x28131,x28132) % 183.90/184.46 [2814]~P95(x28141)+P95(x28142)+~E(x28141,x28142) % 183.90/184.46 [2815]~P126(x28151)+P126(x28152)+~E(x28151,x28152) % 183.90/184.46 [2816]~P118(x28161)+P118(x28162)+~E(x28161,x28162) % 183.90/184.46 [2817]~P136(x28171)+P136(x28172)+~E(x28171,x28172) % 183.90/184.46 [2818]~P92(x28181)+P92(x28182)+~E(x28181,x28182) % 183.90/184.46 [2819]~P56(x28191)+P56(x28192)+~E(x28191,x28192) % 183.90/184.46 [2820]P11(x28202,x28203,x28204)+~E(x28201,x28202)+~P11(x28201,x28203,x28204) % 183.90/184.46 [2821]P11(x28213,x28212,x28214)+~E(x28211,x28212)+~P11(x28213,x28211,x28214) % 183.90/184.46 [2822]P11(x28223,x28224,x28222)+~E(x28221,x28222)+~P11(x28223,x28224,x28221) % 183.90/184.46 [2823]P43(x28232,x28233)+~E(x28231,x28232)+~P43(x28231,x28233) % 183.90/184.46 [2824]P43(x28243,x28242)+~E(x28241,x28242)+~P43(x28243,x28241) % 183.90/184.46 [2825]~P36(x28251)+P36(x28252)+~E(x28251,x28252) % 183.90/184.46 [2826]~P29(x28261)+P29(x28262)+~E(x28261,x28262) % 183.90/184.46 [2827]P46(x28272,x28273,x28274)+~E(x28271,x28272)+~P46(x28271,x28273,x28274) % 183.90/184.46 [2828]P46(x28283,x28282,x28284)+~E(x28281,x28282)+~P46(x28283,x28281,x28284) % 183.90/184.46 [2829]P46(x28293,x28294,x28292)+~E(x28291,x28292)+~P46(x28293,x28294,x28291) % 183.90/184.46 [2830]P17(x28302,x28303,x28304)+~E(x28301,x28302)+~P17(x28301,x28303,x28304) % 183.90/184.46 [2831]P17(x28313,x28312,x28314)+~E(x28311,x28312)+~P17(x28313,x28311,x28314) % 183.90/184.46 [2832]P17(x28323,x28324,x28322)+~E(x28321,x28322)+~P17(x28323,x28324,x28321) % 183.90/184.46 [2833]~P44(x28331)+P44(x28332)+~E(x28331,x28332) % 183.90/184.46 [2834]~P102(x28341)+P102(x28342)+~E(x28341,x28342) % 183.90/184.46 [2835]P48(x28352,x28353)+~E(x28351,x28352)+~P48(x28351,x28353) % 183.90/184.46 [2836]P48(x28363,x28362)+~E(x28361,x28362)+~P48(x28363,x28361) % 183.90/184.46 [2837]P47(x28372,x28373,x28374)+~E(x28371,x28372)+~P47(x28371,x28373,x28374) % 183.90/184.46 [2838]P47(x28383,x28382,x28384)+~E(x28381,x28382)+~P47(x28383,x28381,x28384) % 183.90/184.46 [2839]P47(x28393,x28394,x28392)+~E(x28391,x28392)+~P47(x28393,x28394,x28391) % 183.90/184.46 [2840]P9(x28402,x28403,x28404,x28405,x28406)+~E(x28401,x28402)+~P9(x28401,x28403,x28404,x28405,x28406) % 183.90/184.46 [2841]P9(x28413,x28412,x28414,x28415,x28416)+~E(x28411,x28412)+~P9(x28413,x28411,x28414,x28415,x28416) % 183.90/184.46 [2842]P9(x28423,x28424,x28422,x28425,x28426)+~E(x28421,x28422)+~P9(x28423,x28424,x28421,x28425,x28426) % 183.90/184.46 [2843]P9(x28433,x28434,x28435,x28432,x28436)+~E(x28431,x28432)+~P9(x28433,x28434,x28435,x28431,x28436) % 183.90/184.46 [2844]P9(x28443,x28444,x28445,x28446,x28442)+~E(x28441,x28442)+~P9(x28443,x28444,x28445,x28446,x28441) % 183.90/184.46 [2845]P13(x28452,x28453,x28454,x28455,x28456,x28457)+~E(x28451,x28452)+~P13(x28451,x28453,x28454,x28455,x28456,x28457) % 183.90/184.46 [2846]P13(x28463,x28462,x28464,x28465,x28466,x28467)+~E(x28461,x28462)+~P13(x28463,x28461,x28464,x28465,x28466,x28467) % 183.90/184.46 [2847]P13(x28473,x28474,x28472,x28475,x28476,x28477)+~E(x28471,x28472)+~P13(x28473,x28474,x28471,x28475,x28476,x28477) % 183.90/184.46 [2848]P13(x28483,x28484,x28485,x28482,x28486,x28487)+~E(x28481,x28482)+~P13(x28483,x28484,x28485,x28481,x28486,x28487) % 183.90/184.46 [2849]P13(x28493,x28494,x28495,x28496,x28492,x28497)+~E(x28491,x28492)+~P13(x28493,x28494,x28495,x28496,x28491,x28497) % 183.90/184.46 [2850]P13(x28503,x28504,x28505,x28506,x28507,x28502)+~E(x28501,x28502)+~P13(x28503,x28504,x28505,x28506,x28507,x28501) % 183.90/184.46 [2851]~P86(x28511)+P86(x28512)+~E(x28511,x28512) % 183.90/184.46 [2852]P45(x28522,x28523)+~E(x28521,x28522)+~P45(x28521,x28523) % 183.90/184.46 [2853]P45(x28533,x28532)+~E(x28531,x28532)+~P45(x28533,x28531) % 183.90/184.46 [2854]~P142(x28541)+P142(x28542)+~E(x28541,x28542) % 183.90/184.46 [2855]~P112(x28551)+P112(x28552)+~E(x28551,x28552) % 183.90/184.46 [2856]~P115(x28561)+P115(x28562)+~E(x28561,x28562) % 183.90/184.46 [2857]P41(x28572,x28573)+~E(x28571,x28572)+~P41(x28571,x28573) % 183.90/184.46 [2858]P41(x28583,x28582)+~E(x28581,x28582)+~P41(x28583,x28581) % 183.90/184.46 [2859]~P88(x28591)+P88(x28592)+~E(x28591,x28592) % 183.90/184.46 [2860]~P71(x28601)+P71(x28602)+~E(x28601,x28602) % 183.90/184.46 [2861]~P75(x28611)+P75(x28612)+~E(x28611,x28612) % 183.90/184.46 [2862]~P127(x28621)+P127(x28622)+~E(x28621,x28622) % 183.90/184.46 [2863]P40(x28632,x28633,x28634,x28635)+~E(x28631,x28632)+~P40(x28631,x28633,x28634,x28635) % 183.90/184.46 [2864]P40(x28643,x28642,x28644,x28645)+~E(x28641,x28642)+~P40(x28643,x28641,x28644,x28645) % 183.90/184.46 [2865]P40(x28653,x28654,x28652,x28655)+~E(x28651,x28652)+~P40(x28653,x28654,x28651,x28655) % 183.90/184.46 [2866]P40(x28663,x28664,x28665,x28662)+~E(x28661,x28662)+~P40(x28663,x28664,x28665,x28661) % 183.90/184.46 [2867]~P119(x28671)+P119(x28672)+~E(x28671,x28672) % 183.90/184.46 [2868]P21(x28682,x28683,x28684,x28685,x28686)+~E(x28681,x28682)+~P21(x28681,x28683,x28684,x28685,x28686) % 183.90/184.46 [2869]P21(x28693,x28692,x28694,x28695,x28696)+~E(x28691,x28692)+~P21(x28693,x28691,x28694,x28695,x28696) % 183.90/184.46 [2870]P21(x28703,x28704,x28702,x28705,x28706)+~E(x28701,x28702)+~P21(x28703,x28704,x28701,x28705,x28706) % 183.90/184.46 [2871]P21(x28713,x28714,x28715,x28712,x28716)+~E(x28711,x28712)+~P21(x28713,x28714,x28715,x28711,x28716) % 183.90/184.46 [2872]P21(x28723,x28724,x28725,x28726,x28722)+~E(x28721,x28722)+~P21(x28723,x28724,x28725,x28726,x28721) % 183.90/184.46 [2873]P8(x28732,x28733,x28734)+~E(x28731,x28732)+~P8(x28731,x28733,x28734) % 183.90/184.46 [2874]P8(x28743,x28742,x28744)+~E(x28741,x28742)+~P8(x28743,x28741,x28744) % 183.90/184.46 [2875]P8(x28753,x28754,x28752)+~E(x28751,x28752)+~P8(x28753,x28754,x28751) % 183.90/184.46 % 183.90/184.46 %------------------------------------------- % 183.99/184.51 cnf(10211,plain, % 183.99/184.51 (~E(f333(a115,x102111),x102111)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10214,plain, % 183.99/184.51 (E(f333(f264(x102141,x102141),f265(x102141,x102142)),x102142)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10221,plain, % 183.99/184.51 (~E(f333(a115,x102211),x102211)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10234,plain, % 183.99/184.51 (~E(f333(a115,x102341),x102341)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10239,plain, % 183.99/184.51 (~P1(f333(f62(x102391,x102392,f196(f882(x102391,a870))),x102393))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10242,plain, % 183.99/184.51 (~P1(f333(f62(x102421,x102422,f196(f882(x102421,a870))),x102423))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10245,plain, % 183.99/184.51 (~E(f333(a115,x102451),x102451)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10248,plain, % 183.99/184.51 (~E(f333(a115,x102481),x102481)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10251,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x102511),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10254,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x102541),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10267,plain, % 183.99/184.51 (~P1(f333(f196(f882(x102671,a870)),x102672))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,3075,3243,3118,3179,3125,3269,4543,10251,4540,4498,4546,3260,4533,4563,10239,4567,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039])). % 183.99/184.51 cnf(10271,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x102711)),x102711))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(10274,plain, % 183.99/184.51 (~E(f333(f333(f152(x102741),x102742),x102743),x102743)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(10280,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x102801),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10283,plain, % 183.99/184.51 (E(f333(f264(x102831,x102831),f265(x102831,x102832)),x102832)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10286,plain, % 183.99/184.51 (E(f333(f264(x102861,x102861),f265(x102861,x102862)),x102862)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10293,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x102931),x102932)),x102932))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(10296,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x102961),x102962)),x102962))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(10317,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x103171),x103171))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10320,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f44(a875,x103201,x103202)),x103201))), % 183.99/184.51 inference(rename_variables,[],[3753])). % 183.99/184.51 cnf(10343,plain, % 183.99/184.51 (E(f333(f37(a875),f333(f254(a875),x103431)),x103431)), % 183.99/184.51 inference(rename_variables,[],[3174])). % 183.99/184.51 cnf(10351,plain, % 183.99/184.51 (~E(f333(a115,x103511),x103511)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10354,plain, % 183.99/184.51 (~E(f333(a115,x103541),x103541)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10357,plain, % 183.99/184.51 (~E(f333(a115,x103571),x103571)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10359,plain, % 183.99/184.51 (P1(f333(a201,a100))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,3075,3243,10214,10283,3118,3179,3144,3125,3213,4503,3174,4573,3195,3356,3269,4543,10251,10254,3887,3290,4540,4498,4539,10317,3382,3817,3753,4548,10271,4129,4546,4529,3260,4533,4534,4563,10239,4567,4565,10293,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316])). % 183.99/184.51 cnf(10362,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x103621),f333(a115,x103621)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10371,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x103711),x103711))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(10378,plain, % 183.99/184.51 (E(f333(f264(x103781,x103781),f265(x103781,x103782)),x103782)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10381,plain, % 183.99/184.51 (E(f333(f264(x103811,x103811),f265(x103811,x103812)),x103812)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10400,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x104001),x104001))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(10409,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x104091),x104091))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10414,plain, % 183.99/184.51 (~E(f333(f333(f333(f71(x104141,f879(x104142)),x104143),x104144),f333(f240(x104142),x104145)),f333(f16(f879(x104142),x104141),f209(x104142)))), % 183.99/184.51 inference(rename_variables,[],[4560])). % 183.99/184.51 cnf(10441,plain, % 183.99/184.51 (~E(f333(f333(f152(x104411),x104412),x104413),x104413)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(10444,plain, % 183.99/184.51 (~E(f333(a25,x104441),f32(x104442,x104443))), % 183.99/184.51 inference(rename_variables,[],[4493])). % 183.99/184.51 cnf(10455,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x104551),x104551))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(10460,plain, % 183.99/184.51 (~E(f333(a115,x104601),x104601)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10467,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x104671),x104671))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(10480,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x104801),f333(a115,x104801)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10501,plain, % 183.99/184.51 (~P1(f333(f62(x105011,x105012,f196(f882(x105011,a870))),x105013))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10520,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x105201),x105201))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10535,plain, % 183.99/184.51 (~E(f333(a25,x105351),f32(x105352,x105353))), % 183.99/184.51 inference(rename_variables,[],[4493])). % 183.99/184.51 cnf(10544,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x105441),x105441))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10549,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x105491),f333(a115,x105491)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10552,plain, % 183.99/184.51 (~P1(f333(f62(x105521,x105522,f196(f882(x105521,a870))),x105523))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10555,plain, % 183.99/184.51 (~P1(f333(f62(x105551,x105552,f196(f882(x105551,a870))),x105553))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10560,plain, % 183.99/184.51 (~P1(f333(f62(x105601,x105602,f196(f882(x105601,a870))),x105603))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10571,plain, % 183.99/184.51 (~E(f333(a115,x105711),x105711)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10585,plain, % 183.99/184.51 (P1(f333(f333(f248(a102),f333(a3,x105851)),f333(a3,f333(a115,x105851))))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,4493,10444,3075,3243,10214,10283,10286,10378,3118,3179,3144,3125,3768,3213,4560,4503,10274,3174,4085,4573,3195,3658,3356,10362,10480,10549,3748,3269,4543,10251,10254,10280,4555,3735,3887,3315,3316,3290,4540,4498,4037,3286,10371,3287,3288,10400,3289,4539,10317,10409,10520,3382,3817,3753,10320,4548,10271,4129,4546,4529,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4567,3777,4565,10293,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076])). % 183.99/184.51 cnf(10596,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x105961),x105961))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(10599,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x105991),f333(a115,f333(f333(f79(a875),x105992),x105991))))), % 183.99/184.51 inference(rename_variables,[],[3746])). % 183.99/184.51 cnf(10601,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x106011),f333(f333(f80(a875),f333(a115,x106011)),f333(a115,x106011))))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,4493,10444,3075,3243,10214,10283,10286,10378,3118,3179,3144,3125,3768,3213,4560,4503,10274,3174,4085,4573,3195,3658,3356,10362,10480,10549,3748,3269,4543,10251,10254,10280,4555,3735,3887,3315,3316,3290,4540,4498,4037,3286,10371,10467,3287,3288,10400,3289,4539,10317,10409,10520,3382,3817,3753,10320,4548,10271,4129,4546,4529,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,3559,4567,3777,4565,10293,3746,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101])). % 183.99/184.51 cnf(10602,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x106021),f333(f333(f80(a875),x106021),x106021)))), % 183.99/184.51 inference(rename_variables,[],[3559])). % 183.99/184.51 cnf(10605,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x106051),f333(f333(f80(a875),x106051),x106051)))), % 183.99/184.51 inference(rename_variables,[],[3559])). % 183.99/184.51 cnf(10610,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x106101),f333(a115,x106101)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10613,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x106131),f333(a115,x106131)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10616,plain, % 183.99/184.51 (P1(f333(f333(f335(x106161),x106162),f256(f882(x106161,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(10635,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x106351),x106352)),x106352))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(10638,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x106381),x106382)),x106382))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(10641,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x106411)),x106411))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(10644,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x106441)),x106441))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(10647,plain, % 183.99/184.51 (P1(f333(f256(f882(x106471,a870)),x106472))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(10650,plain, % 183.99/184.51 (E(f333(f37(a875),f333(f254(a875),x106501)),x106501)), % 183.99/184.51 inference(rename_variables,[],[3174])). % 183.99/184.51 cnf(10653,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x106531),f333(a115,x106531)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10660,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x106601),x106601))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(10665,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x106651),x106651))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(10674,plain, % 183.99/184.51 (E(f333(f264(x106741,x106741),f265(x106741,x106742)),x106742)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(10677,plain, % 183.99/184.51 (P1(f333(f256(f882(x106771,a870)),x106772))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(10680,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x106801))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(10683,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x106831,a870)),f196(f882(x106831,a870))),x106832))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(10686,plain, % 183.99/184.51 (P1(f333(f256(f882(x106861,a870)),x106862))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(10688,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(f333(f80(a875),f333(a115,x106881)),f333(a115,x106881))),x106881))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,4493,10444,3075,3243,10214,10283,10286,10378,10381,3118,3179,3144,3125,3768,3213,4560,4503,10274,3174,10343,4085,4573,3195,3658,3595,3356,10362,10480,10549,10610,10613,3748,3269,4543,10251,10254,10280,4555,3735,3501,3887,3315,3316,3290,4540,4498,4037,3286,10371,10467,10596,3287,3288,10400,10455,3289,4539,10317,10409,10520,3446,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,3309,4129,4546,4529,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,4567,3777,4565,10293,10296,10635,3746,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308])). % 183.99/184.51 cnf(10689,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x106891),f333(f333(f80(a875),x106891),x106891)))), % 183.99/184.51 inference(rename_variables,[],[3559])). % 183.99/184.51 cnf(10706,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,f333(a115,f333(f333(f79(a875),x107061),x107062)))),f333(a115,x107062)))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,4493,10444,3075,3243,10214,10283,10286,10378,10381,3220,3118,3179,3144,3125,3768,3213,4560,4503,10274,3174,10343,4085,4573,3195,3658,3595,3356,10362,10480,10549,10610,10613,10653,3748,3269,4543,10251,10254,10280,4555,3735,3501,3887,3315,3316,3290,4540,4498,4037,3286,10371,10467,10596,3287,3288,10400,10455,3289,4539,10317,10409,10520,3446,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,3309,4129,4546,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,4567,3777,4565,10293,10296,10635,3746,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356])). % 183.99/184.51 cnf(10729,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x107291),x107291))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10740,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x107401,f882(x107402,a870))),x107403),x107404))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(10747,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x107471),f333(a115,x107471)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10749,plain, % 183.99/184.51 (P1(f333(f333(f248(a1),f333(f333(f22(a1),x107491),f77(a1))),x107491))), % 183.99/184.51 inference(scs_inference,[],[4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,4493,10444,3075,3243,10214,10283,10286,10378,10381,3220,3118,3179,3144,3125,3768,3213,4560,4503,10274,3174,10343,4085,3939,4573,3195,3658,3595,3356,10362,10480,10549,10610,10613,10653,3748,3269,4543,10251,10254,10280,4555,3735,3501,3887,3315,3316,3290,4540,4498,4037,3286,10371,10467,10596,3287,10729,3288,10400,10455,10665,3289,4539,10317,10409,10520,3446,4551,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,3309,4129,4546,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,4567,4568,3777,4565,10293,10296,10635,3746,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610])). % 183.99/184.51 cnf(10750,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x107501),x107501))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(10755,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x107551),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10768,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x107681),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10771,plain, % 183.99/184.51 (~P1(f333(f333(f248(f882(x107711,a870)),x107712),f196(f882(x107711,a870))))), % 183.99/184.51 inference(rename_variables,[],[4561])). % 183.99/184.51 cnf(10774,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x107741),x107741))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10777,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x107771),x107771))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10792,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x107921),x107921))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10801,plain, % 183.99/184.51 (~P1(f333(f333(f335(x108011),x108012),f196(f882(x108011,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10810,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x108101),x108101))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10813,plain, % 183.99/184.51 (~P1(f333(f333(f335(x108131),x108132),f196(f882(x108131,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10816,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x108161,a870)),f333(f312(x108162,x108161,x108163),f333(f313(x108162,x108161,x108163),x108164))),x108164))), % 183.99/184.51 inference(rename_variables,[],[4189])). % 183.99/184.51 cnf(10823,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x108231,a870)),f333(f174(x108231),f333(f137(x108231,x108232),x108233))),f333(f174(x108231),x108233)))), % 183.99/184.51 inference(rename_variables,[],[3949])). % 183.99/184.51 cnf(10826,plain, % 183.99/184.51 (E(f333(f312(x108261,x108261,f5(x108261)),x108262),x108262)), % 183.99/184.51 inference(rename_variables,[],[3345])). % 183.99/184.51 cnf(10833,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x108331))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(10836,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x108361),x108361))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10839,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x108391),x108391))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10842,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x108421,f882(x108422,a870))),x108423),x108424))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(10849,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x108491),x108491))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(10860,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x108601),f333(a115,f333(f333(f79(a875),x108602),x108601))))), % 183.99/184.51 inference(rename_variables,[],[3746])). % 183.99/184.51 cnf(10863,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x108631),f333(f333(f80(a875),x108631),x108631)))), % 183.99/184.51 inference(rename_variables,[],[3559])). % 183.99/184.51 cnf(10873,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x108731),x108731))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10876,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x108761),x108761))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(10879,plain, % 183.99/184.51 (~E(f333(a115,x108791),x108791)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(10884,plain, % 183.99/184.51 (P1(f333(f333(f335(x108841),x108842),f256(f882(x108841,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(10889,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x108891),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(10904,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x109041))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(10911,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x109111),x109111))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10920,plain, % 183.99/184.51 (~P1(f333(f333(f335(x109201),x109202),f196(f882(x109201,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10924,plain, % 183.99/184.51 (E(f333(f333(f104(f882(x109241,a870)),f333(f333(f104(f882(x109241,a870)),x109242),f333(f78(f882(x109241,a870)),x109243))),x109243),f196(f882(x109241,a870)))), % 183.99/184.51 inference(scs_inference,[],[4570,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,4493,10444,3075,3243,10214,10283,10286,10378,10381,3220,3118,3179,3144,3125,3768,3345,3213,4560,4503,10274,3174,10343,4085,3939,4573,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,3748,3269,4543,10251,10254,10280,10755,10768,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,3659,4037,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,4551,10801,10813,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766])). % 183.99/184.51 cnf(10928,plain, % 183.99/184.51 (P1(f333(f333(f335(x109281),x109282),f256(f882(x109281,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(10931,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x109311),f876(x109311))),f333(f333(f268(f876(x109311),f876(x109311)),x109312),f116(x109311))),f146(x109311,x109313)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(10937,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(x109371,x109371)),x109372),f265(x109371,f196(f882(x109371,a870)))))), % 183.99/184.51 inference(scs_inference,[],[4570,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,4493,10444,3075,3243,10214,10283,10286,10378,10381,3220,3118,3179,3144,3125,3768,3345,3213,4560,4503,10274,3174,10343,4085,3939,4573,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,3748,3269,4543,10251,10254,10280,10755,10768,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,3659,4037,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,4551,10801,10813,10920,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908])). % 183.99/184.51 cnf(10938,plain, % 183.99/184.51 (~P1(f333(f333(f335(x109381),x109382),f196(f882(x109381,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10940,plain, % 183.99/184.51 (~P1(f333(f333(f335(x109401),x109402),f333(f313(x109401,x109403,x109404),f196(f882(x109403,a870)))))), % 183.99/184.51 inference(scs_inference,[],[4570,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,4493,10444,3075,3243,10214,10283,10286,10378,10381,3220,3118,3179,3144,3125,3768,3345,3213,4560,4503,10274,3174,10343,4085,3939,4573,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,3748,3269,4543,10251,10254,10280,10755,10768,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,3659,4037,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,4551,10801,10813,10920,10938,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,4571,3744,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942])). % 183.99/184.51 cnf(10941,plain, % 183.99/184.51 (~P1(f333(f333(f335(x109411),x109412),f196(f882(x109411,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10944,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x109441,a870)),x109442),f333(f333(f311(x109441),x109443),x109442)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(10947,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x109471),x109471))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(10950,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x109501,a870)),x109502),f333(f333(f311(x109501),x109503),x109502)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(10965,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x109651,a870)),x109652),f333(f333(f311(x109651),x109653),x109652)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(10970,plain, % 183.99/184.51 (~P1(f333(f62(x109701,x109702,f196(f882(x109701,a870))),x109703))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(10983,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x109831),f333(a115,x109831)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(10993,plain, % 183.99/184.51 (~E(f333(f312(x109931,f882(x109931,a870),x109932),x109933),f333(f310(x109931),x109933))), % 183.99/184.51 inference(rename_variables,[],[4549])). % 183.99/184.51 cnf(10996,plain, % 183.99/184.51 (~P1(f333(f333(f335(x109961),x109962),f196(f882(x109961,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(10999,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x109991,x109991)),f333(f333(f268(x109991,x109991),x109992),x109992)),f309(x109991,x109993)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(11002,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x110021,a870)),f333(f174(x110021),f178(x110021,x110022,x110023))),f333(f174(x110021),x110022)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(11005,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x110051,a870)),x110052),f256(f882(x110051,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(11021,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x110211,a870)),f196(f882(x110211,a870))),x110212))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(11032,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x110321),f876(x110321))),f333(f333(f268(f876(x110321),f876(x110321)),x110322),f116(x110321))),f148(x110321,x110323)))), % 183.99/184.51 inference(rename_variables,[],[4574])). % 183.99/184.51 cnf(11043,plain, % 183.99/184.51 (~E(f333(a115,x110431),x110431)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11046,plain, % 183.99/184.51 (~E(f333(a115,x110461),x110461)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11048,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f876(x110481),f876(x110481))),f333(f333(f268(f876(x110481),f876(x110481)),f116(x110481)),f116(x110481))),f333(f333(f290(f876(x110481),f876(x110481),f876(x110481)),f159(x110481,x110482)),f309(f876(x110481),f159(x110481,x110482)))))), % 183.99/184.51 inference(scs_inference,[],[4570,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,4560,3937,4503,10274,4549,3174,10343,4085,3939,10999,4573,10931,4574,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3744,10683,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609])). % 183.99/184.51 cnf(11058,plain, % 183.99/184.51 (P25(x110581,x110581,f5(x110581),x110582)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(11063,plain, % 183.99/184.51 (~E(f333(f312(x110631,f882(x110631,a870),x110632),x110633),f333(f310(x110631),x110633))), % 183.99/184.51 inference(rename_variables,[],[4549])). % 183.99/184.51 cnf(11068,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x110681,a870)),x110682),f256(f882(x110681,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(11082,plain, % 183.99/184.51 (~P1(f333(f333(f335(x110821),x110822),f196(f882(x110821,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11085,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x110851)),x110851))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11090,plain, % 183.99/184.51 (~P1(f333(f333(f335(x110901),x110902),f196(f882(x110901,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11102,plain, % 183.99/184.51 (~P1(f333(f333(f335(a875),f333(a115,f333(f143(a875,a875,f79(a875),f2(a875)),x111021))),f333(f174(a875),x111021)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,4573,10931,4574,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3744,10683,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827])). % 183.99/184.51 cnf(11103,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x111031)),x111031))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11106,plain, % 183.99/184.51 (~P1(f333(f333(f335(x111061),x111062),f196(f882(x111061,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11116,plain, % 183.99/184.51 (E(f333(x111161,f710(f333(x111161,x111162),f333(f240(x111163),x111162),x111161,x111164,x111163)),f333(x111161,x111162))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,4573,10931,4574,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3744,10683,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903])). % 183.99/184.51 cnf(11125,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x111251,x111251)),f333(f333(f268(x111251,x111251),x111252),x111252)),f309(x111251,x111253)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(11130,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111301),f876(x111301))),f333(f333(f268(f876(x111301),f876(x111301)),x111302),f116(x111301))),f146(x111301,x111303)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(11133,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111331),f876(x111331))),f333(f333(f268(f876(x111331),f876(x111331)),x111332),f116(x111331))),f148(x111331,x111333)))), % 183.99/184.51 inference(rename_variables,[],[4574])). % 183.99/184.51 cnf(11136,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111361),f876(x111361))),f333(f333(f268(f876(x111361),f876(x111361)),x111362),f116(x111361))),f158(x111361,x111363)))), % 183.99/184.51 inference(rename_variables,[],[4575])). % 183.99/184.51 cnf(11138,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111381),f876(x111381))),f333(f333(f268(f876(x111381),f876(x111381)),f116(x111381)),x111382)),f333(f288(f876(x111381),f876(x111381)),f146(x111381,x111383))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,4573,10931,11130,4574,11032,4575,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,4561,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3744,10683,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051])). % 183.99/184.51 cnf(11141,plain, % 183.99/184.51 (~P1(f333(f333(f248(f882(x111411,a870)),x111412),f196(f882(x111411,a870))))), % 183.99/184.51 inference(rename_variables,[],[4561])). % 183.99/184.51 cnf(11144,plain, % 183.99/184.51 (~P1(f333(f333(f335(x111441),x111442),f196(f882(x111441,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11148,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x111481,a870)),x111482),f333(f333(f113(f882(x111481,a870)),x111483),f256(f882(x111481,a870)))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,4573,10931,11130,4574,11032,4575,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,11068,4561,10771,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3744,10683,3559,10602,10605,10689,10863,4567,4568,10740,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103])). % 183.99/184.51 cnf(11149,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x111491,a870)),x111492),f256(f882(x111491,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(11152,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x111521,f882(x111522,a870))),x111523),x111524))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(11161,plain, % 183.99/184.51 (~P1(f333(f333(f335(x111611),x111612),f196(f882(x111611,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11164,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(x111641,x111641)),f333(f333(f268(x111641,x111641),x111642),x111643)),f154(x111641,f116(f882(x111641,a875)))))), % 183.99/184.51 inference(rename_variables,[],[4571])). % 183.99/184.51 cnf(11167,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x111671,a870)),x111672),x111672))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(11170,plain, % 183.99/184.51 (~P1(f333(f333(f335(x111701),x111702),f196(f882(x111701,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11172,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x111721,a870)),f333(f287(x111722,x111721,f196(f882(f881(x111722,x111721),a870))),x111723)),x111724))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,4573,10931,11130,4574,11032,4575,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,11068,4561,10771,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3591,3744,10683,11021,3559,10602,10605,10689,10863,4567,4568,10740,10842,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274])). % 183.99/184.51 cnf(11173,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x111731,a870)),f196(f882(x111731,a870))),x111732))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(11176,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x111761,x111761)),f333(f333(f268(x111761,x111761),x111762),x111762)),f309(x111761,x111763)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(11182,plain, % 183.99/184.51 (P34(x111821,x111822,x111823,f333(f333(f155(x111824,x111821),x111825),f117(x111824,f116(x111824))),f116(x111822))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,11125,4573,10931,11130,4574,11032,4575,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,11068,4561,10771,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3591,3744,10683,11021,3559,10602,10605,10689,10863,4567,4568,10740,10842,4189,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306])). % 183.99/184.51 cnf(11187,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111871),f876(x111871))),f333(f333(f268(f876(x111871),f876(x111871)),x111872),f116(x111871))),f158(x111871,x111873)))), % 183.99/184.51 inference(rename_variables,[],[4575])). % 183.99/184.51 cnf(11190,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x111901),f876(x111901))),f333(f333(f268(f876(x111901),f876(x111901)),f116(x111901)),x111902)),f146(x111901,x111903)))), % 183.99/184.51 inference(rename_variables,[],[4576])). % 183.99/184.51 cnf(11198,plain, % 183.99/184.51 (P1(f333(f333(f335(x111981),x111982),f256(f882(x111981,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(11203,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x112031,a870)),f196(f882(x112031,a870))),x112032))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(11206,plain, % 183.99/184.51 (~P1(f333(f333(f335(x112061),x112062),f196(f882(x112061,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11209,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x112091,a870)),x112092),f256(f882(x112091,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(11214,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x112141,a870)),f196(f882(x112141,a870))),x112142))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(11216,plain, % 183.99/184.51 (~P1(f333(f66(a875,x112161,x112162,x112163,f256(f882(a875,a870))),x112164))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,4549,10993,3393,3174,10343,4085,3939,10999,11125,4573,10931,11130,4574,11032,4575,11136,4576,4577,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,3349,10647,10677,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4568,10740,10842,4189,4090,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560])). % 183.99/184.51 cnf(11227,plain, % 183.99/184.51 (P1(f333(f256(f882(x112271,a870)),x112272))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(11235,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x112351),f876(x112351))),f333(f333(f268(f876(x112351),f876(x112351)),x112352),f116(x112351))),f146(x112351,x112353)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(11238,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x112381),f876(x112381))),f333(f333(f268(f876(x112381),f876(x112381)),x112382),f116(x112381))),f148(x112381,x112383)))), % 183.99/184.51 inference(rename_variables,[],[4574])). % 183.99/184.51 cnf(11241,plain, % 183.99/184.51 (~E(f333(f333(f152(x112411),x112412),x112413),x112413)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(11244,plain, % 183.99/184.51 (~E(f333(a115,x112441),x112441)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11247,plain, % 183.99/184.51 (~P1(f333(f333(f335(x112471),x112472),f196(f882(x112471,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11252,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f876(x112521),f876(x112521))),f333(f333(f268(f876(x112521),f876(x112521)),x112522),x112522)),f159(x112521,f309(x112521,x112523))))), % 183.99/184.51 inference(rename_variables,[],[4079])). % 183.99/184.51 cnf(11257,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x112571),f876(x112571))),f333(f333(f268(f876(x112571),f876(x112571)),x112572),f116(x112571))),f146(x112571,x112573)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(11267,plain, % 183.99/184.51 (~P1(f333(f333(f335(x112671),x112672),f196(f882(x112671,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11270,plain, % 183.99/184.51 (~P1(f333(f333(f335(x112701),x112702),f196(f882(x112701,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11273,plain, % 183.99/184.51 (~P1(f333(f333(f335(x112731),x112732),f196(f882(x112731,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11276,plain, % 183.99/184.51 (P1(f333(f333(f335(x112761),x112762),f256(f882(x112761,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(11279,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x112791),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11284,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(x112841,x112841)),f333(f333(f268(x112841,x112841),x112842),x112843)),f154(x112841,f116(f882(x112841,a875)))))), % 183.99/184.51 inference(rename_variables,[],[4571])). % 183.99/184.51 cnf(11287,plain, % 183.99/184.51 (~E(f333(f312(x112871,f882(x112871,a870),x112872),x112873),f333(f310(x112871),x112873))), % 183.99/184.51 inference(rename_variables,[],[4549])). % 183.99/184.51 cnf(11290,plain, % 183.99/184.51 (~E(f333(f312(x112901,f882(x112901,a870),x112902),x112903),f333(f310(x112901),x112903))), % 183.99/184.51 inference(rename_variables,[],[4549])). % 183.99/184.51 cnf(11292,plain, % 183.99/184.51 (E(f333(f333(f268(a875,a875),f663(f309(a875,a323),a323,a875,f333(f333(f268(a875,a875),x112921),f333(a115,x112921)),a875,a875)),f664(f309(a875,a323),a323,a875,f333(f333(f268(a875,a875),x112921),f333(a115,x112921)),a875,a875)),f333(f333(f268(a875,a875),x112921),f333(a115,x112921)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,10441,4549,10993,11063,11287,3393,3174,10343,4085,3939,10999,11125,4573,10931,11130,11235,4574,11032,11133,4575,11136,4576,11190,4577,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4079,11252,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,11198,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,3349,10647,10677,10686,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,11164,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4568,10740,10842,4189,4090,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924])). % 183.99/184.51 cnf(11295,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x112951),f876(x112951))),f333(f333(f268(f876(x112951),f876(x112951)),x112952),f116(x112951))),f146(x112951,x112953)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(11298,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x112981),f876(x112981))),f333(f333(f268(f876(x112981),f876(x112981)),x112982),f116(x112981))),f148(x112981,x112983)))), % 183.99/184.51 inference(rename_variables,[],[4574])). % 183.99/184.51 cnf(11301,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x113011),f876(x113011))),f333(f333(f268(f876(x113011),f876(x113011)),x113012),f116(x113011))),f146(x113011,x113013)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(11304,plain, % 183.99/184.51 (~P1(f333(f333(f335(x113041),x113042),f196(f882(x113041,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11308,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x113081,x113082)),f333(f333(f268(x113081,x113082),f333(x113083,x113084)),f333(x113085,x113084))),f333(f312(f881(x113086,x113086),f881(x113081,x113082),f273(x113086,x113081,x113086,x113082,x113083,x113085)),f309(x113086,x113087))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,4493,10444,10535,3075,3128,3243,10214,10283,10286,10378,10381,3220,3755,3118,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,10441,4549,10993,11063,11287,3393,3174,10343,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,4555,3735,3501,3887,3315,3316,3290,4540,4498,4079,11252,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,11198,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,3349,10647,10677,10686,3382,3817,3753,10320,4548,10271,10641,10644,11085,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4563,10239,10242,10501,10552,10555,10560,4571,11164,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4568,10740,10842,4189,4090,3777,4565,10293,10296,10635,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053])). % 183.99/184.51 cnf(11311,plain, % 183.99/184.51 (~P1(f333(f333(f335(x113111),x113112),f196(f882(x113111,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11314,plain, % 183.99/184.51 (~P1(f333(f333(f335(x113141),x113142),f196(f882(x113141,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11317,plain, % 183.99/184.51 (P1(f333(f333(f335(x113171),f333(x113172,x113173)),f333(f312(x113174,x113171,x113172),f256(f882(x113174,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(11320,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(x113201,x113201)),f333(f333(f268(x113201,x113201),x113202),x113203)),f154(x113201,f116(f882(x113201,a875)))))), % 183.99/184.51 inference(rename_variables,[],[4571])). % 183.99/184.51 cnf(11328,plain, % 183.99/184.51 (E(f117(x113281,f116(x113281)),f116(x113281))), % 183.99/184.51 inference(rename_variables,[],[3128])). % 183.99/184.51 cnf(11331,plain, % 183.99/184.51 (~E(f333(a115,x113311),x113311)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11338,plain, % 183.99/184.51 (~E(f333(a115,x113381),x113381)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11343,plain, % 183.99/184.51 (E(f333(f264(x113431,x113431),f265(x113431,x113432)),x113432)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11346,plain, % 183.99/184.51 (E(f333(f264(x113461,x113461),f265(x113461,x113462)),x113462)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11352,plain, % 183.99/184.51 (~E(f333(a115,x113521),x113521)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11359,plain, % 183.99/184.51 (~E(f333(f333(f79(a1),x113591),x113591),a100)), % 183.99/184.51 inference(rename_variables,[],[4501])). % 183.99/184.51 cnf(11368,plain, % 183.99/184.51 (E(f333(f333(f22(a875),f2(a875)),x113681),f2(a875))), % 183.99/184.51 inference(rename_variables,[],[3196])). % 183.99/184.51 cnf(11371,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x113711),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11378,plain, % 183.99/184.51 (E(f333(f333(f79(a1),f333(f333(f80(a1),x113781),f333(f333(f38(a1),x113782),x113781))),f44(a1,x113782,x113781)),x113782)), % 183.99/184.51 inference(rename_variables,[],[3850])). % 183.99/184.51 cnf(11404,plain, % 183.99/184.51 (~E(f333(a115,x114041),x114041)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11407,plain, % 183.99/184.51 (~E(f333(a115,x114071),x114071)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11433,plain, % 183.99/184.51 (~P1(f333(f62(x114331,x114332,f196(f882(x114331,a870))),x114333))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(11436,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x114361,f882(x114362,a870))),x114363),x114364))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(11439,plain, % 183.99/184.51 (P1(f333(f333(f335(x114391),x114392),f256(f882(x114391,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(11451,plain, % 183.99/184.51 (~E(f333(a115,x114511),x114511)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11454,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x114541),x114541))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11461,plain, % 183.99/184.51 (P1(f333(f66(x114611,x114612,x114613,x114614,f196(f882(x114611,a870))),x114614))), % 183.99/184.51 inference(rename_variables,[],[4229])). % 183.99/184.51 cnf(11462,plain, % 183.99/184.51 (E(f333(f264(x114621,x114621),f265(x114621,x114622)),x114622)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11467,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x114671,f882(x114672,a870))),x114673),x114674))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(11478,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x114781),x114782)),x114782))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(11481,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x114811)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(11497,plain, % 183.99/184.51 (~E(f333(f333(f104(a875),f333(a115,x114971)),x114971),f333(a115,x114971))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,4493,10444,10535,3200,2885,2889,2892,2902,2904,2909,2919,2928,2929,2936,2947,2949,2950,2958,2959,2993,3024,3025,3027,3043,3053,3060,3075,4474,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,3220,3755,3118,3850,11378,3179,3144,3125,3768,3345,3213,3392,4560,3937,4503,10274,10441,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,11279,11371,4555,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,11198,11276,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,3349,10647,10677,10686,3382,3817,3753,10320,4548,10271,10641,10644,11085,11103,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4229,4563,10239,10242,10501,10552,10555,10560,10970,4571,11164,11284,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4557,4568,10740,10842,11152,11436,4189,4090,3777,4565,10293,10296,10635,10638,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362])). % 183.99/184.51 cnf(11504,plain, % 183.99/184.51 (E(f333(f264(x115041,x115041),f265(x115041,x115042)),x115042)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11509,plain, % 183.99/184.51 (E(f333(f264(x115091,x115091),f265(x115091,x115092)),x115092)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11512,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x115121)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(11517,plain, % 183.99/184.51 (~E(f333(a115,x115171),x115171)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11521,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f2(a1)),a82))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,4493,10444,10535,3200,2885,2889,2892,2902,2904,2909,2919,2928,2929,2936,2947,2949,2950,2951,2958,2959,2993,3024,3025,3027,3043,3053,3060,3075,4474,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,3220,3755,3118,3850,11378,3179,3144,3139,3125,3126,3768,3345,3213,3392,4560,3937,4503,10274,10441,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,11279,11371,4555,11481,11512,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,3289,4539,10317,10409,10520,10544,10792,10839,3446,10616,10884,10928,11198,11276,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,3349,10647,10677,10686,3388,3382,3817,3753,10320,4548,10271,10641,10644,11085,11103,3309,10680,10833,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,4229,4563,10239,10242,10501,10552,10555,10560,10970,4571,11164,11284,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4557,4568,10740,10842,11152,11436,4189,4090,3777,4565,10293,10296,10635,10638,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454])). % 183.99/184.51 cnf(11526,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x115261),x115261))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11547,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x115471)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(11560,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x115601),x115601))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11563,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x115631)),x115631))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11564,plain, % 183.99/184.51 (~E(f333(a115,x115641),x115641)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11574,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x115741),x115742)),x115741))), % 183.99/184.51 inference(rename_variables,[],[4566])). % 183.99/184.51 cnf(11577,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x115771)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(11580,plain, % 183.99/184.51 (~E(f333(a115,x115801),x115801)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11593,plain, % 183.99/184.51 (P1(f333(f333(f335(x115931),x115932),f333(f333(f311(x115931),x115932),x115933)))), % 183.99/184.51 inference(rename_variables,[],[3606])). % 183.99/184.51 cnf(11594,plain, % 183.99/184.51 (~P1(f333(f333(f247(a1),f2(a1)),f333(f78(a1),f333(f103(a1),f333(a115,x115941)))))), % 183.99/184.51 inference(rename_variables,[],[4567])). % 183.99/184.51 cnf(11597,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),f333(f333(f22(a875),x115971),x115972)),f333(a115,x115971)))), % 183.99/184.51 inference(rename_variables,[],[3748])). % 183.99/184.51 cnf(11600,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f44(a875,x116001,x116002)),x116001))), % 183.99/184.51 inference(rename_variables,[],[3753])). % 183.99/184.51 cnf(11606,plain, % 183.99/184.51 (E(f333(f264(x116061,x116061),f265(x116061,x116062)),x116062)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(11611,plain, % 183.99/184.51 (E(f333(f333(f135(x116111),f171(x116111,x116112,x116113)),f171(x116111,x116114,x116113)),f333(f333(f135(x116111),f171(x116111,x116114,x116113)),f171(x116111,x116112,x116113)))), % 183.99/184.51 inference(rename_variables,[],[3865])). % 183.99/184.51 cnf(11616,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x116161)),x116161))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11625,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x116251),x116251))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11628,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f44(a875,x116281,x116282)),x116281))), % 183.99/184.51 inference(rename_variables,[],[3753])). % 183.99/184.51 cnf(11629,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x116291))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(11631,plain, % 183.99/184.51 (~P1(f333(f333(f247(a1),f77(a1)),f2(a1)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,4493,10444,10535,3200,2885,2889,2890,2892,2893,2902,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2958,2959,2993,3024,3025,3027,3033,3043,3053,3060,3075,4474,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,3220,3755,3118,3494,3850,11378,3179,3144,3139,3125,3126,3768,3345,3213,3392,4560,3937,4503,10274,10441,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4369,4370,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,3269,4543,10251,10254,10280,10755,10768,10889,11279,11371,4555,11481,11512,11547,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,10876,3289,4539,10317,10409,10520,10544,10792,10839,10849,11526,3446,10616,10884,10928,11198,11276,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,3349,10647,10677,10686,3388,3382,3817,3753,10320,11600,4548,10271,10641,10644,11085,11103,11563,3309,10680,10833,10904,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,4571,11164,11284,3904,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,4557,4568,10740,10842,11152,11436,4189,4090,3777,4565,10293,10296,10635,10638,4566,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800])). % 183.99/184.51 cnf(11646,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x116461),x116461))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11649,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x116491),x116491))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11652,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x116521),x116521))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11655,plain, % 183.99/184.51 (P1(f333(f333(f335(x116551),f333(x116552,x116553)),f333(f312(x116554,x116551,x116552),f256(f882(x116554,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(11656,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x116561),x116562)),x116562))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(11659,plain, % 183.99/184.51 (P1(f333(f333(f335(x116591),f333(x116592,x116593)),f333(f312(x116594,x116591,x116592),f256(f882(x116594,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(11660,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x116601)),x116601))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11665,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x116651),x116652)),x116651))), % 183.99/184.51 inference(rename_variables,[],[4566])). % 183.99/184.51 cnf(11668,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x116681),x116681))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11671,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x116711),x116711))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11677,plain, % 183.99/184.51 (~P35(x116771,x116772,f116(x116771))), % 183.99/184.51 inference(rename_variables,[],[4512])). % 183.99/184.51 cnf(11680,plain, % 183.99/184.51 (P1(f333(f333(f335(x116801),x116802),f256(f882(x116801,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(11681,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x116811)),x116811))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11684,plain, % 183.99/184.51 (~P1(f333(f62(x116841,x116842,f196(f882(x116841,a870))),x116843))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(11697,plain, % 183.99/184.51 (~P1(f333(f333(f335(x116971),x116972),f196(f882(x116971,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11700,plain, % 183.99/184.51 (E(f333(f333(f16(x117001,x117002),x117003),x117004),x117003)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(11703,plain, % 183.99/184.51 (E(f333(f333(f16(x117031,x117032),x117033),x117034),x117033)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(11715,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),f2(a875)),f333(a115,x117151)))), % 183.99/184.51 inference(rename_variables,[],[3368])). % 183.99/184.51 cnf(11718,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x117181),x117181))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11721,plain, % 183.99/184.51 (P1(f333(f333(f335(x117211),f333(x117212,x117213)),f333(f312(x117214,x117211,x117212),f256(f882(x117214,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(11724,plain, % 183.99/184.51 (P1(f333(f61(x117241),f333(f174(x117241),x117242)))), % 183.99/184.51 inference(rename_variables,[],[3328])). % 183.99/184.51 cnf(11727,plain, % 183.99/184.51 (P1(f333(f61(x117271),f333(f174(x117271),x117272)))), % 183.99/184.51 inference(rename_variables,[],[3328])). % 183.99/184.51 cnf(11730,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f333(f78(a1),f333(f103(a1),x117301))),f333(f103(a1),x117302)))), % 183.99/184.51 inference(rename_variables,[],[3778])). % 183.99/184.51 cnf(11733,plain, % 183.99/184.51 (~P1(f333(f333(f335(x117331),x117332),f196(f882(x117331,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(11745,plain, % 183.99/184.51 (~P1(f333(f333(f335(a875),x117451),f333(f254(a875),f2(a875))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4511,4512,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,4493,10444,10535,3200,2885,2889,2890,2892,2893,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2954,2958,2959,2993,3024,3025,3027,3033,3043,3053,3060,3075,4474,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,3220,3755,3118,3494,3850,11378,3179,3144,3139,3125,3126,3768,3345,3213,3392,4560,3937,4503,10274,10441,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4369,4370,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,11597,3269,3368,4543,10251,10254,10280,10755,10768,10889,11279,11371,4555,11481,11512,11547,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,3328,11724,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,10876,3289,3364,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,3446,10616,10884,10928,11198,11276,11439,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,3349,10647,10677,10686,3388,3382,3817,3753,10320,11600,4548,10271,10641,10644,11085,11103,11563,11616,11660,3309,10680,10833,10904,3778,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,11433,4571,11164,11284,4014,3904,11317,11655,11659,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,4189,4090,3777,3721,4565,10293,10296,10635,10638,11478,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131])). % 183.99/184.51 cnf(11752,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x117521),x117521))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11755,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x117551),x117551))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11764,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x117641),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11767,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x117671),x117671))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11772,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x117721),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11779,plain, % 183.99/184.51 (P1(f333(f256(f882(x117791,a870)),x117792))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(11784,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x117841))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(11785,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x117851)),x117851))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11788,plain, % 183.99/184.51 (~P1(f333(f62(x117881,x117882,f196(f882(x117881,a870))),x117883))), % 183.99/184.51 inference(rename_variables,[],[4563])). % 183.99/184.51 cnf(11805,plain, % 183.99/184.51 (P1(f333(f333(f248(a1),f333(f78(a1),f77(a1))),f2(a1)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4511,4512,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,4493,10444,10535,3200,2885,2889,2890,2892,2893,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2954,2958,2959,2970,2971,2993,3024,3025,3027,3033,3043,3045,3053,3060,3075,4474,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,3220,3755,3118,3494,3850,11378,3179,3144,3139,3125,3126,3768,3345,3213,3392,4560,3937,4503,10274,10441,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4369,4370,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,11597,3269,3368,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,4555,11481,11512,11547,11577,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,3328,11724,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,10876,11560,11755,3289,3364,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,3446,10616,10884,10928,11198,11276,11439,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,3349,10647,10677,10686,11227,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,3309,10680,10833,10904,11629,3778,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,4014,3904,11317,11655,11659,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,4189,4090,3777,3721,4565,10293,10296,10635,10638,11478,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434])). % 183.99/184.51 cnf(11810,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x118101),x118101))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11813,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x118131),x118131))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11816,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x118161),x118161))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11819,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x118191),x118191))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11822,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x118221)),x118221))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11825,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x118251)),x118251))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11828,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x118281)),x118281))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11831,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x118311)),x118311))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(11847,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),f333(f333(f22(a875),x118471),f333(a115,x118471))),f2(a875)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,4511,4512,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,4493,10444,10535,3200,2885,2889,2890,2892,2893,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2954,2958,2959,2970,2971,2993,3024,3025,3027,3033,3043,3045,3053,3060,3075,4474,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,3220,3755,3118,3494,3850,11378,3179,3144,3139,3125,3126,3768,3345,3213,3392,4560,3937,4503,10274,10441,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,3939,10999,11125,11176,4573,10931,11130,11235,11257,11295,11301,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,3658,4369,4370,4501,3595,3813,3356,10362,10480,10549,10610,10613,10653,10747,10983,3748,11597,3269,3368,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,4555,11481,11512,11547,11577,3735,3501,3887,3315,3316,3290,4540,4498,3484,4556,4079,11252,3616,3328,11724,4048,3949,10823,4000,3659,4037,3677,11005,11068,11149,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,11752,3287,10729,10774,10777,10810,10836,10873,10911,3288,10400,10455,10665,10750,10876,11560,11755,3289,3364,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,3446,10616,10884,10928,11198,11276,11439,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,3349,10647,10677,10686,11227,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,3309,10680,10833,10904,11629,3778,4129,4546,3825,4529,4531,3260,3261,4530,4533,4534,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,4014,3904,11317,11655,11659,3742,10944,10950,3591,3744,10683,11021,11173,11203,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,4189,4090,3777,3721,4565,10293,10296,10635,10638,11478,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510])). % 183.99/184.51 cnf(11848,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x118481),x118481))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11854,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x118541),x118541))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11865,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x118651),x118651))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11868,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(f881(f876(x118681),f876(x118681)),a870)),f159(x118681,x118682)),f309(f876(x118681),f158(x118681,x118682))))), % 183.99/184.51 inference(rename_variables,[],[4005])). % 183.99/184.51 cnf(11875,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x118751),f333(a115,x118751)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(11878,plain, % 183.99/184.51 (P1(f333(f333(f335(f882(x118781,a870)),x118782),f333(f310(x118781),x118782)))), % 183.99/184.51 inference(rename_variables,[],[3659])). % 183.99/184.51 cnf(11879,plain, % 183.99/184.51 (~E(f333(a115,x118791),x118791)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11886,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x118861),x118861))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11891,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x118911),x118911))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11900,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x119001,a870)),x119002),f333(f333(f311(x119001),x119003),x119002)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(11903,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x119031),x119031))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(11904,plain, % 183.99/184.51 (~E(f333(a115,x119041),x119041)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11915,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119151),x119151))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11916,plain, % 183.99/184.51 (~E(f333(a115,x119161),x119161)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11919,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x119191),x119191))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(11922,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x119221),x119221))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(11925,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x119251),x119251))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(11928,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x119281),x119281))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(11931,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x119311),x119311))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11934,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119341),x119341))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11937,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119371),x119371))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11938,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x119381),f333(a115,x119381)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(11945,plain, % 183.99/184.51 (~E(f333(a115,x119451),x119451)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11950,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119501),x119501))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(11951,plain, % 183.99/184.51 (~E(f333(a115,x119511),x119511)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(11956,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x119561),x119561))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11971,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x119711),x119711))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(11976,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x119761))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(11993,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119931),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11996,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x119961),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(11999,plain, % 183.99/184.51 (~P1(f333(f333(f335(x119991),x119992),f196(f882(x119991,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12002,plain, % 183.99/184.51 (~P1(f333(f333(f335(x120021),x120022),f196(f882(x120021,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12005,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120051),x120051))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12008,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120081),x120081))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12011,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120111),x120111))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12014,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120141),x120141))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12017,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x120171),f333(a115,x120171)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12024,plain, % 183.99/184.51 (P1(f333(f333(f335(f882(x120241,a870)),x120242),f333(f310(x120241),x120242)))), % 183.99/184.51 inference(rename_variables,[],[3659])). % 183.99/184.51 cnf(12029,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x120291,a870)),x120292),f333(f333(f311(x120291),x120293),x120292)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(12036,plain, % 183.99/184.51 (~P1(f333(f333(f335(x120361),x120362),f196(f882(x120361,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12045,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x120451,a870)),x120452),f256(f882(x120451,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12046,plain, % 183.99/184.51 (~E(f333(a115,x120461),x120461)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12049,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x120491,a870)),f196(f882(x120491,a870))),x120492))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(12052,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x120521,a870)),f333(f174(x120521),f333(f137(x120521,x120522),x120523))),f333(f174(x120521),x120523)))), % 183.99/184.51 inference(rename_variables,[],[3949])). % 183.99/184.51 cnf(12058,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x120581),f333(a115,x120581)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12067,plain, % 183.99/184.51 (E(f333(f264(x120671,x120671),f265(x120671,x120672)),x120672)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12078,plain, % 183.99/184.51 (P1(f333(f61(x120781),f196(f882(x120781,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12079,plain, % 183.99/184.51 (~P1(f333(f333(f335(x120791),x120792),f196(f882(x120791,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12084,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120841),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12085,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x120851),x120851))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12090,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x120901,a870)),f333(f174(x120901),f178(x120901,x120902,x120903))),f333(f174(x120901),x120902)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(12093,plain, % 183.99/184.51 (P25(x120931,x120931,f5(x120931),x120932)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12098,plain, % 183.99/184.51 (P1(f333(f333(f335(f882(x120981,a870)),x120982),f333(f310(x120981),x120982)))), % 183.99/184.51 inference(rename_variables,[],[3659])). % 183.99/184.51 cnf(12105,plain, % 183.99/184.51 (P1(f333(f333(f202(a24),x121051),x121051))), % 183.99/184.51 inference(rename_variables,[],[3286])). % 183.99/184.51 cnf(12108,plain, % 183.99/184.51 (~P1(f333(f333(f335(x121081),x121082),f196(f882(x121081,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12111,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x121111,a870)),x121112),f333(f333(f311(x121111),x121113),x121112)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(12112,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x121121,a870)),x121122),f256(f882(x121121,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12119,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x121191),f333(a115,x121191)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12122,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x121221),f333(a115,x121221)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12125,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x121251),x121251))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12128,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x121281),x121281))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12131,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x121311),x121311))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12134,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x121341),x121341))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12137,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x121371,a870)),x121372),x121372))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12144,plain, % 183.99/184.51 (P1(f333(f333(f335(f882(x121441,a870)),x121442),f333(f310(x121441),x121442)))), % 183.99/184.51 inference(rename_variables,[],[3659])). % 183.99/184.51 cnf(12153,plain, % 183.99/184.51 (~E(f333(a115,x121531),x121531)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12154,plain, % 183.99/184.51 (E(f333(f312(x121541,x121541,f5(x121541)),x121542),x121542)), % 183.99/184.51 inference(rename_variables,[],[3345])). % 183.99/184.51 cnf(12157,plain, % 183.99/184.51 (P32(x121571,x121572,f116(x121571),f116(x121571))), % 183.99/184.51 inference(rename_variables,[],[3540])). % 183.99/184.51 cnf(12160,plain, % 183.99/184.51 (~E(f333(a115,x121601),x121601)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12163,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x121631,a870)),f333(f174(x121631),f178(x121631,x121632,x121633))),f333(f174(x121631),x121632)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(12164,plain, % 183.99/184.51 (P1(f333(f61(x121641),f333(f174(x121641),x121642)))), % 183.99/184.51 inference(rename_variables,[],[3328])). % 183.99/184.51 cnf(12175,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x121751),x121751))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12178,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x121781),x121781))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12187,plain, % 183.99/184.51 (P14(a875,f333(f170(a875),f333(f333(f155(f876(x121871),a875),f197(f876(x121871))),f182(x121871,x121872))))), % 183.99/184.51 inference(rename_variables,[],[3860])). % 183.99/184.51 cnf(12190,plain, % 183.99/184.51 (P25(x121901,x121901,f5(x121901),x121902)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12193,plain, % 183.99/184.51 (P1(f333(f333(f335(f876(x121931)),f116(x121931)),f162(x121931,x121932)))), % 183.99/184.51 inference(rename_variables,[],[3492])). % 183.99/184.51 cnf(12196,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x121961,f882(x121962,a870))),x121963),x121964))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(12201,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x122011),x122011))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12202,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x122021))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(12205,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x122051,f882(x122052,a870))),x122053),x122054))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(12208,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(f881(f876(x122081),f876(x122081)),a870)),f159(x122081,x122082)),f309(f876(x122081),f158(x122081,x122082))))), % 183.99/184.51 inference(rename_variables,[],[4005])). % 183.99/184.51 cnf(12214,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122141,a870)),f196(f882(x122141,a870))),x122142))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(12217,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122171,a870)),f333(f312(x122172,x122171,x122173),f333(f313(x122172,x122171,x122173),x122174))),x122174))), % 183.99/184.51 inference(rename_variables,[],[4189])). % 183.99/184.51 cnf(12220,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122201,a870)),f333(f174(x122201),f178(x122201,x122202,x122203))),f333(f174(x122201),x122202)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(12221,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122211,a870)),f333(f174(x122211),f333(f137(x122211,x122212),x122213))),f333(f174(x122211),x122213)))), % 183.99/184.51 inference(rename_variables,[],[3949])). % 183.99/184.51 cnf(12224,plain, % 183.99/184.51 (P25(x122241,f879(x122241),f240(x122241),x122242)), % 183.99/184.51 inference(rename_variables,[],[3541])). % 183.99/184.51 cnf(12229,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122291,a870)),f333(f312(x122292,x122291,x122293),f333(f313(x122292,x122291,x122293),x122294))),x122294))), % 183.99/184.51 inference(rename_variables,[],[4189])). % 183.99/184.51 cnf(12232,plain, % 183.99/184.51 (P1(f333(f61(f879(x122321)),f333(f312(x122322,f879(x122321),f333(f180(x122322,x122321),x122323)),f256(f882(x122322,a870)))))), % 183.99/184.51 inference(rename_variables,[],[4014])). % 183.99/184.51 cnf(12237,plain, % 183.99/184.51 (P1(f333(f333(f335(f876(x122371)),f116(x122371)),f162(x122371,x122372)))), % 183.99/184.51 inference(rename_variables,[],[3492])). % 183.99/184.51 cnf(12240,plain, % 183.99/184.51 (~P1(f333(f333(f335(f881(f876(x122401),f876(x122401))),f333(f333(f268(f876(x122401),f876(x122401)),x122402),f116(x122401))),f146(x122401,x122403)))), % 183.99/184.51 inference(rename_variables,[],[4573])). % 183.99/184.51 cnf(12243,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x122431),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12245,plain, % 183.99/184.51 (~P1(f333(f61(x122451),f256(f882(x122451,a870))))), % 183.99/184.51 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% 183.99/184.51 cnf(12246,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122461,a870)),x122462),x122462))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12249,plain, % 183.99/184.51 (~P1(f333(f333(f335(x122491),x122492),f196(f882(x122491,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12252,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x122521,f882(x122522,a870))),x122523),x122524))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(12255,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122551,a870)),f333(f312(x122552,x122551,x122553),f333(f313(x122552,x122551,x122553),x122554))),x122554))), % 183.99/184.51 inference(rename_variables,[],[4189])). % 183.99/184.51 cnf(12256,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122561,a870)),x122562),x122562))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12261,plain, % 183.99/184.51 (E(f333(f264(x122611,x122611),f265(x122611,x122612)),x122612)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12264,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x122641,a870)),f333(f174(x122641),f178(x122641,x122642,x122643))),f333(f174(x122641),x122642)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(12265,plain, % 183.99/184.51 (P1(f333(f61(x122651),f333(f174(x122651),x122652)))), % 183.99/184.51 inference(rename_variables,[],[3328])). % 183.99/184.51 cnf(12271,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x122711),x122711))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12274,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x122741),x122741))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12285,plain, % 183.99/184.51 (P25(x122851,x122851,f5(x122851),x122852)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12290,plain, % 183.99/184.51 (~P1(f333(f333(f335(x122901),x122902),f196(f882(x122901,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12293,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x122931,x122931)),f333(f333(f268(x122931,x122931),x122932),x122932)),f309(x122931,x122933)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(12296,plain, % 183.99/184.51 (~P1(f333(f333(f335(x122961),x122962),f196(f882(x122961,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12299,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x122991,x122991)),f333(f333(f268(x122991,x122991),x122992),x122992)),f309(x122991,x122993)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(12309,plain, % 183.99/184.51 (~E(f333(f333(f152(x123091),x123092),x123093),x123093)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(12312,plain, % 183.99/184.51 (P1(f333(f333(f335(x123121),x123122),f256(f882(x123121,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(12313,plain, % 183.99/184.51 (~E(f333(a115,x123131),x123131)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12316,plain, % 183.99/184.51 (P1(f333(f333(f335(f876(x123161)),f116(x123161)),f162(x123161,x123162)))), % 183.99/184.51 inference(rename_variables,[],[3492])). % 183.99/184.51 cnf(12317,plain, % 183.99/184.51 (~E(f333(f333(f152(x123171),x123172),x123173),f116(x123171))), % 183.99/184.51 inference(rename_variables,[],[4510])). % 183.99/184.51 cnf(12320,plain, % 183.99/184.51 (P1(f333(f333(f335(x123201),f333(x123202,x123203)),f333(f312(x123204,x123201,x123202),f256(f882(x123204,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12321,plain, % 183.99/184.51 (P25(x123211,x123211,f5(x123211),x123212)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12324,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123241,a870)),f196(f882(x123241,a870))),x123242))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(12325,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123251,a870)),x123252),x123252))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12328,plain, % 183.99/184.51 (P1(f333(f333(f335(x123281),f333(x123282,x123283)),f333(f312(x123284,x123281,x123282),f256(f882(x123284,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12329,plain, % 183.99/184.51 (P25(x123291,x123291,f5(x123291),x123292)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12332,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f876(x123321),f876(x123321))),f333(f333(f268(f876(x123321),f876(x123321)),f116(x123321)),f116(x123321))),f159(x123321,x123322)))), % 183.99/184.51 inference(rename_variables,[],[4085])). % 183.99/184.51 cnf(12335,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x123351),x123351))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12336,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x123361),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12342,plain, % 183.99/184.51 (P25(x123421,x123421,f5(x123421),x123422)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12345,plain, % 183.99/184.51 (E(f333(f333(f135(x123451),x123452),f116(x123451)),x123452)), % 183.99/184.51 inference(rename_variables,[],[3214])). % 183.99/184.51 cnf(12346,plain, % 183.99/184.51 (~E(f333(f333(f152(x123461),x123462),x123463),x123463)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(12349,plain, % 183.99/184.51 (E(f333(f333(f135(x123491),x123492),f116(x123491)),x123492)), % 183.99/184.51 inference(rename_variables,[],[3214])). % 183.99/184.51 cnf(12350,plain, % 183.99/184.51 (~E(f333(f333(f152(x123501),x123502),x123503),x123503)), % 183.99/184.51 inference(rename_variables,[],[4503])). % 183.99/184.51 cnf(12353,plain, % 183.99/184.51 (E(f333(f333(f135(x123531),x123532),f116(x123531)),x123532)), % 183.99/184.51 inference(rename_variables,[],[3214])). % 183.99/184.51 cnf(12362,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123621,a870)),x123622),f256(f882(x123621,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12366,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x123661),x123661))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12367,plain, % 183.99/184.51 (~E(f333(a115,x123671),x123671)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12370,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123701,a870)),f196(f882(x123701,a870))),x123702))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(12373,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x123731),x123731))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12376,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123761,a870)),x123762),x123762))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12381,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123811,a870)),x123812),f333(f333(f311(x123811),x123813),x123812)))), % 183.99/184.51 inference(rename_variables,[],[3742])). % 183.99/184.51 cnf(12384,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x123841,a870)),x123842),x123842))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12385,plain, % 183.99/184.51 (~P1(f333(f333(f335(x123851),x123852),f196(f882(x123851,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12388,plain, % 183.99/184.51 (~P1(f333(f333(f335(x123881),x123882),f196(f882(x123881,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12397,plain, % 183.99/184.51 (P25(x123971,x123971,f5(x123971),x123972)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12400,plain, % 183.99/184.51 (E(f333(f197(f876(x124001)),f171(x124001,x124002,x124003)),x124002)), % 183.99/184.51 inference(rename_variables,[],[3355])). % 183.99/184.51 cnf(12403,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x124031),x124031))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12404,plain, % 183.99/184.51 (P1(f333(f256(f882(x124041,a870)),x124042))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(12407,plain, % 183.99/184.51 (~P1(f333(f333(f335(x124071),x124072),f196(f882(x124071,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12410,plain, % 183.99/184.51 (P1(f333(f333(f335(x124101),f333(x124102,x124103)),f333(f312(x124104,x124101,x124102),f256(f882(x124104,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12411,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x124111,x124111)),f333(f333(f268(x124111,x124111),x124112),x124112)),f309(x124111,x124113)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(12414,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x124141,x124141)),f333(f333(f268(x124141,x124141),x124142),x124142)),f309(x124141,x124143)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(12417,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x124171),x124171))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12418,plain, % 183.99/184.51 (P1(f333(f256(f882(x124181,a870)),x124182))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(12421,plain, % 183.99/184.51 (P1(f333(f61(x124211),f333(f174(x124211),x124212)))), % 183.99/184.51 inference(rename_variables,[],[3328])). % 183.99/184.51 cnf(12428,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x124281,x124281)),f333(f333(f268(x124281,x124281),x124282),x124282)),f333(f333(f290(x124281,x124281,x124281),f309(x124281,x124283)),f309(x124281,f309(x124281,x124283)))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,3540,3541,3254,4511,4512,3153,4496,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,4493,10444,10535,3344,3500,3200,2885,2889,2890,2892,2893,2901,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2964,2970,2971,2993,3024,3025,3027,3033,3043,3045,3053,3060,3075,4474,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,3214,12345,12349,12353,3220,3228,3755,3355,3997,3118,4490,3494,3850,11378,3179,3144,3139,3125,3126,3768,3159,3345,10826,12154,3212,3213,3392,4560,3937,4503,10274,10441,11241,12309,12346,4510,12317,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,12332,3939,10999,11125,11176,12293,12299,12411,12414,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,4501,11359,3595,3813,3860,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,3748,11597,3269,3368,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,4555,11481,11512,11547,11577,3735,3501,3887,3315,3316,3290,4540,4498,3686,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,4048,4005,11868,12208,3949,10823,12052,4000,11002,12090,12163,12220,12264,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,3289,3364,12078,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,3446,10616,10884,10928,11198,11276,11439,11680,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,3349,10647,10677,10686,11227,11779,12404,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,3309,10680,10833,10904,11629,11784,11976,3778,4129,4546,3789,3825,4529,4531,3260,3261,4530,4533,4534,3796,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,3904,11317,11655,11659,11721,12320,12328,3742,10944,10950,10965,11900,12029,12111,3591,11167,12137,12246,12256,12325,12376,3744,10683,11021,11173,11203,11214,12049,12214,12324,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,11467,12196,12205,4189,10816,12217,12229,4090,3777,3721,4565,10293,10296,10635,10638,11478,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,878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% 183.99/184.51 cnf(12431,plain, % 183.99/184.51 (~P1(f333(f333(f196(f882(x124311,f882(x124312,a870))),x124313),x124314))), % 183.99/184.51 inference(rename_variables,[],[4568])). % 183.99/184.51 cnf(12434,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x124341,a870)),x124342),f256(f882(x124341,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12437,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(x124371,x124371)),f333(f333(f268(x124371,x124371),x124372),x124372)),f309(x124371,x124373)))), % 183.99/184.51 inference(rename_variables,[],[3939])). % 183.99/184.51 cnf(12440,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x124401),x124402)),x124402))), % 183.99/184.51 inference(rename_variables,[],[4565])). % 183.99/184.51 cnf(12441,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x124411),f333(a115,x124411)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12444,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x124441,a870)),f333(f174(x124441),f333(f137(x124441,x124442),x124443))),f333(f174(x124441),x124443)))), % 183.99/184.51 inference(rename_variables,[],[3949])). % 183.99/184.51 cnf(12447,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x124471,a870)),x124472),f256(f882(x124471,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12450,plain, % 183.99/184.51 (E(f333(f264(x124501,x124501),f265(x124501,x124502)),x124502)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12457,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f881(f876(x124571),f876(x124571)),f881(f876(x124571),f876(x124571)))),f593(f309(f881(f876(x124571),f876(x124571)),x124572),f146(x124571,x124573),f881(f876(x124571),f876(x124571)))),f309(f881(f876(x124571),f876(x124571)),x124572)))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,3540,3541,3254,4511,4512,3153,4496,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,4493,10444,10535,3344,3500,3200,2885,2889,2890,2892,2893,2901,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2964,2970,2971,2993,3024,3025,3027,3033,3043,3045,3053,3060,3075,4474,3632,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,3214,12345,12349,12353,3220,3228,3755,3355,3997,3118,4490,3494,3850,11378,3179,3144,3139,3125,3126,3768,3159,3345,10826,12154,3212,3213,3392,4560,3937,4503,10274,10441,11241,12309,12346,4510,12317,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,12332,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,4501,11359,3595,3813,3860,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,3748,11597,3269,3368,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,4555,11481,11512,11547,11577,3735,3501,3887,3315,3316,3290,4540,4498,3686,4223,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,4048,4005,11868,12208,3949,10823,12052,12221,4000,11002,12090,12163,12220,12264,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,3289,3364,12078,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,3446,10616,10884,10928,11198,11276,11439,11680,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,3349,10647,10677,10686,11227,11779,12404,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,3309,10680,10833,10904,11629,11784,11976,3778,4129,4546,3789,3825,4529,4531,3260,3261,4530,4533,4534,3796,3606,4229,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,3904,11317,11655,11659,11721,12320,12328,3742,10944,10950,10965,11900,12029,12111,3591,11167,12137,12246,12256,12325,12376,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,11467,12196,12205,12252,4189,10816,12217,12229,4090,3777,3721,4565,10293,10296,10635,10638,11478,11656,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8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% 183.99/184.51 cnf(12461,plain, % 183.99/184.51 (~P1(f333(f333(f335(x124611),x124612),f196(f882(x124611,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12462,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f876(x124621),f876(x124621))),f333(f333(f268(f876(x124621),f876(x124621)),f116(x124621)),f116(x124621))),f159(x124621,x124622)))), % 183.99/184.51 inference(rename_variables,[],[4085])). % 183.99/184.51 cnf(12467,plain, % 183.99/184.51 (~P1(f333(f333(f335(x124671),x124672),f196(f882(x124671,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12470,plain, % 183.99/184.51 (P31(x124701,x124702,f116(x124701))), % 183.99/184.51 inference(rename_variables,[],[3219])). % 183.99/184.51 cnf(12473,plain, % 183.99/184.51 (E(f333(f197(f876(x124731)),f171(x124731,x124732,x124733)),x124732)), % 183.99/184.51 inference(rename_variables,[],[3355])). % 183.99/184.51 cnf(12476,plain, % 183.99/184.51 (~P1(f333(f333(f335(x124761),x124762),f196(f882(x124761,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12482,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x124821),x124821))), % 183.99/184.51 inference(rename_variables,[],[4539])). % 183.99/184.51 cnf(12484,plain, % 183.99/184.51 (P1(f333(f333(f335(f881(f876(x124841),f876(x124841))),f333(f333(f268(f876(x124841),f876(x124841)),f171(x124841,f333(f197(f876(x124841)),x124842),x124843)),x124842)),f159(x124841,f256(f882(f881(x124841,x124841),a870)))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,3540,3541,3254,3219,4511,4512,3153,4496,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,4493,10444,10535,3344,3500,3200,2885,2889,2890,2892,2893,2901,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2964,2970,2971,2993,3024,3025,3027,3033,3043,3045,3053,3060,3075,4474,3632,3865,11611,3128,11328,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3118,4490,3494,3850,11378,3179,3144,3139,3125,3126,3768,3159,3345,10826,12154,3212,3213,3392,4560,3937,4503,10274,10441,11241,12309,12346,4510,12317,3276,11700,4549,10993,11063,11287,11290,3393,3174,10343,10650,3175,3451,3097,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,4501,11359,3595,3813,3860,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,3748,11597,3269,3368,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,4555,11481,11512,11547,11577,3735,3501,3887,3315,3316,3290,4540,4498,3686,4223,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,4048,4005,11868,12208,3949,10823,12052,12221,4000,11002,12090,12163,12220,12264,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,3289,3364,12078,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,3446,10616,10884,10928,11198,11276,11439,11680,12312,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,3349,10647,10677,10686,11227,11779,12404,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,3309,10680,10833,10904,11629,11784,11976,3778,4129,4546,3789,3825,4529,4531,3260,3261,4530,4533,4534,3796,3606,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,3904,11317,11655,11659,11721,12320,12328,3742,10944,10950,10965,11900,12029,12111,3591,11167,12137,12246,12256,12325,12376,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,3559,10602,10605,10689,10863,4567,11594,4557,4568,10740,10842,11152,11436,11467,12196,12205,12252,4189,10816,12217,12229,4090,3777,3721,4565,10293,10296,10635,10638,11478,11656,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,85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% 183.99/184.51 cnf(12485,plain, % 183.99/184.51 (P1(f333(f333(f335(x124851),x124852),f256(f882(x124851,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(12492,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x124921,a870)),x124922),x124922))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12495,plain, % 183.99/184.51 (~P1(f333(f333(f335(x124951),x124952),f196(f882(x124951,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12498,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f2(a1)),f333(f333(f258(a1),f333(f74(a1),x124981)),x124982)))), % 183.99/184.51 inference(rename_variables,[],[3777])). % 183.99/184.51 cnf(12501,plain, % 183.99/184.51 (~E(f333(a115,x125011),x125011)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12503,plain, % 183.99/184.51 (E(f333(f264(x125031,x125031),f265(x125031,x125032)),x125032)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12505,plain, % 183.99/184.51 (E(f333(f264(x125051,x125051),f265(x125051,x125052)),x125052)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12513,plain, % 183.99/184.51 (P27(x125131,f2(a875),f333(f333(f333(f91(x125131),x125132),f333(a25,x125133)),x125134))), % 183.99/184.51 inference(rename_variables,[],[3670])). % 183.99/184.51 cnf(12519,plain, % 183.99/184.51 (E(f333(f264(x125191,x125191),f265(x125191,x125192)),x125192)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12521,plain, % 183.99/184.51 (E(f333(f264(x125211,x125211),f265(x125211,x125212)),x125212)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12525,plain, % 183.99/184.51 (E(f333(f264(x125251,x125251),f265(x125251,x125252)),x125252)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12529,plain, % 183.99/184.51 (E(f333(f264(x125291,x125291),f265(x125291,x125292)),x125292)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12531,plain, % 183.99/184.51 (E(f333(f264(x125311,x125311),f265(x125311,x125312)),x125312)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12537,plain, % 183.99/184.51 (E(f333(f264(x125371,x125371),f265(x125371,x125372)),x125372)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12540,plain, % 183.99/184.51 (E(f196(f882(f881(x125401,x125401),a870)),f265(x125401,f196(f882(x125401,a870))))), % 183.99/184.51 inference(rename_variables,[],[3359])). % 183.99/184.51 cnf(12542,plain, % 183.99/184.51 (E(f333(f264(x125421,x125421),f265(x125421,x125422)),x125422)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12544,plain, % 183.99/184.51 (P25(x125441,x125441,f5(x125441),x125442)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12546,plain, % 183.99/184.51 (P25(x125461,x125461,f5(x125461),x125462)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12552,plain, % 183.99/184.51 (P24(x125521,x125522,f196(f882(f874(x125521),a870)))), % 183.99/184.51 inference(rename_variables,[],[3343])). % 183.99/184.51 cnf(12558,plain, % 183.99/184.51 (E(f333(f264(x125581,x125581),f265(x125581,x125582)),x125582)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12560,plain, % 183.99/184.51 (P37(x125601,f154(x125601,x125602))), % 183.99/184.51 inference(rename_variables,[],[3153])). % 183.99/184.51 cnf(12566,plain, % 183.99/184.51 (P39(x125661,x125662,f265(x125661,x125662))), % 183.99/184.51 inference(rename_variables,[],[3253])). % 183.99/184.51 cnf(12568,plain, % 183.99/184.51 (P39(x125681,x125682,f265(x125681,x125682))), % 183.99/184.51 inference(rename_variables,[],[3253])). % 183.99/184.51 cnf(12572,plain, % 183.99/184.51 (P50(x125721,f196(f882(x125721,a870)),x125722)), % 183.99/184.51 inference(rename_variables,[],[3307])). % 183.99/184.51 cnf(12580,plain, % 183.99/184.51 (P15(x125801,f882(x125801,a870),f311(x125801))), % 183.99/184.51 inference(rename_variables,[],[3257])). % 183.99/184.51 cnf(12584,plain, % 183.99/184.51 (P49(x125841,x125841,f265(x125841,x125842))), % 183.99/184.51 inference(rename_variables,[],[3254])). % 183.99/184.51 cnf(12595,plain, % 183.99/184.51 (P32(x125951,x125952,f116(x125951),f116(x125951))), % 183.99/184.51 inference(rename_variables,[],[3540])). % 183.99/184.51 cnf(12597,plain, % 183.99/184.51 (P32(x125971,x125972,f116(x125971),f116(x125971))), % 183.99/184.51 inference(rename_variables,[],[3540])). % 183.99/184.51 cnf(12603,plain, % 183.99/184.51 (P42(x126031,x126032,x126033,x126034,f196(f882(x126031,a870)),x126034)), % 183.99/184.51 inference(rename_variables,[],[4253])). % 183.99/184.51 cnf(12606,plain, % 183.99/184.51 (P42(x126061,x126062,x126063,x126064,f196(f882(x126061,a870)),x126064)), % 183.99/184.51 inference(rename_variables,[],[4253])). % 183.99/184.51 cnf(12618,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),f2(a875)),f333(a115,x126181)))), % 183.99/184.51 inference(rename_variables,[],[3368])). % 183.99/184.51 cnf(12619,plain, % 183.99/184.51 (~E(f333(a115,x126191),x126191)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(12625,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x126251),f333(a115,x126251)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12630,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x126301),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12633,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x126331),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12640,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x126401)),f333(f78(a1),f333(f103(a1),x126402))))), % 183.99/184.51 inference(rename_variables,[],[4562])). % 183.99/184.51 cnf(12650,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x126501),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12653,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x126531),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12656,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126561,x126562)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12659,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126591,x126592)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12662,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126621,x126622)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12665,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126651,x126652)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12672,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f333(f78(a1),f333(f103(a1),x126721))),f333(f103(a1),x126722)))), % 183.99/184.51 inference(rename_variables,[],[3778])). % 183.99/184.51 cnf(12675,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x126751),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12676,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x126761),x126761))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12683,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x126831),f333(a115,x126831)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12686,plain, % 183.99/184.51 (P1(f333(f333(f335(x126861),f333(x126862,x126863)),f333(f312(x126864,x126861,x126862),f256(f882(x126864,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12687,plain, % 183.99/184.51 (~E(f333(a115,x126871),f2(a875))), % 183.99/184.51 inference(rename_variables,[],[4488])). % 183.99/184.51 cnf(12689,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f2(a1)),f333(f106(a1),f2(a1))))), % 183.99/184.51 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,4493,10444,10535,3344,3307,12572,3500,3200,4488,2885,2889,2890,2892,2893,2901,2902,2903,2904,2909,2919,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2964,2970,2971,2993,3024,3025,3027,3033,3043,3044,3045,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3118,4490,3494,3850,11378,3343,12552,3179,3144,3670,12513,3139,3971,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,4510,12317,3276,11700,4549,10993,11063,11287,11290,3695,3393,3617,3359,12540,3174,10343,10650,3175,3451,3167,3097,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,4501,11359,3595,3635,3813,3860,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,3748,11597,3269,3368,11715,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,4555,11481,11512,11547,11577,3735,3501,3502,12656,12659,12662,3887,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,4048,4005,11868,12208,3949,10823,12052,12221,4000,11002,12090,12163,12220,12264,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,4561,10771,11141,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,3289,3364,12078,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,3446,10616,10884,10928,11198,11276,11439,11680,12312,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,3349,10647,10677,10686,11227,11779,12404,3388,3382,3817,3753,10320,11600,11628,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,3309,10680,10833,10904,11629,11784,11976,3778,11730,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,3796,3606,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,3742,10944,10950,10965,11900,12029,12111,3591,11167,12137,12246,12256,12325,12376,12384,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,4090,3777,3721,3722,4565,10293,10296,10635,10638,11478,11656,4566,11574,3746,10599,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,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% 183.99/184.51 cnf(12692,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x126921),x126921))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12695,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126951,x126952)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12698,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x126981,x126982)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(12701,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127011),x127011))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12714,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x127141),f333(a115,x127141)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12719,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f44(a875,x127191,x127192)),x127191))), % 183.99/184.51 inference(rename_variables,[],[3753])). % 183.99/184.51 cnf(12726,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x127261),f333(a115,x127261)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12727,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x127271),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12736,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x127361)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(12737,plain, % 183.99/184.51 (P1(f333(f256(f882(x127371,a870)),x127372))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(12740,plain, % 183.99/184.51 (~P1(f333(f333(f248(a1),f333(f103(a1),x127401)),f2(a1)))), % 183.99/184.51 inference(rename_variables,[],[4555])). % 183.99/184.51 cnf(12741,plain, % 183.99/184.51 (P1(f333(f256(f882(x127411,a870)),x127412))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(12744,plain, % 183.99/184.51 (P1(f333(f256(f882(x127441,a870)),x127442))), % 183.99/184.51 inference(rename_variables,[],[3349])). % 183.99/184.51 cnf(12755,plain, % 183.99/184.51 (~P1(f333(f333(f335(x127551),x127552),f196(f882(x127551,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12756,plain, % 183.99/184.51 (P1(f333(f61(x127561),f196(f882(x127561,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12765,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x127651))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(12768,plain, % 183.99/184.51 (~P1(f333(f333(f335(x127681),x127682),f196(f882(x127681,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12771,plain, % 183.99/184.51 (~P1(f333(f333(f335(x127711),x127712),f196(f882(x127711,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12774,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127741),x127741))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12781,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127811),x127811))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12785,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x127851),f333(a115,x127851)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12788,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127881),x127881))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12793,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127931),x127931))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12796,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127961),x127961))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12799,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x127991),x127991))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12802,plain, % 183.99/184.51 (E(f333(f333(f22(f882(x128021,a870)),f196(f882(x128021,a870))),x128022),f196(f882(x128021,a870)))), % 183.99/184.51 inference(rename_variables,[],[3562])). % 183.99/184.51 cnf(12803,plain, % 183.99/184.51 (P1(f333(f61(x128031),f196(f882(x128031,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12806,plain, % 183.99/184.51 (E(f333(f333(f22(f882(x128061,a870)),f196(f882(x128061,a870))),x128062),f196(f882(x128061,a870)))), % 183.99/184.51 inference(rename_variables,[],[3562])). % 183.99/184.51 cnf(12807,plain, % 183.99/184.51 (P1(f333(f61(x128071),f196(f882(x128071,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12810,plain, % 183.99/184.51 (E(f333(f333(f22(f882(x128101,a870)),f196(f882(x128101,a870))),x128102),f196(f882(x128101,a870)))), % 183.99/184.51 inference(rename_variables,[],[3562])). % 183.99/184.51 cnf(12811,plain, % 183.99/184.51 (P1(f333(f61(x128111),f196(f882(x128111,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12814,plain, % 183.99/184.51 (E(f333(f333(f22(f882(x128141,a870)),f196(f882(x128141,a870))),x128142),f196(f882(x128141,a870)))), % 183.99/184.51 inference(rename_variables,[],[3562])). % 183.99/184.51 cnf(12815,plain, % 183.99/184.51 (P1(f333(f61(x128151),f196(f882(x128151,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12819,plain, % 183.99/184.51 (E(f333(f264(x128191,x128191),f265(x128191,x128192)),x128192)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12824,plain, % 183.99/184.51 (E(f333(f333(f22(f882(x128241,a870)),f196(f882(x128241,a870))),x128242),f196(f882(x128241,a870)))), % 183.99/184.51 inference(rename_variables,[],[3562])). % 183.99/184.51 cnf(12825,plain, % 183.99/184.51 (P1(f333(f61(x128251),f196(f882(x128251,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12829,plain, % 183.99/184.51 (P1(f333(f61(x128291),f196(f882(x128291,a870))))), % 183.99/184.51 inference(rename_variables,[],[3364])). % 183.99/184.51 cnf(12832,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x128321),x128321))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12838,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x128381),x128381))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12841,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x128411),f333(a115,x128411)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12844,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x128441),x128441))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12847,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x128471),f333(a115,x128471)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(12862,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x128621),x128621))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12865,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x128651),x128651))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12868,plain, % 183.99/184.51 (~P1(f333(f333(f335(x128681),x128682),f196(f882(x128681,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12879,plain, % 183.99/184.51 (P1(f333(f333(f335(x128791),x128792),f256(f882(x128791,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(12885,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x128851,a870)),x128852),x128852))), % 183.99/184.51 inference(rename_variables,[],[3591])). % 183.99/184.51 cnf(12891,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x128911),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12892,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x128921),x128921))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12896,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x128961),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12897,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x128971),x128971))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12906,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x129061),x129061))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12913,plain, % 183.99/184.51 (E(f333(f333(f16(x129131,x129132),x129133),x129134),x129133)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(12916,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x129161,a870)),f333(f174(x129161),f178(x129161,x129162,x129163))),f333(f174(x129161),x129162)))), % 183.99/184.51 inference(rename_variables,[],[4000])). % 183.99/184.51 cnf(12920,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x129201),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12921,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),x129211),x129211))), % 183.99/184.51 inference(rename_variables,[],[3288])). % 183.99/184.51 cnf(12925,plain, % 183.99/184.51 (~P1(f333(f333(f248(a875),x129251),f2(a875)))), % 183.99/184.51 inference(rename_variables,[],[4543])). % 183.99/184.51 cnf(12931,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x129311),x129311))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12934,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x129341),x129341))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(12937,plain, % 183.99/184.51 (~P1(f333(f333(f247(a875),f333(a115,x129371)),x129371))), % 183.99/184.51 inference(rename_variables,[],[4548])). % 183.99/184.51 cnf(12943,plain, % 183.99/184.51 (P1(f333(f333(f335(x129431),f333(x129432,x129433)),f333(f312(x129434,x129431,x129432),f256(f882(x129434,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12944,plain, % 183.99/184.51 (P25(x129441,x129441,f5(x129441),x129442)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12948,plain, % 183.99/184.51 (P1(f333(f333(f335(x129481),x129482),f256(f882(x129481,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(12949,plain, % 183.99/184.51 (~P1(f333(f333(f335(x129491),x129492),f196(f882(x129491,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12953,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x129531,a870)),x129532),f256(f882(x129531,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12954,plain, % 183.99/184.51 (P25(x129541,x129541,f5(x129541),x129542)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12958,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x129581,a870)),x129582),f256(f882(x129581,a870))))), % 183.99/184.51 inference(rename_variables,[],[3677])). % 183.99/184.51 cnf(12959,plain, % 183.99/184.51 (P25(x129591,x129591,f5(x129591),x129592)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12963,plain, % 183.99/184.51 (P25(x129631,x129631,f5(x129631),x129632)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12966,plain, % 183.99/184.51 (~P1(f333(f333(f248(f882(x129661,a870)),x129662),f196(f882(x129661,a870))))), % 183.99/184.51 inference(rename_variables,[],[4561])). % 183.99/184.51 cnf(12969,plain, % 183.99/184.51 (P25(x129691,x129691,f5(x129691),x129692)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12972,plain, % 183.99/184.51 (P25(x129721,x129721,f5(x129721),x129722)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12983,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x129831,a870)),f196(f882(x129831,a870))),x129832))), % 183.99/184.51 inference(rename_variables,[],[3744])). % 183.99/184.51 cnf(12987,plain, % 183.99/184.51 (E(f333(f264(x129871,x129871),f265(x129871,x129872)),x129872)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(12991,plain, % 183.99/184.51 (~P1(f333(f333(f335(x129911),x129912),f196(f882(x129911,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(12995,plain, % 183.99/184.51 (P1(f333(f333(f335(x129951),f333(x129952,x129953)),f333(f312(x129954,x129951,x129952),f256(f882(x129954,a870)))))), % 183.99/184.51 inference(rename_variables,[],[3904])). % 183.99/184.51 cnf(12996,plain, % 183.99/184.51 (P25(x129961,x129961,f5(x129961),x129962)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(12999,plain, % 183.99/184.51 (P1(f333(f333(f335(x129991),x129992),f256(f882(x129991,a870))))), % 183.99/184.51 inference(rename_variables,[],[3446])). % 183.99/184.51 cnf(13006,plain, % 183.99/184.51 (~P1(f333(f333(f335(x130061),x130062),f196(f882(x130061,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(13009,plain, % 183.99/184.51 (~P1(f333(f333(f335(x130091),x130092),f196(f882(x130091,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(13013,plain, % 183.99/184.51 (E(f333(f333(f16(x130131,x130132),x130133),x130134),x130133)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(13016,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x130161),f333(a115,x130161)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(13017,plain, % 183.99/184.51 (~E(f333(a115,x130171),x130171)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(13020,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x130201),f333(a115,f333(f333(f79(a875),x130202),x130201))))), % 183.99/184.51 inference(rename_variables,[],[3746])). % 183.99/184.51 cnf(13021,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x130211),f333(a115,x130211)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(13025,plain, % 183.99/184.51 (~E(f333(a115,x130251),x130251)), % 183.99/184.51 inference(rename_variables,[],[4478])). % 183.99/184.51 cnf(13030,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f2(a1)),f333(f103(a1),x130301)))), % 183.99/184.51 inference(rename_variables,[],[3388])). % 183.99/184.51 cnf(13033,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x130331))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(13034,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x130341),x130341))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(13037,plain, % 183.99/184.51 (~E(f333(a115,x130371),f2(a875))), % 183.99/184.51 inference(rename_variables,[],[4488])). % 183.99/184.51 cnf(13046,plain, % 183.99/184.51 (~P1(f333(f333(f335(x130461),x130462),f196(f882(x130461,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(13049,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x130491,x130492)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(13050,plain, % 183.99/184.51 (E(f333(f333(f245(a875),f333(a115,x130501)),f333(a115,x130502)),f333(a115,f333(f333(f245(a875),x130501),x130502)))), % 183.99/184.51 inference(rename_variables,[],[3463])). % 183.99/184.51 cnf(13053,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x130531,x130532)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(13054,plain, % 183.99/184.51 (E(f333(f333(f246(a875),f333(a115,x130541)),f333(a115,x130542)),f333(a115,f333(f333(f246(a875),x130541),x130542)))), % 183.99/184.51 inference(rename_variables,[],[3464])). % 183.99/184.51 cnf(13057,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x130571,x130572)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(13061,plain, % 183.99/184.51 (P1(f333(f61(a875),f306(a875,x130611,x130612)))), % 183.99/184.51 inference(rename_variables,[],[3502])). % 183.99/184.51 cnf(13065,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x130651,a870)),f333(f174(x130651),f333(f137(x130651,x130652),x130653))),f333(f174(x130651),x130653)))), % 183.99/184.51 inference(rename_variables,[],[3949])). % 183.99/184.51 cnf(13066,plain, % 183.99/184.51 (E(f333(f333(f16(x130661,x130662),x130663),x130664),x130663)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(13069,plain, % 183.99/184.51 (P1(f333(f333(f247(f882(x130691,a870)),f333(f174(x130691),f333(f333(f177(x130691),x130692),x130693))),f333(f174(x130691),x130693)))), % 183.99/184.51 inference(rename_variables,[],[3994])). % 183.99/184.51 cnf(13070,plain, % 183.99/184.51 (E(f333(f333(f16(x130701,x130702),x130703),x130704),x130703)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(13074,plain, % 183.99/184.51 (E(f333(f333(f16(x130741,x130742),x130743),x130744),x130743)), % 183.99/184.51 inference(rename_variables,[],[3276])). % 183.99/184.51 cnf(13087,plain, % 183.99/184.51 (P1(f333(f333(f247(a1),f2(a1)),f333(f103(a1),x130871)))), % 183.99/184.51 inference(rename_variables,[],[3388])). % 183.99/184.51 cnf(13090,plain, % 183.99/184.51 (~P1(f333(f333(f335(x130901),x130902),f196(f882(x130901,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(13093,plain, % 183.99/184.51 (~P1(f333(f333(f335(x130931),x130932),f196(f882(x130931,a870))))), % 183.99/184.51 inference(rename_variables,[],[4551])). % 183.99/184.51 cnf(13094,plain, % 183.99/184.51 (E(f333(f264(x130941,x130941),f265(x130941,x130942)),x130942)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(13095,plain, % 183.99/184.51 (P25(x130951,x130951,f5(x130951),x130952)), % 183.99/184.51 inference(rename_variables,[],[3531])). % 183.99/184.51 cnf(13099,plain, % 183.99/184.51 (E(f333(f264(x130991,x130991),f265(x130991,x130992)),x130992)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(13105,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x131051),f333(a115,x131051)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(13107,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),x131071),x131071))), % 183.99/184.51 inference(rename_variables,[],[3287])). % 183.99/184.51 cnf(13108,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x131081))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(13111,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),x131111),f333(a115,x131111)))), % 183.99/184.51 inference(rename_variables,[],[3356])). % 183.99/184.51 cnf(13114,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x131141))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(13118,plain, % 183.99/184.51 (P1(f333(f333(f247(a875),f2(a875)),x131181))), % 183.99/184.51 inference(rename_variables,[],[3309])). % 183.99/184.51 cnf(13119,plain, % 183.99/184.51 (P1(f333(f333(f248(a875),f2(a875)),f333(a115,x131191)))), % 183.99/184.51 inference(rename_variables,[],[3368])). % 183.99/184.51 cnf(13120,plain, % 183.99/184.51 (E(f333(f264(x131201,x131201),f265(x131201,x131202)),x131202)), % 183.99/184.51 inference(rename_variables,[],[3243])). % 183.99/184.51 cnf(13123,plain, % 183.99/184.51 (P1(f333(f47(f333(f264(x131231,x131231),f265(x131231,f333(f333(f79(a875),f333(f333(f80(a875),f333(f267(a875,a875),f333(f333(f268(a875,a875),f2(a875)),x131232))),f333(a115,f333(f333(f79(a875),x131233),f333(f271(a875,a875),f333(f333(f268(a875,a875),f2(a875)),x131232)))))),f333(f271(a875,a875),f333(f333(f268(a875,a875),f2(a875)),x131232))))),f333(a115,f333(f333(f79(a875),x131233),f333(f271(a875,a875),f333(f333(f268(a875,a875),f2(a875)),x131232))))),f333(f333(f268(a875,a875),f2(a875)),x131232)))), % 183.99/184.52 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,12546,12944,12954,12959,12963,12969,12972,12996,13095,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,12619,13017,4493,10444,10535,3344,3307,12572,3500,3200,4488,12687,13037,2884,2885,2889,2890,2892,2893,2901,2902,2903,2904,2909,2910,2919,2925,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2961,2964,2970,2971,2984,2993,2996,2997,3000,3001,3002,3011,3024,3025,3027,3033,3034,3043,3044,3045,3046,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,12558,12819,12987,13094,13099,13120,3878,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3117,3118,4490,3494,3850,11378,3343,12552,3179,3144,3670,12513,3139,3971,3160,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,12350,4510,12317,3276,11700,11703,12913,13013,13066,13070,13074,4549,10993,11063,11287,11290,3695,3271,3393,3617,3385,3359,12540,3174,10343,10650,3175,4537,3451,3167,3097,3281,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,11187,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,3474,4501,11359,3595,3635,3813,3562,12802,12806,12810,12814,12824,3860,12187,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,12683,12714,12726,12785,12841,12847,13016,13021,13105,13111,3748,11597,3269,3368,11715,12618,13119,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,12675,12727,12891,12896,12920,4555,11481,11512,11547,11577,12736,12740,3735,3501,3502,12656,12659,12662,12665,12695,12698,13049,13053,13057,3887,3463,13050,3464,13054,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,12421,4048,4005,11868,12208,3949,10823,12052,12221,12444,13065,3994,13069,4000,11002,12090,12163,12220,12264,12916,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,12953,12958,4561,10771,11141,12966,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,12676,12701,12774,12781,12788,12793,12796,12799,12832,12844,12862,12906,12931,12934,13034,13107,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,11971,12692,12838,12865,12892,12897,12921,3289,3364,12078,12756,12803,12807,12811,12815,12825,12829,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,12482,3446,10616,10884,10928,11198,11276,11439,11680,12312,12485,12879,12948,12999,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,12495,12755,12768,12771,12868,12949,12991,13006,13009,13046,13090,13093,3349,10647,10677,10686,11227,11779,12404,12418,12737,12741,12744,3388,13030,3382,3817,3753,10320,11600,11628,12719,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,12937,3309,10680,10833,10904,11629,11784,11976,12202,12765,13033,13108,13114,13118,3778,11730,12672,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,4306,3796,3606,11593,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,12686,12943,12995,3742,10944,10950,10965,11900,12029,12111,12381,3591,11167,12137,12246,12256,12325,12376,12384,12492,12885,3630,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,12370,12983,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,12255,4090,3777,12498,3721,3722,4565,10293,10296,10635,10638,11478,11656,12440,4566,11574,11665,3746,10599,10860,13020,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510,6515,6530,6531,6532,6533,6568,6573,6575,6580,6581,6589,6593,6606,6631,6632,6633,6634,6645,6650,6667,6671,6690,6723,6724,6725,6730,6744,6765,6767,6769,6771,6774,6780,6782,6797,6802,6805,6841,6844,6845,6858,6859,6860,6861,6880,6881,6898,6924,6946,6957,6959,6960,6962,6964,6965,7000,7001,7006,7007,7008,7009,7011,7013,7038,7047,7048,7060,7070,7109,7119,7123,7130,7141,7147,7149,7155,7163,7164,7177,7194,7212,7214,7231,7280,7282,7283,7284,7290,7295,7318,7363,7396,7410,7427,7460,7463,7489,7513,7531,7534,7535,7545,7563,7564,7566,7568,7570,7572,7598,7623,7624,7656,7658,7659,7660,7665,7688,7697,7708,7713,7719,7721,7727,7739,7740,7742,7774,7797,7863,7864,7911,7919,7920,7944,7945,7962,7963,8030,8031,8032,8057,8090,8097,8099,8108,8120,8153,8159,8166,8179,8198,8204,8226,8269,8299,8311,8329,8332,8362,8385,8451,8452,8455,8457,8560,8561,8562,8563,8588,8617,8645,8689,8707,8762,8808,8811,8824,8831,8868,8889,8917,8918,8936,8937,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9388,9393,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9536,9659,9703,9704,9746,9791,9907,9964,10029,10104,10117,10122,3,2622,2625,2626,2627,2628,2631,2632,2633,2637,2638,2639,2646,2648,2649,2651,2653,2655,2659,2661,2663,2664,2666,2667,2668,2675,2677,2682,2683,2684,2685,2686,2694,2695,2696,2698,2718,2719,2720,2730,2731,2732,2734,2735,2743,2744,2745,2747,2749,2751,2752,2753,2754,2755,2756,2760,2769,2771,2772,2781,2783,2791,2794,2795,2796,2799,2800,2803,2852,2857,2858,5223,5283,5381,5462,5468,5469,5546,5643,5674,5708,5724,5726,5732,5793,5794,5795,5796,5802,5835,5966,6011,6034,6071,6111,6252,6259,6293,6294,6314,6317,6319,6326,6327,6328,6329,6330,6331,6332,6333,6413,6480,6481,6566,6600,6601,6642,6643,6781,6796,6869,6870,6877,6899,6930,6932,6979,7004,7005,7021,7022,7023,7059,7103,7104,7201,7262,7263,7264,7265,7279,7312,7368,7369,7378,7384,7386,7398,7430,7431,7432,7433,7578,7579,7585,7586,7588,7590,7805,7807,7808,7823,7861,7940,7983,8041,8062,8063,8078,8137,8240,8309,8310,8312,8347,8410,8411,8483,8504,8505,8506,8507,8649,8861,8885,8886,8968,8982,9037,9038,9154,9190,9213,9247,9288,9480,9740,9933,9989,9991,6029,6396,6397,6483,6503,6504,6921,7139,8574,8607,8801,8994,8995,9065,9066,9336,9337,9338,9339,9539,9811,10113,10164,10165,6465,8401,8402,8851,8869])). % 183.99/184.52 cnf(13191,plain, % 183.99/184.52 (P1(f333(f333(f248(a1),f2(a1)),f333(f74(a1),f77(a1))))), % 183.99/184.52 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,12546,12944,12954,12959,12963,12969,12972,12996,13095,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,12619,13017,4493,10444,10535,3344,3307,12572,3500,3200,4488,12687,13037,2884,2885,2889,2890,2892,2893,2901,2902,2903,2904,2905,2909,2910,2919,2925,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2961,2964,2968,2970,2971,2984,2993,2996,2997,3000,3001,3002,3011,3024,3025,3027,3033,3034,3043,3044,3045,3046,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,12558,12819,12987,13094,13099,13120,3878,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3117,3118,4490,3494,3850,11378,3343,12552,3179,3144,3670,12513,3139,3971,3160,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,12350,4510,12317,3276,11700,11703,12913,13013,13066,13070,13074,4549,10993,11063,11287,11290,3695,3271,3393,3617,3385,3359,12540,3174,10343,10650,3175,4537,3451,3167,3097,3281,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,11187,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,3474,4501,11359,3595,3635,3813,3562,12802,12806,12810,12814,12824,3860,12187,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,12683,12714,12726,12785,12841,12847,13016,13021,13105,13111,3748,11597,3269,3368,11715,12618,13119,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,12675,12727,12891,12896,12920,12925,4555,11481,11512,11547,11577,12736,12740,3735,3501,3502,12656,12659,12662,12665,12695,12698,13049,13053,13057,3887,3463,13050,3464,13054,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,12421,4048,4005,11868,12208,3949,10823,12052,12221,12444,13065,3994,13069,4000,11002,12090,12163,12220,12264,12916,4001,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,12953,12958,4561,10771,11141,12966,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,12676,12701,12774,12781,12788,12793,12796,12799,12832,12844,12862,12906,12931,12934,13034,13107,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,11971,12692,12838,12865,12892,12897,12921,3289,3364,12078,12756,12803,12807,12811,12815,12825,12829,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,12482,3446,10616,10884,10928,11198,11276,11439,11680,12312,12485,12879,12948,12999,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,12495,12755,12768,12771,12868,12949,12991,13006,13009,13046,13090,13093,3349,10647,10677,10686,11227,11779,12404,12418,12737,12741,12744,3388,13030,13087,3382,3817,3753,10320,11600,11628,12719,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,12937,3309,10680,10833,10904,11629,11784,11976,12202,12765,13033,13108,13114,13118,3778,11730,12672,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,4306,3796,3606,11593,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,12686,12943,12995,3742,10944,10950,10965,11900,12029,12111,12381,3591,11167,12137,12246,12256,12325,12376,12384,12492,12885,3630,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,12370,12983,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,12255,4090,3777,12498,3721,3722,4565,10293,10296,10635,10638,11478,11656,12440,4566,11574,11665,3746,10599,10860,13020,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510,6515,6530,6531,6532,6533,6568,6573,6575,6580,6581,6589,6593,6606,6631,6632,6633,6634,6645,6650,6667,6671,6690,6723,6724,6725,6730,6744,6765,6767,6769,6771,6774,6780,6782,6797,6802,6805,6841,6844,6845,6858,6859,6860,6861,6880,6881,6898,6924,6946,6957,6959,6960,6962,6964,6965,7000,7001,7006,7007,7008,7009,7011,7013,7038,7047,7048,7060,7070,7109,7119,7123,7130,7141,7147,7149,7155,7163,7164,7177,7194,7212,7214,7231,7280,7282,7283,7284,7290,7295,7318,7363,7396,7410,7427,7460,7463,7489,7513,7531,7534,7535,7545,7563,7564,7566,7568,7570,7572,7598,7623,7624,7656,7658,7659,7660,7665,7688,7697,7708,7713,7719,7721,7727,7739,7740,7742,7774,7797,7863,7864,7911,7919,7920,7944,7945,7962,7963,8030,8031,8032,8057,8090,8097,8099,8108,8120,8153,8159,8166,8179,8198,8204,8226,8269,8299,8311,8329,8332,8362,8385,8451,8452,8455,8457,8560,8561,8562,8563,8588,8617,8645,8689,8707,8762,8808,8811,8824,8831,8868,8889,8917,8918,8936,8937,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9388,9393,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9536,9659,9703,9704,9746,9791,9907,9964,10029,10104,10117,10122,3,2622,2625,2626,2627,2628,2631,2632,2633,2637,2638,2639,2646,2648,2649,2651,2653,2655,2659,2661,2663,2664,2666,2667,2668,2675,2677,2682,2683,2684,2685,2686,2694,2695,2696,2698,2718,2719,2720,2730,2731,2732,2734,2735,2743,2744,2745,2747,2749,2751,2752,2753,2754,2755,2756,2760,2769,2771,2772,2781,2783,2791,2794,2795,2796,2799,2800,2803,2852,2857,2858,5223,5283,5381,5462,5468,5469,5546,5643,5674,5708,5724,5726,5732,5793,5794,5795,5796,5802,5835,5966,6011,6034,6071,6111,6252,6259,6293,6294,6314,6317,6319,6326,6327,6328,6329,6330,6331,6332,6333,6413,6480,6481,6566,6600,6601,6642,6643,6781,6796,6869,6870,6877,6899,6930,6932,6979,7004,7005,7021,7022,7023,7059,7103,7104,7201,7262,7263,7264,7265,7279,7312,7368,7369,7378,7384,7386,7398,7430,7431,7432,7433,7578,7579,7585,7586,7588,7590,7805,7807,7808,7823,7861,7940,7983,8041,8062,8063,8078,8137,8240,8309,8310,8312,8347,8410,8411,8483,8504,8505,8506,8507,8649,8861,8885,8886,8968,8982,9037,9038,9154,9190,9213,9247,9288,9480,9740,9933,9989,9991,6029,6396,6397,6483,6503,6504,6921,7139,8574,8607,8801,8994,8995,9065,9066,9336,9337,9338,9339,9539,9811,10113,10164,10165,6465,8401,8402,8851,8869,9812,10163,4655,4657,4658,4714,4722,4860,4876,4877,4904,4905,4936,4991,5051,5110,5160,5180,5217,5219,5226,5227,5253,5328,5349,5483,5551,5552,5553,5670])). % 183.99/184.52 cnf(13207,plain, % 183.99/184.52 (~P1(f333(f333(f248(a875),f333(a115,f333(f333(f79(a875),x132071),x132072))),f333(a115,x132072)))), % 183.99/184.52 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,12546,12944,12954,12959,12963,12969,12972,12996,13095,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,12619,13017,4493,10444,10535,3344,3307,12572,3500,3200,4488,12687,13037,2884,2885,2889,2890,2892,2893,2901,2902,2903,2904,2905,2909,2910,2919,2925,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2961,2964,2968,2970,2971,2984,2993,2996,2997,3000,3001,3002,3011,3024,3025,3027,3033,3034,3043,3044,3045,3046,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,12558,12819,12987,13094,13099,13120,3878,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3117,3118,4490,3494,3850,11378,3343,12552,3179,3144,3670,12513,3139,3971,3160,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,12350,4510,12317,3276,11700,11703,12913,13013,13066,13070,13074,4549,10993,11063,11287,11290,3695,3271,3393,3617,3385,3359,12540,3174,10343,10650,3175,4537,3451,3167,3097,3281,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,11187,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,3474,4501,11359,3595,3635,3813,3562,12802,12806,12810,12814,12824,3860,12187,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,12683,12714,12726,12785,12841,12847,13016,13021,13105,13111,3748,11597,3269,3368,11715,12618,13119,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,12675,12727,12891,12896,12920,12925,4555,11481,11512,11547,11577,12736,12740,3735,3501,3502,12656,12659,12662,12665,12695,12698,13049,13053,13057,3887,3463,13050,3464,13054,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,12421,4048,4005,11868,12208,3949,10823,12052,12221,12444,13065,3994,13069,4000,11002,12090,12163,12220,12264,12916,4001,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,12953,12958,4561,10771,11141,12966,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,12676,12701,12774,12781,12788,12793,12796,12799,12832,12844,12862,12906,12931,12934,13034,13107,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,11971,12692,12838,12865,12892,12897,12921,3289,3364,12078,12756,12803,12807,12811,12815,12825,12829,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,12482,3446,10616,10884,10928,11198,11276,11439,11680,12312,12485,12879,12948,12999,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,12495,12755,12768,12771,12868,12949,12991,13006,13009,13046,13090,13093,3349,10647,10677,10686,11227,11779,12404,12418,12737,12741,12744,3388,13030,13087,3382,3817,3753,10320,11600,11628,12719,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,12937,3309,10680,10833,10904,11629,11784,11976,12202,12765,13033,13108,13114,13118,3778,11730,12672,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,4306,3796,3606,11593,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,12686,12943,12995,3742,10944,10950,10965,11900,12029,12111,12381,3591,11167,12137,12246,12256,12325,12376,12384,12492,12885,3630,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,12370,12983,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,12255,4090,3777,12498,3721,3722,4565,10293,10296,10635,10638,11478,11656,12440,4566,11574,11665,3746,10599,10860,13020,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510,6515,6530,6531,6532,6533,6568,6573,6575,6580,6581,6589,6593,6606,6631,6632,6633,6634,6645,6650,6667,6671,6690,6723,6724,6725,6730,6744,6765,6767,6769,6771,6774,6780,6782,6797,6802,6805,6841,6844,6845,6858,6859,6860,6861,6880,6881,6898,6924,6946,6957,6959,6960,6962,6964,6965,7000,7001,7006,7007,7008,7009,7011,7013,7038,7047,7048,7060,7070,7109,7119,7123,7130,7141,7147,7149,7155,7163,7164,7177,7194,7212,7214,7231,7280,7282,7283,7284,7290,7295,7318,7363,7396,7410,7427,7460,7463,7489,7513,7531,7534,7535,7545,7563,7564,7566,7568,7570,7572,7598,7623,7624,7656,7658,7659,7660,7665,7688,7697,7708,7713,7719,7721,7727,7739,7740,7742,7774,7797,7863,7864,7911,7919,7920,7944,7945,7962,7963,8030,8031,8032,8057,8090,8097,8099,8108,8120,8153,8159,8166,8179,8198,8204,8226,8269,8299,8311,8329,8332,8362,8385,8451,8452,8455,8457,8560,8561,8562,8563,8588,8617,8645,8689,8707,8762,8808,8811,8824,8831,8868,8889,8917,8918,8936,8937,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9388,9393,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9536,9659,9703,9704,9746,9791,9907,9964,10029,10104,10117,10122,3,2622,2625,2626,2627,2628,2631,2632,2633,2637,2638,2639,2646,2648,2649,2651,2653,2655,2659,2661,2663,2664,2666,2667,2668,2675,2677,2682,2683,2684,2685,2686,2694,2695,2696,2698,2718,2719,2720,2730,2731,2732,2734,2735,2743,2744,2745,2747,2749,2751,2752,2753,2754,2755,2756,2760,2769,2771,2772,2781,2783,2791,2794,2795,2796,2799,2800,2803,2852,2857,2858,5223,5283,5381,5462,5468,5469,5546,5643,5674,5708,5724,5726,5732,5793,5794,5795,5796,5802,5835,5966,6011,6034,6071,6111,6252,6259,6293,6294,6314,6317,6319,6326,6327,6328,6329,6330,6331,6332,6333,6413,6480,6481,6566,6600,6601,6642,6643,6781,6796,6869,6870,6877,6899,6930,6932,6979,7004,7005,7021,7022,7023,7059,7103,7104,7201,7262,7263,7264,7265,7279,7312,7368,7369,7378,7384,7386,7398,7430,7431,7432,7433,7578,7579,7585,7586,7588,7590,7805,7807,7808,7823,7861,7940,7983,8041,8062,8063,8078,8137,8240,8309,8310,8312,8347,8410,8411,8483,8504,8505,8506,8507,8649,8861,8885,8886,8968,8982,9037,9038,9154,9190,9213,9247,9288,9480,9740,9933,9989,9991,6029,6396,6397,6483,6503,6504,6921,7139,8574,8607,8801,8994,8995,9065,9066,9336,9337,9338,9339,9539,9811,10113,10164,10165,6465,8401,8402,8851,8869,9812,10163,4655,4657,4658,4714,4722,4860,4876,4877,4904,4905,4936,4991,5051,5110,5160,5180,5217,5219,5226,5227,5253,5328,5349,5483,5551,5552,5553,5670,5671,5697,5701,5759,5761,5770,5776,5848])). % 183.99/184.52 cnf(13227,plain, % 183.99/184.52 (~P1(f333(f333(f248(a875),f2(a875)),f196(a875)))), % 183.99/184.52 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,12546,12944,12954,12959,12963,12969,12972,12996,13095,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,12619,13017,4493,10444,10535,3344,3307,12572,3500,3200,4488,12687,13037,2884,2885,2889,2890,2892,2893,2901,2902,2903,2904,2905,2909,2910,2919,2925,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2961,2964,2968,2970,2971,2984,2993,2996,2997,3000,3001,3002,3011,3024,3025,3027,3033,3034,3043,3044,3045,3046,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,12558,12819,12987,13094,13099,13120,3878,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3117,3118,4490,3494,3850,11378,3343,12552,3179,3144,3670,12513,3139,3971,3160,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,12350,4510,12317,3276,11700,11703,12913,13013,13066,13070,13074,4549,10993,11063,11287,11290,3695,3271,3393,3617,3385,3359,12540,3174,10343,10650,3175,4537,3451,3167,3097,3281,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,4575,11136,11187,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,3474,4501,11359,3595,3635,3813,3562,12802,12806,12810,12814,12824,3860,12187,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,12683,12714,12726,12785,12841,12847,13016,13021,13105,13111,3748,11597,3269,3368,11715,12618,13119,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,12675,12727,12891,12896,12920,12925,4555,11481,11512,11547,11577,12736,12740,3735,3501,3502,12656,12659,12662,12665,12695,12698,13049,13053,13057,3887,3463,13050,3464,13054,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,12421,4048,4005,11868,12208,3949,10823,12052,12221,12444,13065,3994,13069,4000,11002,12090,12163,12220,12264,12916,4001,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,12953,12958,4561,10771,11141,12966,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,12676,12701,12774,12781,12788,12793,12796,12799,12832,12844,12862,12906,12931,12934,13034,13107,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,11971,12692,12838,12865,12892,12897,12921,3289,3364,12078,12756,12803,12807,12811,12815,12825,12829,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,12482,3446,10616,10884,10928,11198,11276,11439,11680,12312,12485,12879,12948,12999,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,12495,12755,12768,12771,12868,12949,12991,13006,13009,13046,13090,13093,3349,10647,10677,10686,11227,11779,12404,12418,12737,12741,12744,3388,13030,13087,3382,3817,3753,10320,11600,11628,12719,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,12937,3309,10680,10833,10904,11629,11784,11976,12202,12765,13033,13108,13114,13118,3778,11730,12672,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,4306,3796,3606,11593,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,12686,12943,12995,3742,10944,10950,10965,11900,12029,12111,12381,3591,11167,12137,12246,12256,12325,12376,12384,12492,12885,3630,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,12370,12983,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,12255,4090,3777,12498,3721,3722,4565,10293,10296,10635,10638,11478,11656,12440,4566,11574,11665,3746,10599,10860,13020,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510,6515,6530,6531,6532,6533,6568,6573,6575,6580,6581,6589,6593,6606,6631,6632,6633,6634,6645,6650,6667,6671,6690,6723,6724,6725,6730,6744,6765,6767,6769,6771,6774,6780,6782,6797,6802,6805,6841,6844,6845,6858,6859,6860,6861,6880,6881,6898,6924,6946,6957,6959,6960,6962,6964,6965,7000,7001,7006,7007,7008,7009,7011,7013,7038,7047,7048,7060,7070,7109,7119,7123,7130,7141,7147,7149,7155,7163,7164,7177,7194,7212,7214,7231,7280,7282,7283,7284,7290,7295,7318,7363,7396,7410,7427,7460,7463,7489,7513,7531,7534,7535,7545,7563,7564,7566,7568,7570,7572,7598,7623,7624,7656,7658,7659,7660,7665,7688,7697,7708,7713,7719,7721,7727,7739,7740,7742,7774,7797,7863,7864,7911,7919,7920,7944,7945,7962,7963,8030,8031,8032,8057,8090,8097,8099,8108,8120,8153,8159,8166,8179,8198,8204,8226,8269,8299,8311,8329,8332,8362,8385,8451,8452,8455,8457,8560,8561,8562,8563,8588,8617,8645,8689,8707,8762,8808,8811,8824,8831,8868,8889,8917,8918,8936,8937,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9388,9393,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9536,9659,9703,9704,9746,9791,9907,9964,10029,10104,10117,10122,3,2622,2625,2626,2627,2628,2631,2632,2633,2637,2638,2639,2646,2648,2649,2651,2653,2655,2659,2661,2663,2664,2666,2667,2668,2675,2677,2682,2683,2684,2685,2686,2694,2695,2696,2698,2718,2719,2720,2730,2731,2732,2734,2735,2743,2744,2745,2747,2749,2751,2752,2753,2754,2755,2756,2760,2769,2771,2772,2781,2783,2791,2794,2795,2796,2799,2800,2803,2852,2857,2858,5223,5283,5381,5462,5468,5469,5546,5643,5674,5708,5724,5726,5732,5793,5794,5795,5796,5802,5835,5966,6011,6034,6071,6111,6252,6259,6293,6294,6314,6317,6319,6326,6327,6328,6329,6330,6331,6332,6333,6413,6480,6481,6566,6600,6601,6642,6643,6781,6796,6869,6870,6877,6899,6930,6932,6979,7004,7005,7021,7022,7023,7059,7103,7104,7201,7262,7263,7264,7265,7279,7312,7368,7369,7378,7384,7386,7398,7430,7431,7432,7433,7578,7579,7585,7586,7588,7590,7805,7807,7808,7823,7861,7940,7983,8041,8062,8063,8078,8137,8240,8309,8310,8312,8347,8410,8411,8483,8504,8505,8506,8507,8649,8861,8885,8886,8968,8982,9037,9038,9154,9190,9213,9247,9288,9480,9740,9933,9989,9991,6029,6396,6397,6483,6503,6504,6921,7139,8574,8607,8801,8994,8995,9065,9066,9336,9337,9338,9339,9539,9811,10113,10164,10165,6465,8401,8402,8851,8869,9812,10163,4655,4657,4658,4714,4722,4860,4876,4877,4904,4905,4936,4991,5051,5110,5160,5180,5217,5219,5226,5227,5253,5328,5349,5483,5551,5552,5553,5670,5671,5697,5701,5759,5761,5770,5776,5848,5924,6052,6075,6239,6359,6513,6715,6716,6933,6972])). % 183.99/184.52 cnf(13265,plain, % 183.99/184.52 (~P1(f333(f333(f247(a875),f333(a115,f333(f143(a875,a875,f79(a875),f2(a875)),f171(a875,f333(a115,f2(a875)),f333(a115,f2(a875)))))),f333(a115,f2(a875))))), % 183.99/184.52 inference(scs_inference,[],[4570,3531,11058,12093,12190,12285,12321,12329,12342,12397,12544,12546,12944,12954,12959,12963,12969,12972,12996,13095,3540,12157,12595,12597,3541,12224,3253,12566,12568,3254,12584,3219,12470,4511,4512,11677,4253,12603,12606,3257,12580,3096,3153,12560,4496,3593,4478,10211,10221,10234,10245,10248,10351,10354,10357,10460,10571,10879,11043,11046,11244,11331,11338,11352,11404,11407,11451,11517,11564,11580,11879,11904,11916,11945,11951,12046,12153,12160,12313,12367,12501,12619,13017,13025,4493,10444,10535,3344,3307,12572,3500,3200,4488,12687,13037,2884,2885,2889,2890,2892,2893,2901,2902,2903,2904,2905,2909,2910,2919,2925,2928,2929,2936,2946,2947,2949,2950,2951,2953,2954,2957,2958,2959,2961,2964,2968,2970,2971,2984,2993,2996,2997,3000,3001,3002,3011,3024,3025,3027,3033,3034,3043,3044,3045,3046,3053,3060,4473,3075,3152,4474,3632,3865,11611,3128,11328,3267,3240,3243,10214,10283,10286,10378,10381,10674,11343,11346,11462,11504,11509,11606,12067,12261,12450,12503,12505,12519,12521,12525,12529,12531,12537,12542,12558,12819,12987,13094,13099,13120,3878,3214,12345,12349,12353,3220,3228,3755,3355,12400,12473,3997,3117,3118,4490,3494,3850,11378,3343,12552,3179,3662,3144,3670,12513,3139,3971,3160,3675,3125,3126,3106,3768,3159,3345,10826,12154,3212,3213,3392,4560,10414,3937,4503,10274,10441,11241,12309,12346,12350,4510,12317,3276,11700,11703,12913,13013,13066,13070,13074,4549,10993,11063,11287,11290,3695,3271,3393,3617,3385,3359,12540,3174,10343,10650,3175,4537,3451,3167,3097,3281,3196,11368,4085,12332,12462,3939,10999,11125,11176,12293,12299,12411,12414,12437,4573,10931,11130,11235,11257,11295,11301,12240,4574,11032,11133,11238,11298,4575,11136,11187,4576,11190,4577,3195,3492,12193,12237,12316,3658,4369,4370,3474,4501,11359,3595,3635,3813,3562,12802,12806,12810,12814,12824,3860,12187,3477,3737,3356,10362,10480,10549,10610,10613,10653,10747,10983,11875,11938,12017,12058,12119,12122,12441,12625,12683,12714,12726,12785,12841,12847,13016,13021,13105,13111,3748,11597,3269,3368,11715,12618,13119,3556,4543,10251,10254,10280,10755,10768,10889,11279,11371,11764,11772,11993,11996,12084,12243,12336,12630,12633,12650,12653,12675,12727,12891,12896,12920,12925,4555,11481,11512,11547,11577,12736,12740,3735,3501,3502,12656,12659,12662,12665,12695,12698,13049,13053,13057,13061,3887,3463,13050,3464,13054,3315,3316,3290,4540,3173,4498,3686,4223,4006,3484,4556,4079,11252,3616,3328,11724,11727,12164,12265,12421,4048,4005,11868,12208,3949,10823,12052,12221,12444,13065,3994,13069,4000,11002,12090,12163,12220,12264,12916,4001,3659,11878,12024,12098,12144,4037,3677,11005,11068,11149,11209,12045,12112,12362,12434,12447,12953,12958,4561,10771,11141,12966,3286,10371,10467,10596,10660,11454,11671,11718,11752,11848,11903,12105,3287,10729,10774,10777,10810,10836,10873,10911,10947,11919,11922,11925,11928,12125,12128,12131,12134,12201,12373,12417,12676,12701,12774,12781,12788,12793,12796,12799,12832,12844,12862,12906,12931,12934,13034,13107,3288,10400,10455,10665,10750,10876,11560,11755,11767,11854,11865,11886,11891,11931,11956,11971,12692,12838,12865,12892,12897,12921,3289,3364,12078,12756,12803,12807,12811,12815,12825,12829,4539,10317,10409,10520,10544,10792,10839,10849,11526,11625,11646,11649,11652,11668,11810,11813,11816,11819,11915,11934,11937,11950,12005,12008,12011,12014,12085,12175,12178,12271,12274,12335,12366,12403,12482,3446,10616,10884,10928,11198,11276,11439,11680,12312,12485,12879,12948,12999,4551,10801,10813,10920,10938,10941,10996,11082,11090,11106,11144,11161,11170,11206,11247,11267,11270,11273,11304,11311,11314,11697,11733,11999,12002,12036,12079,12108,12249,12290,12296,12385,12388,12407,12461,12467,12476,12495,12755,12768,12771,12868,12949,12991,13006,13009,13046,13090,13093,3349,10647,10677,10686,11227,11779,12404,12418,12737,12741,12744,3388,13030,13087,3382,3817,3753,10320,11600,11628,12719,4548,10271,10641,10644,11085,11103,11563,11616,11660,11681,11785,11822,11825,11828,11831,12937,3309,10680,10833,10904,11629,11784,11976,12202,12765,13033,13108,13114,13118,3778,11730,12672,4129,3507,4546,3789,3825,4529,4531,4532,3260,3261,4530,4533,4534,4306,3796,3606,11593,4229,11461,4563,10239,10242,10501,10552,10555,10560,10970,11433,11684,11788,4571,11164,11284,11320,4014,12232,3904,11317,11655,11659,11721,12320,12328,12410,12686,12943,12995,3742,10944,10950,10965,11900,12029,12111,12381,3591,11167,12137,12246,12256,12325,12376,12384,12492,12885,3630,4083,3744,10683,11021,11173,11203,11214,12049,12214,12324,12370,12983,3559,10602,10605,10689,10863,3558,4567,11594,4557,4562,12640,4568,10740,10842,11152,11436,11467,12196,12205,12252,12431,4189,10816,12217,12229,12255,4090,3777,12498,3721,3722,4565,10293,10296,10635,10638,11478,11656,12440,4566,11574,11665,3746,10599,10860,13020,4021,4588,4614,4663,4665,4696,4713,4720,4721,4757,4762,4792,4798,4882,4906,4907,4922,4944,4969,4970,4992,4993,5006,5010,5033,5039,5055,5058,5059,5060,5065,5066,5088,5113,5114,5124,5129,5135,5172,5173,5181,5190,5195,5197,5208,5210,5216,5220,5221,5234,5241,5244,5245,5246,5250,5286,5299,5307,5309,5310,5314,5315,5316,5324,5327,5331,5332,5333,5340,5344,5345,5346,5354,5358,5359,5360,5365,5378,5387,5399,5401,5409,5410,5414,5418,5443,5449,5459,5460,5475,5487,5509,5515,5533,5534,5537,5556,5564,5565,5570,5571,5581,5583,5595,5599,5608,5609,5611,5626,5631,5641,5642,5654,5661,5675,5679,5682,5688,5689,5690,5693,5698,5734,5735,5738,5740,5743,5744,5745,5747,5749,5751,5756,5763,5778,5792,5797,5798,5811,5812,5817,5821,5823,5828,5869,5881,5890,5894,5903,5907,5908,5916,5930,5936,5954,5957,5969,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6163,6164,6169,6172,6178,6182,6218,6220,6222,6224,6233,6235,6237,6243,6245,6251,6254,6262,6269,6270,6271,6276,6298,6299,6300,6302,6308,6313,6347,6348,6352,6353,6354,6355,6356,6357,6358,6365,6398,6399,6408,6429,6430,6450,6452,6463,6464,6470,6500,6502,6516,6554,6556,6557,6610,6635,6677,6697,6706,6707,6708,6709,6728,6729,6735,6748,6751,6753,6755,6756,6757,6759,6773,6784,6786,6787,6800,6804,6855,6866,6868,6872,6889,6890,6926,6938,6969,6988,7003,7057,7085,7140,7161,7170,7173,7228,7236,7294,7296,7311,7319,7322,7323,7342,7348,7350,7399,7409,7412,7428,7480,7481,7485,7529,7530,7548,7615,7634,7657,7681,7696,7712,7722,7731,7732,7761,7764,7766,7776,7814,7825,7850,7908,7942,7975,8022,8038,8054,8055,8130,8184,8203,8227,8247,8271,8369,8371,8377,8394,8398,8414,8437,8448,8450,8465,8470,8474,8497,8511,8512,8528,8529,8534,8535,8536,8537,8538,8556,8557,8558,8566,8579,8581,8593,8597,8599,8600,8601,8609,8614,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8815,8816,8827,8871,8877,8883,8896,8901,8903,8906,8907,8911,8921,9003,9034,9035,9036,9051,9068,9074,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9396,9431,9432,9433,9458,9459,9477,9495,9501,9515,9538,9560,9568,9569,9570,9571,9586,9588,9593,9624,9625,9631,9632,9676,9677,9708,9717,9727,9729,9730,9739,9753,9756,9784,9817,9819,9823,9880,9921,9922,9924,9934,9935,9955,9960,10001,10053,10125,10126,10179,10195,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4783,4797,4827,4923,4924,4937,4957,5013,5014,5017,5018,5020,5022,5023,5032,5035,5036,5044,5056,5057,5063,5083,5084,5101,5106,5107,5108,5109,5112,5120,5123,5130,5187,5193,5194,5202,5231,5242,5248,5264,5284,5285,5292,5293,5294,5303,5313,5320,5322,5323,5329,5336,5337,5350,5351,5352,5353,5355,5356,5361,5362,5363,5364,5395,5396,5397,5405,5406,5407,5408,5454,5456,5458,5494,5496,5497,5499,5500,5502,5503,5505,5514,5519,5521,5522,5523,5524,5525,5526,5535,5545,5548,5559,5575,5576,5579,5589,5591,5592,5593,5618,5628,5644,5645,5655,5656,5658,5660,5665,5700,5705,5707,5765,5799,5800,5804,5810,5813,5814,5815,5816,5822,5833,5834,5836,5837,5845,5866,5895,5911,5914,5915,5917,5926,5947,5948,5949,5952,5953,5971,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6166,6183,6236,6272,6274,6295,6296,6301,6304,6305,6309,6315,6324,6340,6360,6361,6366,6376,6391,6411,6417,6419,6434,6435,6438,6439,6441,6443,6444,6445,6447,6449,6451,6457,6458,6459,6460,6466,6468,6510,6515,6530,6531,6532,6533,6568,6573,6575,6580,6581,6589,6593,6606,6631,6632,6633,6634,6645,6650,6667,6671,6690,6723,6724,6725,6730,6744,6765,6767,6769,6771,6774,6780,6782,6797,6802,6805,6841,6844,6845,6858,6859,6860,6861,6880,6881,6898,6924,6946,6957,6959,6960,6962,6964,6965,7000,7001,7006,7007,7008,7009,7011,7013,7038,7047,7048,7060,7070,7109,7119,7123,7130,7141,7147,7149,7155,7163,7164,7177,7194,7212,7214,7231,7280,7282,7283,7284,7290,7295,7318,7363,7396,7410,7427,7460,7463,7489,7513,7531,7534,7535,7545,7563,7564,7566,7568,7570,7572,7598,7623,7624,7656,7658,7659,7660,7665,7688,7697,7708,7713,7719,7721,7727,7739,7740,7742,7774,7797,7863,7864,7911,7919,7920,7944,7945,7962,7963,8030,8031,8032,8057,8090,8097,8099,8108,8120,8153,8159,8166,8179,8198,8204,8226,8269,8299,8311,8329,8332,8362,8385,8451,8452,8455,8457,8560,8561,8562,8563,8588,8617,8645,8689,8707,8762,8808,8811,8824,8831,8868,8889,8917,8918,8936,8937,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9388,9393,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9536,9659,9703,9704,9746,9791,9907,9964,10029,10104,10117,10122,3,2622,2625,2626,2627,2628,2631,2632,2633,2637,2638,2639,2646,2648,2649,2651,2653,2655,2659,2661,2663,2664,2666,2667,2668,2675,2677,2682,2683,2684,2685,2686,2694,2695,2696,2698,2718,2719,2720,2730,2731,2732,2734,2735,2743,2744,2745,2747,2749,2751,2752,2753,2754,2755,2756,2760,2769,2771,2772,2781,2783,2791,2794,2795,2796,2799,2800,2803,2852,2857,2858,5223,5283,5381,5462,5468,5469,5546,5643,5674,5708,5724,5726,5732,5793,5794,5795,5796,5802,5835,5966,6011,6034,6071,6111,6252,6259,6293,6294,6314,6317,6319,6326,6327,6328,6329,6330,6331,6332,6333,6413,6480,6481,6566,6600,6601,6642,6643,6781,6796,6869,6870,6877,6899,6930,6932,6979,7004,7005,7021,7022,7023,7059,7103,7104,7201,7262,7263,7264,7265,7279,7312,7368,7369,7378,7384,7386,7398,7430,7431,7432,7433,7578,7579,7585,7586,7588,7590,7805,7807,7808,7823,7861,7940,7983,8041,8062,8063,8078,8137,8240,8309,8310,8312,8347,8410,8411,8483,8504,8505,8506,8507,8649,8861,8885,8886,8968,8982,9037,9038,9154,9190,9213,9247,9288,9480,9740,9933,9989,9991,6029,6396,6397,6483,6503,6504,6921,7139,8574,8607,8801,8994,8995,9065,9066,9336,9337,9338,9339,9539,9811,10113,10164,10165,6465,8401,8402,8851,8869,9812,10163,4655,4657,4658,4714,4722,4860,4876,4877,4904,4905,4936,4991,5051,5110,5160,5180,5217,5219,5226,5227,5253,5328,5349,5483,5551,5552,5553,5670,5671,5697,5701,5759,5761,5770,5776,5848,5924,6052,6075,6239,6359,6513,6715,6716,6933,6972,7145,7370,7439,7781,7783,7877,8039,8809,8965,9069,9302,9574,4890,4938,5076,5663,5898])). % 183.99/184.52 cnf(13394,plain, % 183.99/184.52 (~P1(f333(f333(f335(x133941),x133942),f196(f882(x133941,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13405,plain, % 183.99/184.52 (~E(f333(a115,x134051),f2(a875))), % 183.99/184.52 inference(rename_variables,[],[4488])). % 183.99/184.52 cnf(13410,plain, % 183.99/184.52 (~P1(f333(f333(f335(a875),x134101),f333(f254(a875),f2(a875))))), % 183.99/184.52 inference(rename_variables,[],[11745])). % 183.99/184.52 cnf(13413,plain, % 183.99/184.52 (P1(f333(f333(f247(a875),f2(a875)),x134131))), % 183.99/184.52 inference(rename_variables,[],[3309])). % 183.99/184.52 cnf(13424,plain, % 183.99/184.52 (P1(f333(f333(f247(f882(x134241,a870)),f333(f174(x134241),f178(x134241,x134242,x134243))),f333(f174(x134241),x134242)))), % 183.99/184.52 inference(rename_variables,[],[4000])). % 183.99/184.52 cnf(13427,plain, % 183.99/184.52 (P1(f333(f333(f247(f882(x134271,a870)),x134272),x134272))), % 183.99/184.52 inference(rename_variables,[],[3591])). % 183.99/184.52 cnf(13442,plain, % 183.99/184.52 (P1(f333(f333(f247(f882(x134421,a870)),f333(f174(x134421),f178(x134421,x134422,x134423))),f333(f174(x134421),x134422)))), % 183.99/184.52 inference(rename_variables,[],[4000])). % 183.99/184.52 cnf(13451,plain, % 183.99/184.52 (P1(f333(f333(f247(a875),x134511),f333(f333(f80(a875),x134511),x134511)))), % 183.99/184.52 inference(rename_variables,[],[3559])). % 183.99/184.52 cnf(13454,plain, % 183.99/184.52 (P1(f333(f333(f247(f882(x134541,a870)),f333(f174(x134541),f178(x134541,x134542,x134543))),f333(f174(x134541),x134542)))), % 183.99/184.52 inference(rename_variables,[],[4000])). % 183.99/184.52 cnf(13467,plain, % 183.99/184.52 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x134671),x134672)),x134671))), % 183.99/184.52 inference(rename_variables,[],[4566])). % 183.99/184.52 cnf(13474,plain, % 183.99/184.52 (~P1(f333(f333(f335(x134741),x134742),f196(f882(x134741,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13483,plain, % 183.99/184.52 (~P1(f333(f333(f335(x134831),x134832),f196(f882(x134831,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13492,plain, % 183.99/184.52 (P1(f333(f333(f248(a875),x134921),f333(f333(f80(a875),f333(a115,x134921)),f333(a115,x134921))))), % 183.99/184.52 inference(rename_variables,[],[10601])). % 183.99/184.52 cnf(13500,plain, % 183.99/184.52 (~P1(f333(f333(f335(x135001),x135002),f196(f882(x135001,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13503,plain, % 183.99/184.52 (~P1(f333(f333(f335(f881(f876(x135031),f876(x135031))),f333(f333(f268(f876(x135031),f876(x135031)),x135032),f116(x135031))),f146(x135031,x135033)))), % 183.99/184.52 inference(rename_variables,[],[4573])). % 183.99/184.52 cnf(13506,plain, % 183.99/184.52 (~P1(f333(f333(f335(x135061),x135062),f196(f882(x135061,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13521,plain, % 183.99/184.52 (~P1(f333(f333(f248(a875),f333(f333(f79(a875),x135211),x135212)),x135212))), % 183.99/184.52 inference(rename_variables,[],[4565])). % 183.99/184.52 cnf(13526,plain, % 183.99/184.52 (P1(f333(f333(f247(a875),x135261),f333(f333(f79(a875),x135261),x135262)))), % 183.99/184.52 inference(rename_variables,[],[3558])). % 183.99/184.52 cnf(13531,plain, % 183.99/184.52 (~P1(f333(f333(f335(x135311),x135312),f196(f882(x135311,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13538,plain, % 183.99/184.52 (P1(f333(f333(f248(a1),f333(f333(f22(a1),x135381),f77(a1))),x135381))), % 183.99/184.52 inference(rename_variables,[],[10749])). % 183.99/184.52 cnf(13573,plain, % 183.99/184.52 (P1(f333(f333(f247(f882(x135731,a870)),f333(f174(x135731),f178(x135731,x135732,x135733))),f333(f174(x135731),x135732)))), % 183.99/184.52 inference(rename_variables,[],[4000])). % 183.99/184.52 cnf(13576,plain, % 183.99/184.52 (~E(f333(f333(f152(x135761),x135762),x135763),x135763)), % 183.99/184.52 inference(rename_variables,[],[4503])). % 183.99/184.52 cnf(13590,plain, % 183.99/184.52 (~P1(f333(f333(f335(f881(x135901,x135901)),x135902),f265(x135901,f196(f882(x135901,a870)))))), % 183.99/184.52 inference(rename_variables,[],[10937])). % 183.99/184.52 cnf(13619,plain, % 183.99/184.52 (~P1(f333(f333(f335(x136191),x136192),f196(f882(x136191,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13624,plain, % 183.99/184.52 (~P1(f333(f333(f335(x136241),x136242),f196(f882(x136241,a870))))), % 183.99/184.52 inference(rename_variables,[],[4551])). % 183.99/184.52 cnf(13627,plain, % 183.99/184.52 (E(f333(f264(x136271,x136271),f265(x136271,x136272)),x136272)), % 183.99/184.52 inference(rename_variables,[],[3243])). % 183.99/184.52 cnf(13640,plain, % 183.99/184.52 (~P1(f333(f333(f335(f881(x136401,x136401)),x136402),f265(x136401,f196(f882(x136401,a870)))))), % 183.99/184.52 inference(rename_variables,[],[10937])). % 183.99/184.52 cnf(13675,plain, % 183.99/184.52 (P1(f333(f333(f248(a1),f333(f333(f22(a1),x136751),f77(a1))),x136751))), % 183.99/184.52 inference(rename_variables,[],[10749])). % 183.99/184.52 cnf(13686,plain, % 183.99/184.52 (P1(f333(f333(f248(a1),f333(f333(f22(a1),x136861),f77(a1))),x136861))), % 183.99/184.52 inference(rename_variables,[],[10749])). % 183.99/184.52 cnf(13704,plain, % 183.99/184.52 (~P1(f333(f333(f335(f881(x137041,x137041)),x137042),f265(x137041,f196(f882(x137041,a870)))))), % 183.99/184.52 inference(rename_variables,[],[10937])). % 183.99/184.52 cnf(13743,plain, % 183.99/184.52 ($false), % 183.99/184.52 inference(scs_inference,[],[3315,3735,3887,4085,3075,4567,3287,4555,4540,3939,4573,13503,3382,3748,4551,13394,13474,13483,13500,13506,13531,13619,13624,3368,4000,13424,13442,13454,13573,3904,4493,4488,13405,4560,4503,13576,4501,3269,3949,3288,3753,3309,13413,3742,3591,13427,3559,13451,3558,13526,3746,3243,13627,3214,3238,4574,4575,4539,4562,4565,13521,4566,13467,3500,11497,10359,11805,11847,11308,13191,10601,13492,10585,11521,11048,12428,12457,13123,11148,10749,13538,13675,13686,3661,12484,11172,4317,11116,10924,11292,3227,13207,10706,13227,11631,11138,12245,10267,11745,13410,13265,12689,11102,10937,13590,13640,13704,10940,11216,10688,11182,2882,3851,8,5331,5583,5969,6056,6093,8529,8556,5226,5690,9103,5693,8437,5869,9569,8130,8566,8827,6313,9921,5823,6430,8768,9586,7634,5881,5409,5459,8816,9538,8642,9220,5058,6399,6751,8815,9173,5763,6756,6868,8414,5749,6077,6076,6759,8227,5114,5197,7294,9934,6055,8746,6707,9819,8686,5241,6079,6098,6300,9571,9035,9960,9432,6516,5365,5181,5220,5414,7003,7140,5358,6308,8599,4969,5051,5060,5509,5608,5443,9102,9935,7319,6450,6556,10179,8597,6926,5761,6172,7161,8038,8371,4614,6075,4936,5299,5551,7057,8474,4992,8557,9708,4882,7409,9477,7681,8184,9717,5065,6890,9624,6163,8708,8054,6804,8593,8581,9147,10126,6126,7485,5173,4721,5475,5778,6735,6855,9632,6933,5924,5533,5160,5734,5811,6357,7530,8614,2,6408,8883,7322,9729,6270,8497,9431,9756,10125,5515,6352,7908,8511,5307,5310,5907,5682,5812,8528,9955,5848,8673,4696]), % 183.99/184.52 ['proof']). % 183.99/184.52 % SZS output end Proof % 183.99/184.52 % Total time :169.430000s %------------------------------------------------------------------------------